**Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures**

Alexei Simaschevici, Dormidont Serban and Leonid Bruc *Institute of Applied Physics, Academy of Sciences, Moldova* 

#### **1. Introduction**

298 Solar Cells – Silicon Wafer-Based Technologies

Vasic,A., Loncar, B., Vujisic, M., Stankovic, K., & Osmokrovic, P. (2010). Aging of the

Microelectronics, pp. 487-490, ISBN 1-4244-0116-x, Nis, Serbia, May 2010

Photovoltaic Solar Cells, Proceedings of 27th IEEE International Conference on

The conventional energy production is not based on sustainable methods, hence exhausting the existing natural resources of oil, gas, coal, nuclear fuel. The conventional energy systems also cause the majority of environmental problems. Only renewable energy systems can meet, in a sustainable way, the growing energy demands without detriment to the environment.

The photovoltaic conversion of solar energy, which is a direct conversion of radiation energy into electricity, is one of the main ways to solve the above-mentioned problem. The first PV cells were fabricated in 1954 at Bell Telephone Laboratories (Chapin et al., 1954); the first applications for space exploration were made in the USA and the former USSR in 1956. The first commercial applications for terrestrial use of PV cells were ten years later. The oil crisis of 1972 stimulated the research programs on PV all over the word and in 1975 the terrestrial market exceeds the spatial one 10 times. Besides classical solar cells (SC) based on p-n junctions new types of SC were elaborated and investigated: photoelectrochemical cells, SC based on Schottky diodes or MIS structures and semiconductor-insulator-semiconductor (SIS) structures, SC for concentrated radiation, bifacial SC. Currently, researchers are focusing their attention on lowering the cost of electrical energy produced by PV modules. In this regard, SC on the base of SIS structures are very promising, and recently the SIS structures have been recommended as low cost photovoltaic solar energy converters. For their fabrication, it is not necessary to obtain a p-n junction because the separation of the charge carriers generated by solar radiation is realized by an electric field at the insulatorsemiconductor interface. Such SIS structures are obtained by the deposition of thin films of transparent conductor oxides (TCO) on the oxidized silicon surface. A overview on this subject was presented in (Malik et al., 2009).

Basic investigations of the ITO/Si SIS structures have been carried out and published in the USA (DuBow et al., 1976; Mizrah et al., 1976; Shewchun et al., 1978; Shewchun et al, 1979) Theoretical and experimental aspects of the processes that take place in these structures are examined in those papers. Later on the investigations of SC based on SIS structures using, as an absorber component, Si, InP and other semiconductor materials have been continued in Japan (Nagatomo et al., 1982; Kobayashi, et al., 1991), India (Vasu & Subrahmanyam, 1992; Vasu et al., 1993), France (Manifacier & Szepessy, 1977; Caldererer et al., 1979), Ukraine

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 301

the silicon wafer where the electrical field is localized is not affected by the impurity diffusion. The TCO films with the band gap of the order of 3.3-3.7eV are transparent in the whole region of solar spectrum, especially in the blue and ultraviolet regions, which increase the photoresponce comparative to the traditional SC. The TCO layer assists with the collection of separated charge carriers and at the same time is an antireflection coating. In SC fabrication the most utilized TCO materials are tin oxide, indium oxide and their mixture known as indium tin oxide (ITO). Thin ITO layers have been deposited onto different semiconductors to obtain SIS structures: Si (Malik et al., 1979), InP (Botnariuc et al., 1990), CdTe (Adeeb et al., 1987), GaAs (Simashkevich et al., 1992). Therefore, solar cells fabricated on the base of SIS structures have been recommended as low cost photovoltaic solar energy converters. The reduction in cost of such solar cells is due to the simple technology used for the junction fabrication. The separation of light generated carriers is achieved by a space

The number of publications concerning the fabrication and investigation of SIS structures is very big, therefore we will limited our consideration of the given structures only to those on the base of the most widespread solar materials – silicon and indium phosphide. To be

As shown above, one of the ways to solve the problem of the cost reduction of the electrical energy provided by SC is to use SIS structures. First publications regarding the obtaining and investigation of ITO/nSi structures appeared in 1976. (Mizrah & Adler, 1976). Power conversion efficiencies of 1% were reported for an ITO/nSi cell, obtained by the magnetron dispersion of ITO layers on the surface of nSi crystals with an active area of 0.13 cm2. The data obtained from the investigated I-V dark characteristics and known band gaps and the work functions of ITO and Si allows to make the band diagram of these structures (Fig. 1). The efficiency of 10% was observed for ITO/nSi cells, obtained by the spray deposition of ITO layers onto nSi crystals with the area of 0.1 cm2 (Manifacier & Szepessy 1977; Calderer et al., 1979). ITO/nSi SC with the power conversion efficiencies of 10% were fabricated by deposition onto n-type Si crystals by the electron- beam evaporation of a mixture of 90:10

The results of those works have been analyzed in detail (Shewchun et al., 1978; Shewchun et al., 1979) from both experimental and theoretical points of view. Given the general theory of heterojunctions is incomprehensible, how they can work as effective SC formed by materials with different crystalline types and lattice constants, when an intermediate layer with many defects appears at the interface. It is intriguing to note here that various authors have received quite contradictory results. Examining these data, authors in (Shewchun et al., 1979) concluded that the performance of those SC depended on the intermediate thin insulator layer. Its main function is the compensation of the defects due to the mismatches of the crystalline lattices. Its thickness is not greater than 30Å, which ensures the tunnel transport of the carriers through the barrier. The theoretical analysis of ITO/nSi solar cell has shown that they are similar to MIS structures: their parameters depend on the thickness of the insulating layer at the interface, the substrate doping level, concentration of surface states, oxide electric charge and temperature. The optimization of these parameters can

In (Shewchun et al., 1979) this issue was examined in terms of energy losses during conversion of sunlight into electricity. Different mechanisms of energy loss that limit

exact, main attention will be focused on SC on the base of ITO/nSi and ITO/pInP.

charge region that in the basic semiconductor is near the insulator layer.

**2.1 SIS structures on the base of silicon crystals** 

molar % In2O3: SnO2 powder (Feng et al., 1979).

provide 20% efficiency.

(Malik et al., 1979; Malik et al., 1980), Russia (Untila et al., 1998), the USA (Shewchun et al., 1980; Gessert et al., 1990; Gessert et al., 1991), Brasil (Marques & Chambouleyron, 1986) and the Republic of Moldova (Adeeb et al., 1987; Botnariuc et al., 1990; Gagara et al., 1996; Simashkevich et al., 1999). The results of SIS structures fabrication by different methods, especially by pyrolitic pulverization and radiofrequency sputtering, are discussed in those papers. The investigation of electrical and photoelectrical properties of the Si based SIS structures shows that their efficiency is of the order of 10% for laboratory-produced samples with an active area that does not exceed a few square centimeters. The spray deposition method of ITO layer onto the silicon crystal surface results in an efficient junction only in the case of n-type Si crystals, whereas in the case of p-type silicon crystals radiofrequency sputtering must be used to obtain good results.

Bifacial solar cells (BSC) are promising devices because they are able to convert solar energy coming from both sides of the cell, thus increasing its efficiency. Different constructions of BSC have been proposed and investigated. In the framework of the classification suggested in (Cuevas, 2005) the BSC structures could be divided into groups according to the number of junctions: a) two p-n junctions, b) one p-n junction and one high-low junction, and c) just one p-n junction. In all those types of BSC are based on a heteropolar p-n junction. In this case, it is necessary to obtain two junctions: a heteropolar p-n junction at the frontal side of the silicon wafer and a homopolar n/n+ or p/p+ junction at its rear side. Usually these junctions are fabricated by impurity diffusion in the silicon wafer. The diffusion takes place at temperatures higher than 8000*C* and requires special conditions and strict control. In the case of the back surface field (BSF) fabrication, these difficulties increase since it is necessary to carry out the simultaneous diffusion of impurities that have an opposite influence on the silicon properties. Therefore the problem arises concerning the protection of silicon surface from undesirable impurities.

The main purpose of this overview is to demonstrate the possibility to manufacture, on the base of nSi, monofacial as well as a novel type of bifacial solar cells with efficiencies over 10%, containing only homopolar junctions with an enlarged active area, using spray pyrolysis technique, the simplest method of obtaining SIS structures with a shallow junction. The utilization of such structures removes a considerable part of the abovementioned problems in BSC fabrication. The results of the investigations of ITO/pInP SC obtained by spray pyrolysis are also discussed.

#### **2. The history of semiconductor-insulator-semiconductor solar cells**

First, it must be noted that SC obtained on the base of MIS and SIS structures are practically the same type of SC, even though they are sometimes considered as being different devices. The similarity of these structures was demonstrated experimentally and theoretically for two of the most common systems, Al/SiOx/pSi and ITO/SiOx/pSi (Schewchun et al, 1980). The tunnel current through the insulator layer at the interface is the transport mechanism between the metal or oxide semiconductor and the radiation-absorbing semiconductor, silicon in this case.

One of the main advantages of SIS based SC is the elimination of high temperature diffusion process from the technological chain, the maximum temperature at the SIS structure fabrication not being higher than 450oC. The films can be deposited by a variety of techniques among which the spray deposition method is particularly attractive since it is simple, relatively fast, and vacuumless (Chopra et al., 1983). Besides, the superficial layer of

(Malik et al., 1979; Malik et al., 1980), Russia (Untila et al., 1998), the USA (Shewchun et al., 1980; Gessert et al., 1990; Gessert et al., 1991), Brasil (Marques & Chambouleyron, 1986) and the Republic of Moldova (Adeeb et al., 1987; Botnariuc et al., 1990; Gagara et al., 1996; Simashkevich et al., 1999). The results of SIS structures fabrication by different methods, especially by pyrolitic pulverization and radiofrequency sputtering, are discussed in those papers. The investigation of electrical and photoelectrical properties of the Si based SIS structures shows that their efficiency is of the order of 10% for laboratory-produced samples with an active area that does not exceed a few square centimeters. The spray deposition method of ITO layer onto the silicon crystal surface results in an efficient junction only in the case of n-type Si crystals, whereas in the case of p-type silicon crystals radiofrequency

Bifacial solar cells (BSC) are promising devices because they are able to convert solar energy coming from both sides of the cell, thus increasing its efficiency. Different constructions of BSC have been proposed and investigated. In the framework of the classification suggested in (Cuevas, 2005) the BSC structures could be divided into groups according to the number of junctions: a) two p-n junctions, b) one p-n junction and one high-low junction, and c) just one p-n junction. In all those types of BSC are based on a heteropolar p-n junction. In this case, it is necessary to obtain two junctions: a heteropolar p-n junction at the frontal side of the silicon wafer and a homopolar n/n+ or p/p+ junction at its rear side. Usually these junctions are fabricated by impurity diffusion in the silicon wafer. The diffusion takes place at temperatures higher than 8000*C* and requires special conditions and strict control. In the case of the back surface field (BSF) fabrication, these difficulties increase since it is necessary to carry out the simultaneous diffusion of impurities that have an opposite influence on the silicon properties. Therefore the problem arises concerning the protection of silicon surface

The main purpose of this overview is to demonstrate the possibility to manufacture, on the base of nSi, monofacial as well as a novel type of bifacial solar cells with efficiencies over 10%, containing only homopolar junctions with an enlarged active area, using spray pyrolysis technique, the simplest method of obtaining SIS structures with a shallow junction. The utilization of such structures removes a considerable part of the abovementioned problems in BSC fabrication. The results of the investigations of ITO/pInP SC

First, it must be noted that SC obtained on the base of MIS and SIS structures are practically the same type of SC, even though they are sometimes considered as being different devices. The similarity of these structures was demonstrated experimentally and theoretically for two of the most common systems, Al/SiOx/pSi and ITO/SiOx/pSi (Schewchun et al, 1980). The tunnel current through the insulator layer at the interface is the transport mechanism between the metal or oxide semiconductor and the radiation-absorbing semiconductor,

One of the main advantages of SIS based SC is the elimination of high temperature diffusion process from the technological chain, the maximum temperature at the SIS structure fabrication not being higher than 450oC. The films can be deposited by a variety of techniques among which the spray deposition method is particularly attractive since it is simple, relatively fast, and vacuumless (Chopra et al., 1983). Besides, the superficial layer of

**2. The history of semiconductor-insulator-semiconductor solar cells** 

sputtering must be used to obtain good results.

obtained by spray pyrolysis are also discussed.

from undesirable impurities.

silicon in this case.

the silicon wafer where the electrical field is localized is not affected by the impurity diffusion. The TCO films with the band gap of the order of 3.3-3.7eV are transparent in the whole region of solar spectrum, especially in the blue and ultraviolet regions, which increase the photoresponce comparative to the traditional SC. The TCO layer assists with the collection of separated charge carriers and at the same time is an antireflection coating. In SC fabrication the most utilized TCO materials are tin oxide, indium oxide and their mixture known as indium tin oxide (ITO). Thin ITO layers have been deposited onto different semiconductors to obtain SIS structures: Si (Malik et al., 1979), InP (Botnariuc et al., 1990), CdTe (Adeeb et al., 1987), GaAs (Simashkevich et al., 1992). Therefore, solar cells fabricated on the base of SIS structures have been recommended as low cost photovoltaic solar energy converters. The reduction in cost of such solar cells is due to the simple technology used for the junction fabrication. The separation of light generated carriers is achieved by a space charge region that in the basic semiconductor is near the insulator layer.

The number of publications concerning the fabrication and investigation of SIS structures is very big, therefore we will limited our consideration of the given structures only to those on the base of the most widespread solar materials – silicon and indium phosphide. To be exact, main attention will be focused on SC on the base of ITO/nSi and ITO/pInP.

#### **2.1 SIS structures on the base of silicon crystals**

As shown above, one of the ways to solve the problem of the cost reduction of the electrical energy provided by SC is to use SIS structures. First publications regarding the obtaining and investigation of ITO/nSi structures appeared in 1976. (Mizrah & Adler, 1976). Power conversion efficiencies of 1% were reported for an ITO/nSi cell, obtained by the magnetron dispersion of ITO layers on the surface of nSi crystals with an active area of 0.13 cm2. The data obtained from the investigated I-V dark characteristics and known band gaps and the work functions of ITO and Si allows to make the band diagram of these structures (Fig. 1). The efficiency of 10% was observed for ITO/nSi cells, obtained by the spray deposition of ITO layers onto nSi crystals with the area of 0.1 cm2 (Manifacier & Szepessy 1977; Calderer et al., 1979). ITO/nSi SC with the power conversion efficiencies of 10% were fabricated by deposition onto n-type Si crystals by the electron- beam evaporation of a mixture of 90:10 molar % In2O3: SnO2 powder (Feng et al., 1979).

The results of those works have been analyzed in detail (Shewchun et al., 1978; Shewchun et al., 1979) from both experimental and theoretical points of view. Given the general theory of heterojunctions is incomprehensible, how they can work as effective SC formed by materials with different crystalline types and lattice constants, when an intermediate layer with many defects appears at the interface. It is intriguing to note here that various authors have received quite contradictory results. Examining these data, authors in (Shewchun et al., 1979) concluded that the performance of those SC depended on the intermediate thin insulator layer. Its main function is the compensation of the defects due to the mismatches of the crystalline lattices. Its thickness is not greater than 30Å, which ensures the tunnel transport of the carriers through the barrier. The theoretical analysis of ITO/nSi solar cell has shown that they are similar to MIS structures: their parameters depend on the thickness of the insulating layer at the interface, the substrate doping level, concentration of surface states, oxide electric charge and temperature. The optimization of these parameters can provide 20% efficiency.

In (Shewchun et al., 1979) this issue was examined in terms of energy losses during conversion of sunlight into electricity. Different mechanisms of energy loss that limit

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 303

series resistance of the intermediate layer series resistance of the contacts shunt

efficiency of 20%

Si wafers surface.

efficiency of this layer as an anti reflection coating.

thickness must be not more than some tens of Å.

been used to fabricate ITO/nSi SIS structures by spray deposition.

efficiency will be discussed in the next section of this overview.

Table 1. The energy loss mechanisms, which do not provide the maximum possible

An increase of the conversion efficiency of SC based on ITO/nSi structures can be achieved by the optimization of the thickness of the frontal ITO layer and of the insulator SiO2 layer; the optimization of the concentration of electrons in absorbing Si wafers; the texturing of the

The thickness of the frontal ITO layer is a very important factor because it affects the quantity of the absorbed solar radiation depending on both absorption and reflection. It is necessary to select such ITO layer thickness that determines a large minimum of the reflection in the region of maximum sensitivity of the n+ITO/SiO2/nSi SC. At the same time, the thickness of the frontal ITO layer determines their electrical resistance and, therefore, the value of the photocurrent, but for all that, the growing of the ITO layer thickness has an contrary effect on the solar cells efficiency, diminishing the absorption and increasing the photocurrent. At the same time, the thickness of the frontal ITO layer determines the

The properties of the SIS structures, largely, also depend on the thickness of the SiO2 insulator layer at ITO/Si interface. This SiO2 layer increases the height of the junction potential barrier and diminishes the saturation current. Besides, the insulator SiO2 layer must be tunnel transparent for charge carrier transport. The optimal SiO2 insulator layer

All silicon wafers must be oriented in the (100) plane because only such crystallographic orientation could be used to get a potential barrier by ITO spray deposition. Single crystalline Si wafers with different carrier concentration from 1015cm-3 up to 1018cm-3 have

The influence of the structural state of the Si single crystalline wafers on the conversion

The paper (Feng et al., 1979) studied the current transport mechanism of ITO/Si structures, the TCO layer beings obtained by evaporation under the action of an electron beam. Pretreatment of Si crystals with Cl2 has led to the increased yield from 2.3% to 5.5%. In this case the current transport mechanism was dominated by recombination in the space charge

1. Absorption and reflection in the ITO layer up to 8% 2. Recombination in space charge region 0.1 1%

**Mechanism Loss rate** 

3. VCD height reduction 0 – 12% too high work function 0-3% inhomogeneous SiOx layer 0-3% low doped ITO layer 0-3% too large saturation current 0-3%

4. Low fill factor 0-10%

ITO/nSi solar cell efficiency are probably valid for other SIS structures too. Dark currentvoltage characteristics were used as experimental material and it was shown that after a certain threshold of direct voltage these characteristics do not differ from similar characteristics of p-n junctions in silicon, and the current is controlled by diffusion processes in silicon volume. Different mechanisms of energy loss that limit ITO/nSi solar cell efficiency are presented in Table 1 (Shewchun et al., 1979).

Fig. 1. Energy band diagram of the ITO/nSi/n +Si structure (a) - in the dark, (b) - at solar illumination under open circuit conditions. The shaded area - the insulating SiOx layer.

ITO/nSi solar cell efficiency are probably valid for other SIS structures too. Dark currentvoltage characteristics were used as experimental material and it was shown that after a certain threshold of direct voltage these characteristics do not differ from similar characteristics of p-n junctions in silicon, and the current is controlled by diffusion processes in silicon volume. Different mechanisms of energy loss that limit ITO/nSi solar cell

Fig. 1. Energy band diagram of the ITO/nSi/n +Si structure (a) - in the dark, (b) - at solar illumination under open circuit conditions. The shaded area - the insulating SiOx layer.

efficiency are presented in Table 1 (Shewchun et al., 1979).


Table 1. The energy loss mechanisms, which do not provide the maximum possible efficiency of 20%

An increase of the conversion efficiency of SC based on ITO/nSi structures can be achieved by the optimization of the thickness of the frontal ITO layer and of the insulator SiO2 layer; the optimization of the concentration of electrons in absorbing Si wafers; the texturing of the Si wafers surface.

The thickness of the frontal ITO layer is a very important factor because it affects the quantity of the absorbed solar radiation depending on both absorption and reflection. It is necessary to select such ITO layer thickness that determines a large minimum of the reflection in the region of maximum sensitivity of the n+ITO/SiO2/nSi SC. At the same time, the thickness of the frontal ITO layer determines their electrical resistance and, therefore, the value of the photocurrent, but for all that, the growing of the ITO layer thickness has an contrary effect on the solar cells efficiency, diminishing the absorption and increasing the photocurrent. At the same time, the thickness of the frontal ITO layer determines the efficiency of this layer as an anti reflection coating.

The properties of the SIS structures, largely, also depend on the thickness of the SiO2 insulator layer at ITO/Si interface. This SiO2 layer increases the height of the junction potential barrier and diminishes the saturation current. Besides, the insulator SiO2 layer must be tunnel transparent for charge carrier transport. The optimal SiO2 insulator layer thickness must be not more than some tens of Å.

All silicon wafers must be oriented in the (100) plane because only such crystallographic orientation could be used to get a potential barrier by ITO spray deposition. Single crystalline Si wafers with different carrier concentration from 1015cm-3 up to 1018cm-3 have been used to fabricate ITO/nSi SIS structures by spray deposition.

The influence of the structural state of the Si single crystalline wafers on the conversion efficiency will be discussed in the next section of this overview.

The paper (Feng et al., 1979) studied the current transport mechanism of ITO/Si structures, the TCO layer beings obtained by evaporation under the action of an electron beam. Pretreatment of Si crystals with Cl2 has led to the increased yield from 2.3% to 5.5%. In this case the current transport mechanism was dominated by recombination in the space charge

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 305

trap –assisted multi step tunneling through the depletion layer is the determinant current flow mechanism (Ashok et al., 1980; Saim & Campbell, 1987; Kobayashi et al., 1990;

The mechanism of the current transport through the potential barrier is determined by the energetic band diagram and the height of the barrier. When the later is very high, a physical p-n junction is formed in Si crystals near the surface (Fig. 2). Otherwise, the ITO/nSi SC operate as MIS structures or Schottky diodes (Fig. 1). Some data about the efficiencies of

Mizrah et al., 1976 R.F. Sputtering 0.13 1 Manifacier et al., 1977 Spray 1.5 10 Feng et al., 1979 Electron beam 1 - 4 10 Calderer et al., 1979 Spray 1.5 10

Nagatomo et al., 1982 Spray 11-13 Gagara et al., 1996 Spray 10.1 Vasu et al., 2005 Electron beam 1.0 5.5 Malik et al., 2008 Spray 1 - 4 11.2 Table 2. Efficiencies of ITO/nSI solar cells fabricated by various deposition techniques of

The analysis of the works referred to shows that the conversion efficiency of ITO/nSi solar cells obtained by various methods is about 10% and in some cases reaches 12%. Their active area is not more than a few square centimeters, which is not enough for practical

As can be seen from Table 1, the optical losses of ITO/nSI solar cells are up to 8%, other estimates show that they can exceed 10% (Garcia et al., 1982). Those losses depend on the surface state of silicon wafers and can be minimized by creating a textured surface of the light absorbing semiconductor material, thus reducing the reflection and increasing the absorption. The texturization leads to the enlargement of the junction area of a photovoltaic cell and to the increase of the conversion efficiency. The enlargement of the junction area in the case of silicon crystals is usually achieved by means of selective chemical etching in KOH (Bobeico et al., 2001; Dikusar et al., 2008; Simashkevich et al., 2011). As a result, pyramids or truncated cones with the base dimensions of 5μmx5μm or with a diameter of

The efficiency of 12.6% under AM1 simulated irradiation was obtained for SnO2: P/SiO2/nSi SC with the active area of 2cm2(Wishwakarma et al., 1993) Those cells were fabricated by deposition of SnO2 layers doped with P by CVD method on the textured surface of the Si crystals with resistivity of 0.1 Ohm.cm. SiO2 insulating layer was obtained by chemical

**References ITO deposition method Area (cm2) Eff. (%) Note** 

Ashok et al., 1980 Spray 0.3 11.5 BSF

Simashkevich et al., 2009).

application.

10μm on the Si surface are formed.

ITO/nSi SC are presented in Table 2.

ITO films on smooth (non textured) Si crystal surfaces

**2.2 ITO/nSi solar cells with textured surface of Si crystalls** 

layer, while there is the thermo emission over the potential barrier in the absence of Cl2. Systematical studies of the properties of the ITO/nSi structures, obtained by spray pyrolysis, were carried out in 1980 (Ashok et al., 1980). The optical and electrical **c**haracteristics of the IT0 layer as well as the thickness of the insulator layer have been optimized to yield the following photovoltaic parameters on 0.5Ohm·cm nSi: Voc= 0.52V, Jsc=31.5mA/cm2, FF=0.70, conversion efficiency is 11.5%. The dark I-V and C-V characteristics have also been evaluated to identify the mechanisms of barrier formation and current flow. C-V data indicate an abrupt heterojuncton, while dark I-V characteristics are suggestive of a tunneling process to determine current flow in these devices in conformity with the Riben and Feucht model (Riben & Feucht, 1966). A comparison of spray deposited ITO/nSi and SnO2/nSi was presented by Japanese researchers (Nagatomo et al. 1982). The diode and photovoltaic properties of these structures are very similar, but the conversion efficiency of ITO/nSi is higher, up to 11-13%, whereas for SnO2/nSi these values do not exceed 7.2% (Nagatomo et al., 1979). As is reported in the paper (Malik et al., 2008; Malik et al., 2009), the authors fabricated ITO/nSi solar cells using n-type single crystalline silicon wafers with a 10Ohm·cm resistivity and an 80nm thick ITO film with a sheet resistance of 30Ohm/□ that was deposited by spray pyrolysis on the silicon substrate treated in the H2O2 solution. This ITO thickness was chosen in order to obtain an effective antireflection action of the film. The cells obtained in such a way can be considered as structures presenting an inverted p-n junction (Fig. 2).

Fig. 2. Energy diagram (in *kT* units) of the heavy doped ITO/n-Si heterojunction

Under the AM0 and AM1.5 solar illumination conditions, the efficiency is 10.8% and 12.2%, respectively. The theoretical modeling based on p-n solar cells shows an excellent agreement between the theoretical and the experimental results. It is also shown that using 1Ω·cm silicon substrates is a promising alternative for obtaining solar cells with 14% efficiency under AM1.5 illumination conditions.

Various models for energetic band diagrams and the carrier transport mechanism in SIS ITO/nSi cells have been proposed so far. Among them are the thermo ionic emission as the dominant charge transport mechanism in the SC obtained by spray deposition of SnO2 onto nSi crystals (Kato et al., 1975), and the recombination current in the depletion layer for the CVD deposited ITO/nSi junction (Varma et al., 1984). Majority of authors suggested that

layer, while there is the thermo emission over the potential barrier in the absence of Cl2. Systematical studies of the properties of the ITO/nSi structures, obtained by spray pyrolysis, were carried out in 1980 (Ashok et al., 1980). The optical and electrical **c**haracteristics of the IT0 layer as well as the thickness of the insulator layer have been optimized to yield the following photovoltaic parameters on 0.5Ohm·cm nSi: Voc= 0.52V, Jsc=31.5mA/cm2, FF=0.70, conversion efficiency is 11.5%. The dark I-V and C-V characteristics have also been evaluated to identify the mechanisms of barrier formation and current flow. C-V data indicate an abrupt heterojuncton, while dark I-V characteristics are suggestive of a tunneling process to determine current flow in these devices in conformity with the Riben and Feucht model (Riben & Feucht, 1966). A comparison of spray deposited ITO/nSi and SnO2/nSi was presented by Japanese researchers (Nagatomo et al. 1982). The diode and photovoltaic properties of these structures are very similar, but the conversion efficiency of ITO/nSi is higher, up to 11-13%, whereas for SnO2/nSi these values do not exceed 7.2% (Nagatomo et al., 1979). As is reported in the paper (Malik et al., 2008; Malik et al., 2009), the authors fabricated ITO/nSi solar cells using n-type single crystalline silicon wafers with a 10Ohm·cm resistivity and an 80nm thick ITO film with a sheet resistance of 30Ohm/□ that was deposited by spray pyrolysis on the silicon substrate treated in the H2O2 solution. This ITO thickness was chosen in order to obtain an effective antireflection action of the film. The cells obtained in such a way can be considered as structures presenting an

Fig. 2. Energy diagram (in *kT* units) of the heavy doped ITO/n-Si heterojunction

Under the AM0 and AM1.5 solar illumination conditions, the efficiency is 10.8% and 12.2%, respectively. The theoretical modeling based on p-n solar cells shows an excellent agreement between the theoretical and the experimental results. It is also shown that using 1Ω·cm silicon substrates is a promising alternative for obtaining solar cells with 14% efficiency

Various models for energetic band diagrams and the carrier transport mechanism in SIS ITO/nSi cells have been proposed so far. Among them are the thermo ionic emission as the dominant charge transport mechanism in the SC obtained by spray deposition of SnO2 onto nSi crystals (Kato et al., 1975), and the recombination current in the depletion layer for the CVD deposited ITO/nSi junction (Varma et al., 1984). Majority of authors suggested that

inverted p-n junction (Fig. 2).

under AM1.5 illumination conditions.

trap –assisted multi step tunneling through the depletion layer is the determinant current flow mechanism (Ashok et al., 1980; Saim & Campbell, 1987; Kobayashi et al., 1990; Simashkevich et al., 2009).

The mechanism of the current transport through the potential barrier is determined by the energetic band diagram and the height of the barrier. When the later is very high, a physical p-n junction is formed in Si crystals near the surface (Fig. 2). Otherwise, the ITO/nSi SC operate as MIS structures or Schottky diodes (Fig. 1). Some data about the efficiencies of ITO/nSi SC are presented in Table 2.


Table 2. Efficiencies of ITO/nSI solar cells fabricated by various deposition techniques of ITO films on smooth (non textured) Si crystal surfaces

The analysis of the works referred to shows that the conversion efficiency of ITO/nSi solar cells obtained by various methods is about 10% and in some cases reaches 12%. Their active area is not more than a few square centimeters, which is not enough for practical application.

#### **2.2 ITO/nSi solar cells with textured surface of Si crystalls**

As can be seen from Table 1, the optical losses of ITO/nSI solar cells are up to 8%, other estimates show that they can exceed 10% (Garcia et al., 1982). Those losses depend on the surface state of silicon wafers and can be minimized by creating a textured surface of the light absorbing semiconductor material, thus reducing the reflection and increasing the absorption. The texturization leads to the enlargement of the junction area of a photovoltaic cell and to the increase of the conversion efficiency. The enlargement of the junction area in the case of silicon crystals is usually achieved by means of selective chemical etching in KOH (Bobeico et al., 2001; Dikusar et al., 2008; Simashkevich et al., 2011). As a result, pyramids or truncated cones with the base dimensions of 5μmx5μm or with a diameter of 10μm on the Si surface are formed.

The efficiency of 12.6% under AM1 simulated irradiation was obtained for SnO2: P/SiO2/nSi SC with the active area of 2cm2(Wishwakarma et al., 1993) Those cells were fabricated by deposition of SnO2 layers doped with P by CVD method on the textured surface of the Si crystals with resistivity of 0.1 Ohm.cm. SiO2 insulating layer was obtained by chemical

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 307

(a)

(b) Fig. 3. Images of the silicon wafers surface landform a) irregular etching; b) regular etching It is evident that the micro structured surface represents a plane with a hexagonal ornament

After the deposition of ITO layers on the both types of the textured surfaces of the silicon wafers (Fig. 3) and Cu evaporated grid on the frontal side and continuous Cu layer on the

Fig. 4. The schematic image of ITO/SiO2/nSi/n+Si solar cell with optimized parameters and

formed by inverse quadrangular pyramids with 4μm base and 2-3μm depth.

rear side, two types of the optimized structures have been fabricated (Fig. 4).

textured Si surface

methods. The textured surface of the Si crystals reduces the frontal reflectivity, and consequently increases the short circuit current by around 10%.

ITO/nSI obtained by spray deposition of ITO layers on nSi wafers oriented in (100) plane, were obtained in Japan (Kobayashi et al, 1990). The final size of the active area of the cell was 0.9cm x 0.9cm. Mat-textured Si surfaces were produced by the immersion of the Si wafers in NaOH solution at 850C. For so treated specimens the solar energy conversion efficiency of 13% was attained under AM1 illumination.

The paper (Simashkevich et al., 2011) studied the properties of ITO/nSi SC with improved parameters. The performed optimization consists in the following: the optimization of the thickness of the frontal ITO layer and of the thickness of the insulator SiO2 layer; the optimization of the concentration of the electrons in absorbing Si wafers; the texturing of the Si wafers surface.

The performed investigations make it possible to come to the following conclusions. The optimum thickness of the frontal ITO layer was determined experimentally from the photoelectric investigations and is equal to 0.5μm. The SiO2 layer can be obtained by different methods. In the case of fabrication n+ITO/SiO2/nSi solar cells by spray pyrolysis, the optimal SiO2 layer thickness was obtained by a combined thermo chemical method selecting the temperature regime and the speed of the gas flow during ITO layer deposition. The optimal SiO2 insulator layer thickness, measured by means of ellipsometric method, is about 30-40Å.

To determine the optimal electron concentration ITO/nSi SIS structures were investigated obtained by ITO spray deposition on the surface of phosphor and antimony doped single crystalline Si wafers with different carrier concentrations: 1015cm-3, 51015cm-3, 61016cm-3, and 21018cm-3, produced in Russia (STB Telecom) and Germany (Siltronix, Semirep). The investigation of the electrical properties of n+ITO/SiO2/nSi SC shows that the optimum values of the barrier height, equal to 0.53eV and the space charge region thickness equal to W=0.36μm, have been obtained in the case of Si crystals with the electron concentration 5·1015cm-3. Carrier diffusion length (L) is one of the main parameters for bifacial solar cells. For this silicon crystal L is about 200μm. The BSF region at the rear side of the cell was obtained by phosphor diffusion.

To enlarge the active area and reduce optical losses due to radiation reflection, the active area of Si wafer, oriented in a plane (100), was exposed to the anisotropic etching.

The etching was spent by two expedients for reception of the irregular and regular landform. In both cases, the boiling 50% aqueous solution of KOH was used as the etching agent. The processing time was 60 - 80s. In the first case, the etching process was yielded without initially making a landform on the silicon wafer surface for the subsequent orientation of the etching process.

Fig. 3a shows that the landform of the silicon surface is irregular and unequal in depth. The depth of poles of etching is within the limits of 2-3μm.

In the second case, the method of making the ranked landform in the form of an inverse pyramid was applied. The chemical micro structurisation of the silicon wafer surface was carried out in the following order: the deposition of a SiO2 thin film with 0.1μm thickness by electron beam method; the deposition on the SiO2 thin film of a photo resists layer and its exposure to an ultraviolet radiation through a special mask; removal of the irradiated photo resist and etching SiO2 with HF through the formed windows; removal of the remaining photo resist thin film. The anisotropic etching of the silicon surface through the windows in SiO2 thin film was carried out. The result of this type of etching is shown in Fig. 3b.

methods. The textured surface of the Si crystals reduces the frontal reflectivity, and

ITO/nSI obtained by spray deposition of ITO layers on nSi wafers oriented in (100) plane, were obtained in Japan (Kobayashi et al, 1990). The final size of the active area of the cell was 0.9cm x 0.9cm. Mat-textured Si surfaces were produced by the immersion of the Si wafers in NaOH solution at 850C. For so treated specimens the solar energy conversion

The paper (Simashkevich et al., 2011) studied the properties of ITO/nSi SC with improved parameters. The performed optimization consists in the following: the optimization of the thickness of the frontal ITO layer and of the thickness of the insulator SiO2 layer; the optimization of the concentration of the electrons in absorbing Si wafers; the texturing of the

The performed investigations make it possible to come to the following conclusions. The optimum thickness of the frontal ITO layer was determined experimentally from the photoelectric investigations and is equal to 0.5μm. The SiO2 layer can be obtained by different methods. In the case of fabrication n+ITO/SiO2/nSi solar cells by spray pyrolysis, the optimal SiO2 layer thickness was obtained by a combined thermo chemical method selecting the temperature regime and the speed of the gas flow during ITO layer deposition. The optimal SiO2 insulator layer thickness, measured by means of ellipsometric method, is

To determine the optimal electron concentration ITO/nSi SIS structures were investigated obtained by ITO spray deposition on the surface of phosphor and antimony doped single crystalline Si wafers with different carrier concentrations: 1015cm-3, 51015cm-3, 61016cm-3, and 21018cm-3, produced in Russia (STB Telecom) and Germany (Siltronix, Semirep). The investigation of the electrical properties of n+ITO/SiO2/nSi SC shows that the optimum values of the barrier height, equal to 0.53eV and the space charge region thickness equal to W=0.36μm, have been obtained in the case of Si crystals with the electron concentration 5·1015cm-3. Carrier diffusion length (L) is one of the main parameters for bifacial solar cells. For this silicon crystal L is about 200μm. The BSF region at the rear side of the cell was

To enlarge the active area and reduce optical losses due to radiation reflection, the active

The etching was spent by two expedients for reception of the irregular and regular landform. In both cases, the boiling 50% aqueous solution of KOH was used as the etching agent. The processing time was 60 - 80s. In the first case, the etching process was yielded without initially making a landform on the silicon wafer surface for the subsequent

Fig. 3a shows that the landform of the silicon surface is irregular and unequal in depth. The

In the second case, the method of making the ranked landform in the form of an inverse pyramid was applied. The chemical micro structurisation of the silicon wafer surface was carried out in the following order: the deposition of a SiO2 thin film with 0.1μm thickness by electron beam method; the deposition on the SiO2 thin film of a photo resists layer and its exposure to an ultraviolet radiation through a special mask; removal of the irradiated photo resist and etching SiO2 with HF through the formed windows; removal of the remaining photo resist thin film. The anisotropic etching of the silicon surface through the windows in

SiO2 thin film was carried out. The result of this type of etching is shown in Fig. 3b.

area of Si wafer, oriented in a plane (100), was exposed to the anisotropic etching.

consequently increases the short circuit current by around 10%.

efficiency of 13% was attained under AM1 illumination.

Si wafers surface.

about 30-40Å.

obtained by phosphor diffusion.

orientation of the etching process.

depth of poles of etching is within the limits of 2-3μm.

(a)

(b)

Fig. 3. Images of the silicon wafers surface landform a) irregular etching; b) regular etching

It is evident that the micro structured surface represents a plane with a hexagonal ornament formed by inverse quadrangular pyramids with 4μm base and 2-3μm depth.

After the deposition of ITO layers on the both types of the textured surfaces of the silicon wafers (Fig. 3) and Cu evaporated grid on the frontal side and continuous Cu layer on the rear side, two types of the optimized structures have been fabricated (Fig. 4).

Fig. 4. The schematic image of ITO/SiO2/nSi/n+Si solar cell with optimized parameters and textured Si surface

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 309

with regular landform (Fig.3b) were used for ITO/SiO2/nSi solar cell fabrication. The

The summary data regarding the methods of ITO layer deposition onto the textured silicon

Kobayashi et al., 1991 Spray 2.25 13 Textured Si surface

Table 3. Efficiencies of ITO/SiO2/nSi solar cells fabricated by various deposition techniques

Indium phosphide is known to be one of the most preferable materials for the fabrication of solar cells due to its optimum band gap; therefore, it is possible to obtain solar energy conversion into electric power with high efficiency. On the base of InP, SC have been fabricated with the efficiency of more than 20 % (Gessert, et al, 1990). In addition, InP based SC are stable under harsh radiation conditions. It was shown (Botnaryuk, Gorchiak et al., 1990, Yamamoto et al, 1984, Horvath et al, 1998) that the efficiency of these SC after proton and electron irradiation decreases less than in the case of Si or GaAs based SC. However, due to the high price of InP wafers, in terrestrial applications, indium phosphide based SC could not be competitive with SC fabricated on other existing semiconductor solar materials

Let us consider the fabrication process of ITO/InP photovoltaic devices. Two main methods of the ITO layer deposition onto InP crystals are used. The first method consists in the utilization of an ion beam sputtering system (Aharoni et al., 1986). The fabrication process of InP photovoltaic devices using this method and the obtained results are described in detail

A schematic diagram of the ITO/InP solar cell fabricated by the above-mentioned method is presented in Fig. 7. The operation of solar cells shown in Fig. 7 can be attributed to two possible mechanisms. One is that the conductive ITO and the substrate form an nITO/pInP Schottky type barrier junction. The second is the formation of a homojunction due to the formation of a "dead" layer (thickness – d) at the top of the InP substrate. This "dead" layer is caused by the crystal damage, which results from the impingement of the particles sputtered from the target on the InP top surface. The "dead" layer volume is characterized by extremely short free carrier's life times, i.e. high carrier recombination rates, with respect

<sup>1993</sup>CVD 2.0 12.6 Textured Si surface

<sup>2011</sup>Spray 4.0 11.88 Irregular texture Si

<sup>2011</sup>Spray 4.0 15.79 Regular texture Si surface

**Area (cm2)**  **Eff.** 

**(%) Note** 

surface

respective load I-V characteristic is presented in Fig. 6.

**References ITO deposition** 

of ITO layers onto the textured silicon wafers

**2.3 SIS structures on the base of InP and other crystals** 

**2.3.1 Fabrication of ITO/InP photovoltaic devices** 

elsewhere (Gessert et al., 1990; Aharoni et al., 1999).

to the underlying InP crystal.

Vishvakarma et al.,

Simashkevich et al.,

Simashkevich et al.,

such as silicon.

wafers and the obtained efficiencies are presented in Table 3.

**method** 

The measurements of these characteristics and of solar energy conversion efficiency have been carried out under standard conditions (AM1.5, 1000W/m2, 250C) with the solar simulator ST 1000. The load I-V characteristics of the n+ITO/SiO2/n/n+Si SC are presented in Fig. 5 and Fig. 6.

Fig. 5. Load I-V characteristic of ITO/SiO2/nSi solar cells with irregular landform Si surface

Fig. 6. Load I-V characteristic of ITO/SiO2/nSi solar cells with regular landform Si surface

For samples obtained on textured Si wafers with irregular landform (Fig. 5), the efficiency and other photoelectric parameters increased in comparison with the SC described earlier (Gagara et al, 1996, Simashkevich et al, 1999). Besides, the results improved when Si wafers

The measurements of these characteristics and of solar energy conversion efficiency have been carried out under standard conditions (AM1.5, 1000W/m2, 250C) with the solar simulator ST 1000. The load I-V characteristics of the n+ITO/SiO2/n/n+Si SC are presented

 **Standart condition**

**Jsc= 34.0mA/cm2**

**, 25<sup>o</sup>**

**C, AM1.5**

**1000W/m2**

**Uoc= 0.504V FF = 69.3% Eff.= 11.88% Rser= 3.586 Ohm Rsh= 9131 Ohm**

**0.0 0.1 0.2 0.3 0.4 0.5**

Fig. 5. Load I-V characteristic of ITO/SiO2/nSi solar cells with irregular landform Si surface

 **Standart condition**

**Jsc= 40.6mA/cm2**

**, 25o**

**C, AM1.5**

**1000W/m2**

**Uoc= 0.507V FF = 76.5% Eff.= 15.79% Rser= 3.860 Ohm Rsh= 1389 Ohm**

**0.0 0.1 0.2 0.3 0.4 0.5**

Fig. 6. Load I-V characteristic of ITO/SiO2/nSi solar cells with regular landform Si surface For samples obtained on textured Si wafers with irregular landform (Fig. 5), the efficiency and other photoelectric parameters increased in comparison with the SC described earlier (Gagara et al, 1996, Simashkevich et al, 1999). Besides, the results improved when Si wafers

**Voltage,V**

**Voltage,V**

in Fig. 5 and Fig. 6.

**0**

**0**

**10**

**20**

**Current density,mA/cm2**

**30**

**40**

**5**

**10**

**15**

**20**

**Current density,mA/cm2**

**25**

**30**

**35**

with regular landform (Fig.3b) were used for ITO/SiO2/nSi solar cell fabrication. The respective load I-V characteristic is presented in Fig. 6.

The summary data regarding the methods of ITO layer deposition onto the textured silicon wafers and the obtained efficiencies are presented in Table 3.


Table 3. Efficiencies of ITO/SiO2/nSi solar cells fabricated by various deposition techniques of ITO layers onto the textured silicon wafers

#### **2.3 SIS structures on the base of InP and other crystals**

Indium phosphide is known to be one of the most preferable materials for the fabrication of solar cells due to its optimum band gap; therefore, it is possible to obtain solar energy conversion into electric power with high efficiency. On the base of InP, SC have been fabricated with the efficiency of more than 20 % (Gessert, et al, 1990). In addition, InP based SC are stable under harsh radiation conditions. It was shown (Botnaryuk, Gorchiak et al., 1990, Yamamoto et al, 1984, Horvath et al, 1998) that the efficiency of these SC after proton and electron irradiation decreases less than in the case of Si or GaAs based SC. However, due to the high price of InP wafers, in terrestrial applications, indium phosphide based SC could not be competitive with SC fabricated on other existing semiconductor solar materials such as silicon.

#### **2.3.1 Fabrication of ITO/InP photovoltaic devices**

Let us consider the fabrication process of ITO/InP photovoltaic devices. Two main methods of the ITO layer deposition onto InP crystals are used. The first method consists in the utilization of an ion beam sputtering system (Aharoni et al., 1986). The fabrication process of InP photovoltaic devices using this method and the obtained results are described in detail elsewhere (Gessert et al., 1990; Aharoni et al., 1999).

A schematic diagram of the ITO/InP solar cell fabricated by the above-mentioned method is presented in Fig. 7. The operation of solar cells shown in Fig. 7 can be attributed to two possible mechanisms. One is that the conductive ITO and the substrate form an nITO/pInP Schottky type barrier junction. The second is the formation of a homojunction due to the formation of a "dead" layer (thickness – d) at the top of the InP substrate. This "dead" layer is caused by the crystal damage, which results from the impingement of the particles sputtered from the target on the InP top surface. The "dead" layer volume is characterized by extremely short free carrier's life times, i.e. high carrier recombination rates, with respect to the underlying InP crystal.

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 311

Structures with different crystallographic orientation and holes concentration in the InP substrates were obtained. The optimum concentration of the charge carriers in plnP substrates was 1016cm-3, but the InP wafers with these carrier concentrations and the thickness of 400 nm had a high resistance. For this reason, p/p+InP substrates were used in order to obtain efficient solar cells with a low series resistance. In some cases a plnP layer with the thickness up to 4 µm and concentration p = (3...30)·1016 cm-3 was deposited by the gas epitaxy method from the InPCl3 H2 system on the (100) oriented surface of InP heavily doped substrate with the concentrations p+= (1...3)·1018 cm-3 for the fabrication of ITO/pInP/p+InP structures. Ag and 5 % Zn alloy evaporated in a vacuum through a special mask were used as an ohmic contact to the ITO and to InP crystal. A schematic diagram of

ITO/p/p+InP structure obtained by spray pyrolitic method is presented in Fig. 8.

Fig. 8. Schematic diagram of the ITO/InP structure obtained by spray pyrolitic method.

Fig. 9. Energy band diagram of ITO/InP structure obtained in oxygen atmosphere

The energy band diagram of the ITO/pInP structure proposed in (Botnariuc et al., 1990) is presented in Fig. 9. The current flow mechanism of the ITO/InP structures, obtained in different fabrication conditions, was clarified in (Andronic et al., 1998) on the base of the

**2.3.2 Electrical properties of ITO/InP solar cells** 

energy band diagram below.

Fig. 7. Schematic diagram of the ITO/InP photovoltaic device obtained by ion bean sputtering.

Accordingly, it forms the "n" side of a homojunction with the "p" type underlying InP. The formation of an n-p junction in InP may be due to tin diffusion from the ITO into the InP, where tin acts as a substitution donor on In sites. The record efficiency of 18.9% was obtained in (Li et al., 1989) for ITO/InP structures, when the ITO layer was deposited by magnetron dispersion on p+p/InP treated preliminary in Ar/O2 plasma.

Using the above-described sputtering process, a small-scale production of 4cm2 ITO/InP photovoltaic solar cells has been organized at Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, Colorado, the USA (Gessert et al., 1991). Although only a small number of the 4cm2 ITO/InP cells (approximately 10 cells total) were fabricated, the average cell efficiency is determined to be 15.5%, the highest cell performance being 16.1% AM0. Dark I-V data analysis indicates that the cells demonstrate near-ideal characteristics, with a diode ideality factor and reverse saturation current density of 1.02 and 1.1·10-12mA/cm2, respectively (Gessert et al, 1990).

The second, a simpler, method of ITO/InP photovoltaic devices fabrication consists in spray-pyrolitic deposition of ITO layers onto InP substrates (Andronic et al., 1998; Simashkevich et al., 1999; Gagara et al., 1986; Vasu et al, 1993). ITO layers were deposited on the surface of InP wafers by spraying an alcoholic solution of InCl3 and SnCl4 in different proportions. The following chemical reactions took place on the heated up substrate:

$$4\text{InCl}\_3 + \text{CO}\_2 = 2\text{In}\_2\text{O}\_3 + 6\text{Cl}\_2\tag{1}$$

$$\text{SnCl}\_4 + \text{O}\_2 = \text{SnO}\_2 + 2\text{Cl}\_2 \tag{2}$$

ITO thin films with the thickness of 150-250nm were deposited by the above-mentioned spray method in various gaseous environments: O2, Ar, or air atmosphere. When the inert gas was carrier gas, the installation could be completely isolated from the environment that allowed obtaining the structures in the atmosphere without oxygen. A thin insulator layer with the thickness up to 10nm is formed on InP surface due to the oxidation of the substrate during spraying. The oxidation of InP wafers in HNO3 for 20-30s was realized in the case of inert gas atmosphere. In the case of InP crystals, a thin insulator P2O5 layer with the thickness 3-4 nm was formed on InP wafer surface during the ITO layers deposition. Ohmic contacts to pInP were obtained by thermal vacuum evaporation of 95 % Ag and 5 % Zn alloy on the previously polished rear surface of the wafer.

Fig. 7. Schematic diagram of the ITO/InP photovoltaic device obtained by ion bean sputtering. Accordingly, it forms the "n" side of a homojunction with the "p" type underlying InP. The formation of an n-p junction in InP may be due to tin diffusion from the ITO into the InP, where tin acts as a substitution donor on In sites. The record efficiency of 18.9% was obtained in (Li et al., 1989) for ITO/InP structures, when the ITO layer was deposited by

Using the above-described sputtering process, a small-scale production of 4cm2 ITO/InP photovoltaic solar cells has been organized at Solar Energy Research Institute (now National Renewable Energy Laboratory), Golden, Colorado, the USA (Gessert et al., 1991). Although only a small number of the 4cm2 ITO/InP cells (approximately 10 cells total) were fabricated, the average cell efficiency is determined to be 15.5%, the highest cell performance being 16.1% AM0. Dark I-V data analysis indicates that the cells demonstrate near-ideal characteristics, with a diode ideality factor and reverse saturation current density of 1.02 and

The second, a simpler, method of ITO/InP photovoltaic devices fabrication consists in spray-pyrolitic deposition of ITO layers onto InP substrates (Andronic et al., 1998; Simashkevich et al., 1999; Gagara et al., 1986; Vasu et al, 1993). ITO layers were deposited on the surface of InP wafers by spraying an alcoholic solution of InCl3 and SnCl4 in different

4InCl3 + 3O2 = 2In2O3 + 6Cl2 (1)

 SnCl4 + O2 = SnO2 + 2Cl2 (2) ITO thin films with the thickness of 150-250nm were deposited by the above-mentioned spray method in various gaseous environments: O2, Ar, or air atmosphere. When the inert gas was carrier gas, the installation could be completely isolated from the environment that allowed obtaining the structures in the atmosphere without oxygen. A thin insulator layer with the thickness up to 10nm is formed on InP surface due to the oxidation of the substrate during spraying. The oxidation of InP wafers in HNO3 for 20-30s was realized in the case of inert gas atmosphere. In the case of InP crystals, a thin insulator P2O5 layer with the thickness 3-4 nm was formed on InP wafer surface during the ITO layers deposition. Ohmic contacts to pInP were obtained by thermal vacuum evaporation of 95 % Ag and 5 % Zn alloy

proportions. The following chemical reactions took place on the heated up substrate:

magnetron dispersion on p+p/InP treated preliminary in Ar/O2 plasma.

1.1·10-12mA/cm2, respectively (Gessert et al, 1990).

on the previously polished rear surface of the wafer.

Structures with different crystallographic orientation and holes concentration in the InP substrates were obtained. The optimum concentration of the charge carriers in plnP substrates was 1016cm-3, but the InP wafers with these carrier concentrations and the thickness of 400 nm had a high resistance. For this reason, p/p+InP substrates were used in order to obtain efficient solar cells with a low series resistance. In some cases a plnP layer with the thickness up to 4 µm and concentration p = (3...30)·1016 cm-3 was deposited by the gas epitaxy method from the InPCl3 H2 system on the (100) oriented surface of InP heavily doped substrate with the concentrations p+= (1...3)·1018 cm-3 for the fabrication of ITO/pInP/p+InP structures. Ag and 5 % Zn alloy evaporated in a vacuum through a special mask were used as an ohmic contact to the ITO and to InP crystal. A schematic diagram of ITO/p/p+InP structure obtained by spray pyrolitic method is presented in Fig. 8.

Fig. 8. Schematic diagram of the ITO/InP structure obtained by spray pyrolitic method.

#### **2.3.2 Electrical properties of ITO/InP solar cells**

The energy band diagram of the ITO/pInP structure proposed in (Botnariuc et al., 1990) is presented in Fig. 9. The current flow mechanism of the ITO/InP structures, obtained in different fabrication conditions, was clarified in (Andronic et al., 1998) on the base of the energy band diagram below.

Fig. 9. Energy band diagram of ITO/InP structure obtained in oxygen atmosphere

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 313

homojunction solar cells. The current short circuit Isc linearly depends on the illumination intensity; the open circuit voltage Uoc changes with the illumination after the usual

> ln 1 *sc oc o*

The dependence of ITO/InP cells parameters in AM 0 conditions versus InP substrate orientation and hole concentration was studied. InP wafers with the orientation in (100) and (111) B directions were used to obtain solar cells by the deposition of ITO layers (Table 4).

**Substrate p, 1016cm-3 Voc, (mV) Isc, (mA/cm2) η, (%)** 

674 699 689

707 695 707

568 722 545

(3)

28.3 23.8 25.3

25.9 28.6 30.8

22.0 17.7 14.3

10.4 9.6 9.5

11.1 11.0 11.6

> 5.0 5.3 3.7

*kT <sup>I</sup> <sup>U</sup> q I* 

where IL - light induced current, Is- the saturation current, T- temperature.

2.6 6.5 15

10 30 2.0

3.7 5.7 37

Table 4. The dependence of ITO/InP cells parameters in AM0 conditions versus InP

The photo sensibility spectral distribution of the p+/pInP(100) structure is presented in Fig. 11.

**400 500 600 700 800 900 1000**

The region of the spectral sensibility of Сu/nITO/pInP/Ag:Zn structure is situated between

Fig. 11. The photo sensibility spectral characteristic of the p+/pInP (100) SC

 **(nm)**

logarithmic dependence:

pInP (111)B

p+/pInP (100)

pInP (111)A

substrate crystallographic orientation

**0.0**

400 - 50 nm.

**0.1**

**0.2**

**0.3**

**I**

**sc/E (A/W)**

**0.4**

**0.5**

**0.6**

The I-V characteristics of ITO/pInP structures at different temperatures, obtained in the non- oxide environment are given in Fig. 10a.

Fig. 10. Dark current-voltage characteristics at direct bias a) obtained in nitrogen atmosphere: b) obtained in oxygen atmosphere

One can suppose the existence of two channels of carriers transport through the structure interface (insertion in Fig. 10a). The first channel is the following: the majority carriers from InP are tunneling through the barrier at the interface and then recombining step by step with electrons from ITO conduction band (Riben & Feucht, 1966). According to this model, the I-V characteristic slope should not depend on temperature. The second channel appears at the direct bias of more than 0.6V and is determined by the emission of electrons from the ГГО conduction band to the InP conduction band This emission should occur by changing the I-V curves slope at different temperatures. As one can see from the experimental data, these two channels are displayed by two segments on I-V characteristics.

Fig. 10b shows the I-V characteristics of the ITO/InP structures achieved in an oxygen environment or under substrate oxidation. In this case, the presence of the insulator layer on the interface could be expected. The ITO/InP structures capacity-voltage measurements confirm this supposition. During the fabrication of the ITO/InP structure in oxygen atmosphere, a thin insulator layer on the interface is obtained. Changing the segment II from the ITO/InP structure I-V characteristics shows the presence of a thin insulator layer. The insulator presence leads to changing the process of electron emission from the ITO conduction band to the InP conduction band on the tunneling process through this insulator layer. Thus, the form of segment II on the I-V characteristics becomes similar to the segment I form.

#### **2.3.3 Photoelectric properties of ITO/InP solar cells**

Photoelectric properties of these SC have been investigated at the illumination of the heterostructures through the wide gap oxide layer. For all investigated samples, the currentvoltage characteristics at illumination do not differ from the characteristics of respective

The I-V characteristics of ITO/pInP structures at different temperatures, obtained in the

(a) (b)

One can suppose the existence of two channels of carriers transport through the structure interface (insertion in Fig. 10a). The first channel is the following: the majority carriers from InP are tunneling through the barrier at the interface and then recombining step by step with electrons from ITO conduction band (Riben & Feucht, 1966). According to this model, the I-V characteristic slope should not depend on temperature. The second channel appears at the direct bias of more than 0.6V and is determined by the emission of electrons from the ГГО conduction band to the InP conduction band This emission should occur by changing the I-V curves slope at different temperatures. As one can see from the experimental data,

Fig. 10b shows the I-V characteristics of the ITO/InP structures achieved in an oxygen environment or under substrate oxidation. In this case, the presence of the insulator layer on the interface could be expected. The ITO/InP structures capacity-voltage measurements confirm this supposition. During the fabrication of the ITO/InP structure in oxygen atmosphere, a thin insulator layer on the interface is obtained. Changing the segment II from the ITO/InP structure I-V characteristics shows the presence of a thin insulator layer. The insulator presence leads to changing the process of electron emission from the ITO conduction band to the InP conduction band on the tunneling process through this insulator layer. Thus,

the form of segment II on the I-V characteristics becomes similar to the segment I form.

Photoelectric properties of these SC have been investigated at the illumination of the heterostructures through the wide gap oxide layer. For all investigated samples, the currentvoltage characteristics at illumination do not differ from the characteristics of respective

Fig. 10. Dark current-voltage characteristics at direct bias a) obtained in nitrogen

these two channels are displayed by two segments on I-V characteristics.

**2.3.3 Photoelectric properties of ITO/InP solar cells** 

non- oxide environment are given in Fig. 10a.

atmosphere: b) obtained in oxygen atmosphere

homojunction solar cells. The current short circuit Isc linearly depends on the illumination intensity; the open circuit voltage Uoc changes with the illumination after the usual logarithmic dependence:

$$\mathcal{U}L\_{\rm oc} = \frac{kT}{q} \text{ln}\left(\frac{I\_{sc}}{I\_o} + \mathbf{1}\right) \tag{3}$$

where IL - light induced current, Is- the saturation current, T- temperature. The dependence of ITO/InP cells parameters in AM 0 conditions versus InP substrate orientation and hole concentration was studied. InP wafers with the orientation in (100) and (111) B directions were used to obtain solar cells by the deposition of ITO layers (Table 4).


Table 4. The dependence of ITO/InP cells parameters in AM0 conditions versus InP substrate crystallographic orientation

The photo sensibility spectral distribution of the p+/pInP(100) structure is presented in Fig. 11.

Fig. 11. The photo sensibility spectral characteristic of the p+/pInP (100) SC

The region of the spectral sensibility of Сu/nITO/pInP/Ag:Zn structure is situated between 400 - 50 nm.

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 315

SIS structures for SC fabrication were also obtained on the base of other semiconductor materials besides Si and InP. ITO/CdTe (Adeeb et al., 1987) and ITO/GaAs (Simashkevich et al., 1992) structures were obtained by spray pyrolysis of ITO layers on pCdTe and pGaAs crystals. For ITO/CdTe the efficiency was 6%, for ITO/GaAs SC it did not exceed 2.5%.

**400 500 600 700 800 900 1000**

 **(nm)**

Fig. 13. The spectral photo sensibility of Cu/n+ITO/pInP/Ag:Zn structure: 1- before H2

**2.3.4 Degradation of photoelectric parameters of ITO/InP solar cells exposed to** 

Higher efficiency of 11.6% is obtained if the InP substrate is oriented in [100] plane.

Fig. 14. The degradation of ITO/InP heterostructures photoelectric parameters under

The degradation of photoelectric parameters of ITO/InP solar cells after their irradiation by protons with energies Ep=20.6MeV and flux density up to Fp=1013cm-2 and by electrons with Ec=1MeV and Fe≤1015cm-2 was investigated (Andronic et al., 1998). The results of the photoelectrical parameter measurements at AM0 conditions after the irradiation are

protons (a) and (b) electrons irradiation

**Isc (arb.un.)**

annealing, 2- after H2 annealing

**ionizing radiation** 

presented in Fig. 14.

**1**

**2**

The minimum efficiency was observed when solar cells were obtained by deposition of ITO layers onto InP wafers oriented in (111) A direction. To increase the efficiency, those solar cells were thermally treated in H2 atmosphere at the temperature of 3500C during 10 minutes to reduce the series resistance (Bruk et al, 2007).

It was shown that before the thermal treatment the following parameters had been obtained under AM 1.5 illumination conditions: Uoc= 0.651 V, Isc= 18.12 mA/cm2, FF = 58 %, Eff. = 6.84 % (Fig. 12, curve 1).

Fig. 12. Load I-V characteristics of Сu/nITO/pInP/Ag:Zn solar cells: 1-before thermal treatment; 2-after thermal treatment in H2; 3-best parameters after thermal treatment in H2

After the thermal treatment the parameters were: Uoc= 0.658 V, Isc= 20.13 mA/cm2, FF = 58%, Eff.= 7.68 % (Fig.12, curve 2). The photoelectric parameters of the SC received on InP wafers with the concentration p = 3.1017cm-3 after the thermal treatment were Uoc=0.626 V, Isc= 22.72 mA/cm2, FF = 71 %, Eff.= 10.1 % (Fig. 12, curve 3), that is better than for analogous SC without treatment in H2.

The thermal treatment in H2 leads to the undesirable decrease of the photo sensibility in the short wave region of the spectrum (Fig.13).

The highest sensibility is observed at 870nm, which indicates that the maximum contribution in the photo sensibility is due to the absorption in InP.

ITO/InP structures grown by spray pyrolysis were also investigated in Semiconductor Laboratory of the Indian Institute of Technology, Madras (Vasu & Subrahmanyam, 1992; Vasu, et al., 1993). The maximum efficiency of 10.7% was achieved under 100mW/cm2 illumination for junctions having 5% by weight of tin in the ITO films. The texturing of the InP crystal surface in ITO/InP SC (Jenkins et al., 1992) reduces the surface reflection. These cells showed improvement in both short circuit current and fill factor, the efficiency can be increased by 6.74%. The texturing reduces the need for an optimum antireflection coating.

The minimum efficiency was observed when solar cells were obtained by deposition of ITO layers onto InP wafers oriented in (111) A direction. To increase the efficiency, those solar cells were thermally treated in H2 atmosphere at the temperature of 3500C during 10

It was shown that before the thermal treatment the following parameters had been obtained under AM 1.5 illumination conditions: Uoc= 0.651 V, Isc= 18.12 mA/cm2, FF = 58 %,

**-0.2 0.0 0.2 0.4 0.6 0.8**

Fig. 12. Load I-V characteristics of Сu/nITO/pInP/Ag:Zn solar cells: 1-before thermal treatment; 2-after thermal treatment in H2; 3-best parameters after thermal treatment in H2 After the thermal treatment the parameters were: Uoc= 0.658 V, Isc= 20.13 mA/cm2, FF = 58%, Eff.= 7.68 % (Fig.12, curve 2). The photoelectric parameters of the SC received on InP wafers with the concentration p = 3.1017cm-3 after the thermal treatment were Uoc=0.626 V, Isc= 22.72 mA/cm2, FF = 71 %, Eff.= 10.1 % (Fig. 12, curve 3), that is better than for analogous SC

The thermal treatment in H2 leads to the undesirable decrease of the photo sensibility in the

The highest sensibility is observed at 870nm, which indicates that the maximum

ITO/InP structures grown by spray pyrolysis were also investigated in Semiconductor Laboratory of the Indian Institute of Technology, Madras (Vasu & Subrahmanyam, 1992; Vasu, et al., 1993). The maximum efficiency of 10.7% was achieved under 100mW/cm2 illumination for junctions having 5% by weight of tin in the ITO films. The texturing of the InP crystal surface in ITO/InP SC (Jenkins et al., 1992) reduces the surface reflection. These cells showed improvement in both short circuit current and fill factor, the efficiency can be increased by 6.74%. The texturing reduces the need for an optimum antireflection

**U (V)**

minutes to reduce the series resistance (Bruk et al, 2007).

Eff. = 6.84 % (Fig. 12, curve 1).

**-0.02**

without treatment in H2.

coating.

3 2 1

short wave region of the spectrum (Fig.13).

contribution in the photo sensibility is due to the absorption in InP.

**-0.01**

**0.00**

**J (A/cm2**

**)**

**0.01**

SIS structures for SC fabrication were also obtained on the base of other semiconductor materials besides Si and InP. ITO/CdTe (Adeeb et al., 1987) and ITO/GaAs (Simashkevich et al., 1992) structures were obtained by spray pyrolysis of ITO layers on pCdTe and pGaAs crystals. For ITO/CdTe the efficiency was 6%, for ITO/GaAs SC it did not exceed 2.5%.

Fig. 13. The spectral photo sensibility of Cu/n+ITO/pInP/Ag:Zn structure: 1- before H2 annealing, 2- after H2 annealing

#### **2.3.4 Degradation of photoelectric parameters of ITO/InP solar cells exposed to ionizing radiation**

The degradation of photoelectric parameters of ITO/InP solar cells after their irradiation by protons with energies Ep=20.6MeV and flux density up to Fp=1013cm-2 and by electrons with Ec=1MeV and Fe≤1015cm-2 was investigated (Andronic et al., 1998). The results of the photoelectrical parameter measurements at AM0 conditions after the irradiation are presented in Fig. 14.

Higher efficiency of 11.6% is obtained if the InP substrate is oriented in [100] plane.

Fig. 14. The degradation of ITO/InP heterostructures photoelectric parameters under protons (a) and (b) electrons irradiation

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 317

spraying and the deposition speed. ITO films had a microcrystalline structure that was influenced by the crystal lattice of the support as the X-ray analysis showed. They had cubic structure with the lattice constant 10.14Å (Bruk et al., 2009)). The SEM image of such an ITO

(a) (b)

ITO/SiO2/nSi solar cells with the active area of 8.1cm2 and 48.6cm2 were fabricated. In some

Fig. 15. Schematic a) and real b) view of the installation for ITO thin films deposition

cases a BSF region was obtained at the rear contact by phosphor diffusion.

film is presented in Fig. 17.

Fig. 16. SC process sequence.

We notice that after the irradiation of ITO/InP solar cells with an integral proton flux of 1013cm-2, their efficiency decreases by 26%, that is less than in the case of Si and GaAs based solar cells. In the spectral characteristics of ITO/pInP solar cells after proton irradiation a small decrease of the photosensitivity in the long wavelength region of the spectrum was observed due to the decrease of the diffusion length.

Comparing the results of the radiation stability study of ITO/InP SC, fabricated by spray pyrolysis, with the results of similar investigations of other InP based structures, it is possible to conclude that in this case the radiation stability is also determined by the low efficiency of radiation defects generation and, hence, by the low concentration of deep recombination centers, reducing the efficiency of solar energy conversion in electric power.

#### **3. Fabrication of ITO/nSi solar cells with enlarged area by spray pyrolisys**

From the brief discussion above it can be concluded that the deposition of ITO layers by spray pyrolysis on the surface of different semiconductor materials allows manufacturing SC through a simple and less expensive technology. The most effective are ITO/InP SC but because of a very high cost of the InP crystals they cannot be widely used in terrestrial applications. To this effect ITO/nSi SC with the efficiency higher than 10% may be used, but it is necessary to develop the technology for SC fabrication with the active area enlarged up to 70-80 cm2 as is the case of traditional silicon SC with p-n junction.

#### **3.1 Deposition of ITO layers on enlarged silicon wafers**

ITO layers are deposited on the nSi crystals surface using the specially designed installation (Simashkevich et al., 2004; Simashkevich et al., 2005) (Fig. 15) that has four main units: the spraying system (7), the system of displacement and rotation of the support on which the substrate is fixed (4, 5), the system of heating the substrate, and the system of the evacuation of the residual products of the pyrolysis (8). The heating system consists of an electric furnace (2) and a device for automatic regulation of the substrate temperature with the thermocouple (3). The rest of the installation parts are: the power unit (1), the cover (10), and the shielding plate (12). Silicon wafers (11) are located on the support (9) and with the displacement mechanism are moved into the deposition zone of the electric furnace (6). The construction of this mechanism provides the rotation of the support with the velocity of 60 rotations per minute, the speed necessary for the obtaining of thin films with uniform thickness on the all wafer surface. The alcoholic solution of the mixture SnCl4 + InCl3 is sprayed with compressed oxygen into the stove on the silicon wafer substrate, where the ITO thin film is formed due to thermal decomposition of the solution and the oxidation reaction. On the heated up substrate there are the chemical reactions describe above in formulas (1) and (2).

The BSF n/n+ junction was fabricated on the rear side of the wafer by a diffusion process starting from POCl3 gas mixture. The junction formation ended with a wet chemical etching of POCl3 residual in a 10% HF bath. A junction depth of 1μm was chosen in order to minimize recombination. To reduce the surface recombination velocity the wafers were thermally oxidized at the temperature of 850oC. The main steps of the fabrication of BSC are schematized in Fig. 16.

#### **3.2 Properties of ITO layers**

The properties of the thus obtained ITO films depend on the concentration of indium chloride and tin chloride in the solution, the temperature of the substrate, the time of

We notice that after the irradiation of ITO/InP solar cells with an integral proton flux of 1013cm-2, their efficiency decreases by 26%, that is less than in the case of Si and GaAs based solar cells. In the spectral characteristics of ITO/pInP solar cells after proton irradiation a small decrease of the photosensitivity in the long wavelength region of the spectrum was

Comparing the results of the radiation stability study of ITO/InP SC, fabricated by spray pyrolysis, with the results of similar investigations of other InP based structures, it is possible to conclude that in this case the radiation stability is also determined by the low efficiency of radiation defects generation and, hence, by the low concentration of deep recombination centers, reducing the efficiency of solar energy conversion in electric power.

**3. Fabrication of ITO/nSi solar cells with enlarged area by spray pyrolisys** 

to 70-80 cm2 as is the case of traditional silicon SC with p-n junction.

there are the chemical reactions describe above in formulas (1) and (2).

schematized in Fig. 16.

**3.2 Properties of ITO layers** 

**3.1 Deposition of ITO layers on enlarged silicon wafers** 

From the brief discussion above it can be concluded that the deposition of ITO layers by spray pyrolysis on the surface of different semiconductor materials allows manufacturing SC through a simple and less expensive technology. The most effective are ITO/InP SC but because of a very high cost of the InP crystals they cannot be widely used in terrestrial applications. To this effect ITO/nSi SC with the efficiency higher than 10% may be used, but it is necessary to develop the technology for SC fabrication with the active area enlarged up

ITO layers are deposited on the nSi crystals surface using the specially designed installation (Simashkevich et al., 2004; Simashkevich et al., 2005) (Fig. 15) that has four main units: the spraying system (7), the system of displacement and rotation of the support on which the substrate is fixed (4, 5), the system of heating the substrate, and the system of the evacuation of the residual products of the pyrolysis (8). The heating system consists of an electric furnace (2) and a device for automatic regulation of the substrate temperature with the thermocouple (3). The rest of the installation parts are: the power unit (1), the cover (10), and the shielding plate (12). Silicon wafers (11) are located on the support (9) and with the displacement mechanism are moved into the deposition zone of the electric furnace (6). The construction of this mechanism provides the rotation of the support with the velocity of 60 rotations per minute, the speed necessary for the obtaining of thin films with uniform thickness on the all wafer surface. The alcoholic solution of the mixture SnCl4 + InCl3 is sprayed with compressed oxygen into the stove on the silicon wafer substrate, where the ITO thin film is formed due to thermal decomposition of the solution and the oxidation reaction. On the heated up substrate

The BSF n/n+ junction was fabricated on the rear side of the wafer by a diffusion process starting from POCl3 gas mixture. The junction formation ended with a wet chemical etching of POCl3 residual in a 10% HF bath. A junction depth of 1μm was chosen in order to minimize recombination. To reduce the surface recombination velocity the wafers were thermally oxidized at the temperature of 850oC. The main steps of the fabrication of BSC are

The properties of the thus obtained ITO films depend on the concentration of indium chloride and tin chloride in the solution, the temperature of the substrate, the time of

observed due to the decrease of the diffusion length.

spraying and the deposition speed. ITO films had a microcrystalline structure that was influenced by the crystal lattice of the support as the X-ray analysis showed. They had cubic structure with the lattice constant 10.14Å (Bruk et al., 2009)). The SEM image of such an ITO film is presented in Fig. 17.

Fig. 15. Schematic a) and real b) view of the installation for ITO thin films deposition

ITO/SiO2/nSi solar cells with the active area of 8.1cm2 and 48.6cm2 were fabricated. In some cases a BSF region was obtained at the rear contact by phosphor diffusion.

Fig. 16. SC process sequence.

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 319

The nSi wafers oriented in the (100) plane with resistivity 1.0 Ohm.cm and 4.5 Ohm.cm (concentrations 5·1015 cm-3 and 1·1015 cm-3) were used for the fabrication of SIS structures. Insulator layers were obtained on the wafers surface by different methods: anodic, thermal or chemical oxidation. The best results have been obtained at the utilization of the two last methods. The chemical oxidation of the silicon surface was realized by immersing the silicon wafer into the concentrated nitric acid for 15 seconds. A tunnel transparent for minority carriers insulator layers at the ITO/Si interface have been obtained thermally, if the deposition occurs in an oxygen containing atmosphere. Ellipsometrical measurement showed that the thickness of the SiO2 insulator layer varies from 30 Å to 60 Å. The frontal grid was obtained by Cu vacuum evaporation. The investigation of the electrical properties of the obtained SIS structures demonstrates that these insulator layers are tunnel transparent for the current carriers. Thereby the obtained ITO/nSi SIS structures represent asymmetrical doped barrier structures in which a wide band gap oxide semiconductor plays the role of

**ITO/SiO2/nSi structures** 

Current-voltage characteristics in the temperature range 293K–413K were studied. The general behavior of the I-V curves of directly biased devices in Fig. 18 is characterized by the presence of two straight-line regions with different slopes (Simashkevich et al., 2009). Two regions with different behavior could be observed from this figure In the first region, at external voltages lower than 0.3 V, the I-V curves are parallel, i.e., the angle of their inclination is constant.

**0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7**

 **region 1** Equal slope

**U (V)**

Fig. 18. Temperature dependent direct I-V characteristics in the dark of the n+ITO/SiO2/nSi

In this case, according to (Riben & Feucht, 1966), the charge carrier transport through the potential barrier is implemented through the tunnel recombination processes in the

**region 2** Different

**7 1**

**1-T= 20<sup>o</sup>**

**2-T= 40<sup>o</sup>**

**3-T= 60<sup>o</sup>**

**4-T= 80<sup>o</sup>**

**5-T=100<sup>o</sup>**

**6-T=120<sup>o</sup>**

**7-T=140<sup>o</sup>**

**C**

**C**

**C**

**C**

**C**

**C**

**C**

slope

**3.3 Obtaining of ITO/nSi structures** 

the transparent metal.

**4.1 Electric properties** 

**4. Physical properties of n<sup>+</sup>**

**10-7**

**10-6**

**10-5**

**10-4**

**I (A)**

solar cells

**10-3**

**10-2**

**10-1**

Fig. 17. SEM image of ITO film

From Fig. 17 it is clear that the ITO film with the thickness of 400nm has a columnar structure, the column height being about 300nm and the width 50-100nm.

ITO films with the maximum conductivity 4.7·103 Om-1cm-1, the electron concentration (3.5÷15)·1021cm-3, , the mobility (15÷30)cm2/(V·s). and maximum transmission coefficient in the visible range of the spectrum (87 %) were obtained from solutions containing 90 % InCl3 and 10 % SnCl4 at the substrate temperature 450°C, deposition rate 100 Å/min, spraying time 45 s. ITO layers with the thickness 0.2mm to 0.7mm and uniform properties on the surface up to 75cm2 were obtained.

The dependence of the electrical parameters of ITO layers as a function of their composition is given in Table 5.


Table 5. The dependence of the electrical parameters of ITO layers as a function of their composition

The band gap width determined from the spectral dependence of the transmission coefficient is equal to 3.90eV and changes only for the content of 90-100% of InCl3 in the spraying solution. If the content of InCl3 is less than 90% the band gap remains constant and equal to 3.44eV. The optical transmission and reflectance spectra of the deposited on the glass substrate ITO thin films (Simashkevich et al., 2004) shows that the transparence in the visible range of spectrum is about 80%, 20% of the incident radiation is reflected.

The ITO thin film thickness was varied by changing the quantity of the sprayed solution and it was evaluated from the reflectance spectrum (Simashkevich et al., 2004). The thickness of the layer was determined using the relationship (Moss et al., 1973):

$$\mathbf{d} = \lambda\_1 \cdot \lambda\_2 / \{ (\lambda\_2, \lambda\_1) \cdot 2\mathbf{n} \} \tag{4}$$

where: n-refraction index equal to 1.8 for ITO (Chopra et al., 1983); λ-the wavelengths for two neighboring maximum and minimum; d-the thickness of the ITO layer. Using this relation the thickness of ITO layers deposited on the nSi wafer surface in dependence on the quantity of the pulverized solution has been determined. This relation is linear and the layer thickness varies from 0.35μm up to 0.5μm.

#### **3.3 Obtaining of ITO/nSi structures**

318 Solar Cells – Silicon Wafer-Based Technologies

From Fig. 17 it is clear that the ITO film with the thickness of 400nm has a columnar

ITO films with the maximum conductivity 4.7·103 Om-1cm-1, the electron concentration

the visible range of the spectrum (87 %) were obtained from solutions containing 90 % InCl3 and 10 % SnCl4 at the substrate temperature 450°C, deposition rate 100 Å/min, spraying time 45 s. ITO layers with the thickness 0.2mm to 0.7mm and uniform properties on the

The dependence of the electrical parameters of ITO layers as a function of their composition

**, S·cm-1** 2.6·102 2.6·103 4.7·103 2.6·103 1.3·103 42.4 **n, cm-3** 1.1·1020 5.5·1020 1.1·1021 6.5·1020 5.8·1020 5.3·1019 **μ, cm-2/(V·s)** 15 29 27 25 14 5 Table 5. The dependence of the electrical parameters of ITO layers as a function of their

The band gap width determined from the spectral dependence of the transmission coefficient is equal to 3.90eV and changes only for the content of 90-100% of InCl3 in the spraying solution. If the content of InCl3 is less than 90% the band gap remains constant and equal to 3.44eV. The optical transmission and reflectance spectra of the deposited on the glass substrate ITO thin films (Simashkevich et al., 2004) shows that the transparence in the

The ITO thin film thickness was varied by changing the quantity of the sprayed solution and it was evaluated from the reflectance spectrum (Simashkevich et al., 2004). The thickness of

 d=λ1·λ2/{(λ2-λ1)·2n} (4) where: n-refraction index equal to 1.8 for ITO (Chopra et al., 1983); λ-the wavelengths for two neighboring maximum and minimum; d-the thickness of the ITO layer. Using this relation the thickness of ITO layers deposited on the nSi wafer surface in dependence on the quantity of the pulverized solution has been determined. This relation is linear and the layer

visible range of spectrum is about 80%, 20% of the incident radiation is reflected.

the layer was determined using the relationship (Moss et al., 1973):

thickness varies from 0.35μm up to 0.5μm.

**Parameters Ratio of InCl3:SnCl4:C2H5OH component in the solution** 

the mobility (15÷30)cm2/(V·s). and maximum transmission coefficient in

10:0:10 9.5:0.5:10 9:1:10 8.5:1.5:10 8:2:10 0:10:10

structure, the column height being about 300nm and the width 50-100nm.

Fig. 17. SEM image of ITO film

surface up to 75cm2 were obtained.

(3.5÷15)·1021cm-3, ,

is given in Table 5.

composition

The nSi wafers oriented in the (100) plane with resistivity 1.0 Ohm.cm and 4.5 Ohm.cm (concentrations 5·1015 cm-3 and 1·1015 cm-3) were used for the fabrication of SIS structures. Insulator layers were obtained on the wafers surface by different methods: anodic, thermal or chemical oxidation. The best results have been obtained at the utilization of the two last methods. The chemical oxidation of the silicon surface was realized by immersing the silicon wafer into the concentrated nitric acid for 15 seconds. A tunnel transparent for minority carriers insulator layers at the ITO/Si interface have been obtained thermally, if the deposition occurs in an oxygen containing atmosphere. Ellipsometrical measurement showed that the thickness of the SiO2 insulator layer varies from 30 Å to 60 Å. The frontal grid was obtained by Cu vacuum evaporation. The investigation of the electrical properties of the obtained SIS structures demonstrates that these insulator layers are tunnel transparent for the current carriers. Thereby the obtained ITO/nSi SIS structures represent asymmetrical doped barrier structures in which a wide band gap oxide semiconductor plays the role of the transparent metal.

#### **4. Physical properties of n<sup>+</sup> ITO/SiO2/nSi structures**

#### **4.1 Electric properties**

Current-voltage characteristics in the temperature range 293K–413K were studied. The general behavior of the I-V curves of directly biased devices in Fig. 18 is characterized by the presence of two straight-line regions with different slopes (Simashkevich et al., 2009). Two regions with different behavior could be observed from this figure In the first region, at external voltages lower than 0.3 V, the I-V curves are parallel, i.e., the angle of their inclination is constant.

Fig. 18. Temperature dependent direct I-V characteristics in the dark of the n+ITO/SiO2/nSi solar cells

In this case, according to (Riben & Feucht, 1966), the charge carrier transport through the potential barrier is implemented through the tunnel recombination processes in the

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 321

Such an I-V dependence expressed by relations (7) and (8) is typical for transport mechanisms involving emission of electrons over potential barriers (Fig. 19b). Thus, at temperatures higher than 20°C, an initial voltage that stimulates the electron emission from Si into ITO over the potential barrier at the Si/ITO interface in n+ITO/SiO2/nSi structures is of about 0.3 *V*. From lnI = f (1/kT) it is possible to determine the height of the potential barrier φB in ITO/nSi structures because the slope of the above-mentioned dependence is equal to φB-qVa. The calculated value of φB is 0.65eV, which is in correlation with the experimental data. A close value of the height of the potential barrier φB equal to 0.68 eV

To sum up, in n+ITO/SiO2/nSi structures two mechanisms of the direct current flow are observed: (i) tunneling recombination at direct voltages of less than 0.3 *V* and (ii) over barrier emission at voltages higher than 0.3 *V*. In the former case, the direct current flow could be interpreted as multi-step tunnel recombination transitions of electrons from the silicon conduction band into the ITO conduction band, the number of steps being of about 100. The reduction of the influence of the former as well as a fine adjustment of the SiO2 thickness in investigated structures will lead to an increased efficiency of converting solar

The spectral distribution of the quantum efficiency as well as the photosensitivity of the obtained PV cells have been studied (Simashkevich et al., 2004). The monochromatic light from the spectrograph is falling on a semitransparent mirror and is divided into two equal fluxes. One flux fall on the surface of a calibrated solar cell for the determination of the incident flux energy and the number (N) of incident photons. The second flux falls on the surface of the analyzed sample and the short circuit current Jsc is measured, thus permitting the calculation of the number of charge carriers, generated by the light and separated by the

**400 600 800 1000 1200**

**Wavelength (nm)** Fig. 20. Spectral distribution of the quantum efficiency (1) and photo sensitivity (2) of the

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

**Photo Sensitivity (A/W)**

was determined also from relation (8) (Simashkevich et al., 2009).

junction, and then the quantum efficiency for each wavelength (Fig. 20).

**1**

**2**

energy into electric energy.

**4.2 Photoelectric properties** 

**0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0**

**Quantum Efficiency**

n+ITO/SiO2/nSi solar cells

space charge region, and the current-voltage dependence could be described by the relation:

$$\mathbf{I} = \mathbf{I}\_o \exp(\mathbf{A} \mathbf{V}) \exp(\mathbf{B} \mathbf{I}) \tag{5}$$

where A and B are constant and do not depend on voltage and temperature, respectively. The numerical value of the constant A, determined from dependences presented in Fig. 18 is equal to 15 V-1. The value of the constant B, which is equal to 0.045 K-1, was calculated from the same dependences that have been re-plotted as lnI = f(T). In (Riben & Feucht, 1966) the constant A is expressed by the relation:

$$\mathbf{A} = 8\text{n} / 3\text{h} \cdot (\text{m}^\bullet \text{ e s} \, \text{S} / \text{N}\_\text{d})^{1/2} \tag{6}$$

where m٭e – is the electron effective mass (in Si in the case considered); εs – the dielectric permeability of the silicon, and S represents the relative change of the electron energy after each step of the tunneling process. Note that 1/S represents the number of tunneling steps.

Fig. 19. The energy band diagram for: a) biases lower than 0.3 V (the region 1 in Fig. 18), b) biases higher than 0.3 V (region 2 in Fig. 18)

The numerical value of A is easily calculated, since the other parameters in the respective expression represent fundamental constants or Si physical parameters. Hence, the mechanism of the charge carrier transport at direct biases of less than 0.3 *V* could be interpreted as multi-step tunnel recombination transitions of electrons from the silicon conduction band into the ITO conduction band (see the energy band diagram in Fig.19a), the number of steps being about 100.

At voltages higher than 0.3 V (see different slope region in Fig. 18) the current flow mechanism through the ITO/nSi structure changes. The slopes of the I-V curves become temperature dependent that is confirmed by the constant value n about 1.6 of the parameter n in the relation:

$$\mathbf{I} = \mathbf{I}\_0 \exp(\mathbf{q} \mathbf{V}\_\mathbf{a} / \mathbf{n} \mathbf{k} \mathbf{T}) \tag{7}$$

where

$$\mathbf{I}\_0 = \mathbf{C} \exp(\mathbf{-q}\mathbf{p}/\mathbf{kT})\tag{8}$$

C is a constant depending on the flux current model (emission or diffusion) (Milnes & Feucht, 1972).

Such an I-V dependence expressed by relations (7) and (8) is typical for transport mechanisms involving emission of electrons over potential barriers (Fig. 19b). Thus, at temperatures higher than 20°C, an initial voltage that stimulates the electron emission from Si into ITO over the potential barrier at the Si/ITO interface in n+ITO/SiO2/nSi structures is of about 0.3 *V*. From lnI = f (1/kT) it is possible to determine the height of the potential barrier φB in ITO/nSi structures because the slope of the above-mentioned dependence is equal to φB-qVa. The calculated value of φB is 0.65eV, which is in correlation with the experimental data. A close value of the height of the potential barrier φB equal to 0.68 eV was determined also from relation (8) (Simashkevich et al., 2009).

To sum up, in n+ITO/SiO2/nSi structures two mechanisms of the direct current flow are observed: (i) tunneling recombination at direct voltages of less than 0.3 *V* and (ii) over barrier emission at voltages higher than 0.3 *V*. In the former case, the direct current flow could be interpreted as multi-step tunnel recombination transitions of electrons from the silicon conduction band into the ITO conduction band, the number of steps being of about 100. The reduction of the influence of the former as well as a fine adjustment of the SiO2 thickness in investigated structures will lead to an increased efficiency of converting solar energy into electric energy.

#### **4.2 Photoelectric properties**

320 Solar Cells – Silicon Wafer-Based Technologies

space charge region, and the current-voltage dependence could be described by the

where A and B are constant and do not depend on voltage and temperature, respectively. The numerical value of the constant A, determined from dependences presented in Fig. 18 is equal to 15 V-1. The value of the constant B, which is equal to 0.045 K-1, was calculated from the same dependences that have been re-plotted as lnI = f(T). In (Riben & Feucht, 1966) the

where m٭e – is the electron effective mass (in Si in the case considered); εs – the dielectric permeability of the silicon, and S represents the relative change of the electron energy after each step of the tunneling process. Note that 1/S represents the number of tunneling steps.

(a) (b)

The numerical value of A is easily calculated, since the other parameters in the respective expression represent fundamental constants or Si physical parameters. Hence, the mechanism of the charge carrier transport at direct biases of less than 0.3 *V* could be interpreted as multi-step tunnel recombination transitions of electrons from the silicon conduction band into the ITO conduction band (see the energy band diagram in Fig.19a), the

At voltages higher than 0.3 V (see different slope region in Fig. 18) the current flow mechanism through the ITO/nSi structure changes. The slopes of the I-V curves become temperature dependent that is confirmed by the constant value n about 1.6 of the parameter

 I0 = Cexp(-φB/kT) (8) C is a constant depending on the flux current model (emission or diffusion) (Milnes &

Fig. 19. The energy band diagram for: a) biases lower than 0.3 V (the region 1 in Fig. 18), b)

I = Ioexp(AV) exp(BT) (5)

A = 8π/3h·(m٭<sup>e</sup> εs S/Nd)1/2 (6)

I = I0exp(qVa/nkT) (7)

relation:

constant A is expressed by the relation:

biases higher than 0.3 V (region 2 in Fig. 18)

number of steps being about 100.

n in the relation:

Feucht, 1972).

where

The spectral distribution of the quantum efficiency as well as the photosensitivity of the obtained PV cells have been studied (Simashkevich et al., 2004). The monochromatic light from the spectrograph is falling on a semitransparent mirror and is divided into two equal fluxes. One flux fall on the surface of a calibrated solar cell for the determination of the incident flux energy and the number (N) of incident photons. The second flux falls on the surface of the analyzed sample and the short circuit current Jsc is measured, thus permitting the calculation of the number of charge carriers, generated by the light and separated by the junction, and then the quantum efficiency for each wavelength (Fig. 20).

Fig. 20. Spectral distribution of the quantum efficiency (1) and photo sensitivity (2) of the n+ITO/SiO2/nSi solar cells

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 323

the monofacial SC and reduces their efficiency. As was presented in (Cuevas, 2005), different types of BSC have been fabricated since then, but all those BSC are based on p-n junctions fabricated by impurity diffusion in the silicon wafer. In case of BSF fabrication, these difficulties increase since it is necessary to realize the simultaneous diffusion of different impurities, which have an adverse influence on the silicon properties. Therefore, the problem of protecting the silicon surface from the undesirable

(a) (b)

Fig. 22. General view of ITO/nSi photovoltaic converters a) SC with active aria 48.6 cm2, b)

A novel type of BSC formed only by isotype junctions was proposed in (Simashkevich et al., 2007), where the possibility was demonstrated to build BSC on the base of nSi crystals and indium tin oxide mixture (ITO) layers obtained by spraying that contain only homopolar junctions with a n+/n/n+ structure The utilization of such structures removes a considerable part of the above-mentioned problems of BSC fabrication because a single diffusion process

In the work (Simashkevich et al., 2007) the results are presented of producing and investigating the silicon based BSC only on majority carriers. The first frontal junction is a SIS structure formed by an ITO layer deposited on the surface of n-type silicon crystal. The starting material is an n-type doped (0.7–4.5Ohm·cm) single crystalline (100) oriented Cz-Silicon 375μm thick nSi wafer with the diameter of 4 inches. The electron concentrations

An usual BSF structure consisting of a highly doped nSi layer obtained by phosphorus diffusion was fabricated on the topside of the wafer by a diffusion process starting from POCl3 gas mixture. The rear n/n+ junction formation ends with a wet chemical etching of POCl3 residual in a 10 % HF bath. A junction depth of 1 μm has been chosen in order to

To reduce the surface recombination velocity the wafers have been thermally oxidized at a temperature of 850oC. Grids obtained by Cu evaporation in vacuum were deposited on the

**ITO/SiO2/n/n<sup>+</sup>**

**Si bifacial solar cells** 

impurities appears.

solar modules with different power

**5.1 Fabrication and characterization of n+**

is carried out.

were 1015cm-3 - 1017 cm-3.

minimize recombination.

The reproducibility of the process and the performances of the devices during samples realization were checked in each batch of samples as well as batch-to-batch. The enlargement of the area of the solar cells up to 48.6cm2 leads to the increasing of the series resistance and to the diminishing of the efficiency down to 7%. Thus, the method of obtaining n+ITO/SiO2/nSi structures based on the thin In2O3: Sn layers, which are formed on the surface of Si wafers, traditionally chemically treated, passivated and heated to the temperature of 450°C, by spraying chemical solutions of indium tin chloride was elaborated. Solar cells based on n+ITO/SiO2/nSi structures with an active surface up to 48.6cm2 have been fabricated.

Maximum efficiency of 10.52% is obtained in the case of (100) crystallographic orientation of Si wafer with BSF region at the rear surface and active area of 8.1 cm2 , ITO thickness 0.3mm, SiO2 thickness - 30Å and the concentration of charge carriers (electrons) in silicon (1-5)×1015cm-3 (Fig. 21).

Fig. 21. Load I-V characteristic of the n+ITO–SiO2–nSi cells with active area 8.1cm2 and BSF region at rear surface.

The developed technology demonstrates the viability of manufacturing solar cells based on n+ITO/SiO2/nSi junctions by assembling two 15W and two 30W power solar panels (Fig. 22) (Usatii, 2011).

#### **5. Bifacial n<sup>+</sup> Si/nSi/SiO2/n<sup>+</sup> ITO solar cells**

For the first time BSC that are able to convert the solar radiation incident of both sides of the cell into electric power have been produced and investigated fifty years ago (Mori, 1960). This type of SC has potential advantages over traditional monofacial SC. First, there is the possibility of producing more electric power due to the absorption of solar energy by the frontal and rear sides of the device, next, they do not have a continuous metallic rear contact, therefore they are transparent to the infrared radiation, which warms

The reproducibility of the process and the performances of the devices during samples realization were checked in each batch of samples as well as batch-to-batch. The enlargement of the area of the solar cells up to 48.6cm2 leads to the increasing of the series resistance and to the diminishing of the efficiency down to 7%. Thus, the method of obtaining n+ITO/SiO2/nSi structures based on the thin In2O3: Sn layers, which are formed on the surface of Si wafers, traditionally chemically treated, passivated and heated to the temperature of 450°C, by spraying chemical solutions of indium tin chloride was elaborated. Solar cells based on n+ITO/SiO2/nSi structures with an active surface up to 48.6cm2 have

Maximum efficiency of 10.52% is obtained in the case of (100) crystallographic orientation of Si wafer with BSF region at the rear surface and active area of 8.1 cm2 , ITO thickness 0.3mm, SiO2 thickness - 30Å and the concentration of charge carriers (electrons) in silicon (1-5)×1015cm-3

**Jsc = 36.3 mA/cm2**

**, 25o**

**C, AM1.5**

 **= 0.085 Ohm Rsh = 6 Ohm FF = 60.9 % Eff.= 10.58 %**

**Voc = 0.475 V**

**Standart conditions**

**Rs**

**1000W/m2**

**0.0 0.1 0.2 0.3 0.4 0.5**

**Voltage,V**

Fig. 21. Load I-V characteristic of the n+ITO–SiO2–nSi cells with active area 8.1cm2 and BSF

The developed technology demonstrates the viability of manufacturing solar cells based on n+ITO/SiO2/nSi junctions by assembling two 15W and two 30W power solar panels

For the first time BSC that are able to convert the solar radiation incident of both sides of the cell into electric power have been produced and investigated fifty years ago (Mori, 1960). This type of SC has potential advantages over traditional monofacial SC. First, there is the possibility of producing more electric power due to the absorption of solar energy by the frontal and rear sides of the device, next, they do not have a continuous metallic rear contact, therefore they are transparent to the infrared radiation, which warms

**ITO solar cells** 

been fabricated.

**0**

**Si/nSi/SiO2/n<sup>+</sup>**

**10**

**20**

**Current density,mA/cm2**

region at rear surface.

(Fig. 22) (Usatii, 2011).

**5. Bifacial n<sup>+</sup>**

**30**

**40**

(Fig. 21).

the monofacial SC and reduces their efficiency. As was presented in (Cuevas, 2005), different types of BSC have been fabricated since then, but all those BSC are based on p-n junctions fabricated by impurity diffusion in the silicon wafer. In case of BSF fabrication, these difficulties increase since it is necessary to realize the simultaneous diffusion of different impurities, which have an adverse influence on the silicon properties. Therefore, the problem of protecting the silicon surface from the undesirable impurities appears.

Fig. 22. General view of ITO/nSi photovoltaic converters a) SC with active aria 48.6 cm2, b) solar modules with different power

A novel type of BSC formed only by isotype junctions was proposed in (Simashkevich et al., 2007), where the possibility was demonstrated to build BSC on the base of nSi crystals and indium tin oxide mixture (ITO) layers obtained by spraying that contain only homopolar junctions with a n+/n/n+ structure The utilization of such structures removes a considerable part of the above-mentioned problems of BSC fabrication because a single diffusion process is carried out.

#### **5.1 Fabrication and characterization of n+ ITO/SiO2/n/n<sup>+</sup> Si bifacial solar cells**

In the work (Simashkevich et al., 2007) the results are presented of producing and investigating the silicon based BSC only on majority carriers. The first frontal junction is a SIS structure formed by an ITO layer deposited on the surface of n-type silicon crystal. The starting material is an n-type doped (0.7–4.5Ohm·cm) single crystalline (100) oriented Cz-Silicon 375μm thick nSi wafer with the diameter of 4 inches. The electron concentrations were 1015cm-3 - 1017 cm-3.

An usual BSF structure consisting of a highly doped nSi layer obtained by phosphorus diffusion was fabricated on the topside of the wafer by a diffusion process starting from POCl3 gas mixture. The rear n/n+ junction formation ends with a wet chemical etching of POCl3 residual in a 10 % HF bath. A junction depth of 1 μm has been chosen in order to minimize recombination.

To reduce the surface recombination velocity the wafers have been thermally oxidized at a temperature of 850oC. Grids obtained by Cu evaporation in vacuum were deposited on the

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 325

The I-V load characteristics at AM1.5 spectral distribution and 1000W/m2 illumination are

**Rear illum.**

**Frontal illum.**

**Voc = 0.425 V FF = 68.29 % Eff.= 9.47%**

**Jsc = 32.63 mA/cm2**

**Voc = 0.392 V FF = 69.28 %** Eff.= **3.60%**

**Jsc = 13.23 mA/cm2**

Fig. 25. The I-V load characteristics and the photoelectric parameters of the elaborated BSC

The photoelectric parameters of the elaborated BSC have been determined in standard AM1,5 conditions: for the frontal side Voc=0.425V, Jsc=32.63mA/cm2, FF=68.29%, Eff.=9.47%, Rser=2.08Ohm, Rsh=6.7·103Ohm; for the back side Voc=0.392V, Jsc=13.23mA/cm2, FF=69.28%,

Using the method of n+ITO/SiO2/n/n+Si bifacial solar cells fabrication described in (Simashkevich et al., 2007) with improved parameters in conformity with p.2 of this communication, in (Simashkevich et al., 2011) two types of bifacial solar cells have been

It is seen from these data that the effected technology optimization allows to increase of the summary efficiency from 13.07% to 15.73% in the case of irregular etching of the silicon surface and to 20.89% in the case of regular etching. The bifaciality ratio also increases from

On the basis of physical parameters of the silicon wafer, ITO layers and of the results of our experiments, the energy band diagram of the n+Si/nSi/SiO2/n+ITO structure was proposed

obtained which have different profiles of silicon wafer surface (Fig. 26 and Fig. 27).

at AM1.5 spectral distribution and 1000W/m2 illumination

The summary efficiency of the BSC is equal to 13.07%.

Eff.=3.6%, Rser=3.40Ohm, Rsh=1.26·104Ohm.

**0.0 0.1 0.2 0.3 0.4**

**Si bifacial solar cells with textured surface of Si crystals** 

**Voltage, V**

presented in Fig.25.

**0.000**

**ITO/SiO2/n/n<sup>+</sup>**

(Simashkevich et al., 2007).

**0.005**

**0.010**

**0.015**

**0.020**

**Current density, A/cm2**

**5.2 n<sup>+</sup>**

0.38 up to 0.75.

**0.025**

**0.030**

**0.035**

frontal and back surfaces for BSC fabrication. The schematic view of the bifacial ITO/nSi solar cell is presented in Fig. 23.

Fig. 23. The schematic a) and real b) view of the ITO/nSi BSC

The spectral distribution of the quantum efficiency of BSC, obtained on silicon wafers with different electron concentration, has been studied at frontal and back illumination (Fig.24). With the frontal illumination, in the region of the wavelengths from 400nm to 870nm the value of QY changes in the limits 0.65–0.95. With the back illumination, QY is equal to 0.6– 0.8 in the same region of the spectrum (Bruk et al., 2009).

Fig. 24. Spectral distribution of the quantum efficiency 1, 2-frontal illumination; 3, 4-rear illumination

frontal and back surfaces for BSC fabrication. The schematic view of the bifacial ITO/nSi

The spectral distribution of the quantum efficiency of BSC, obtained on silicon wafers with different electron concentration, has been studied at frontal and back illumination (Fig.24). With the frontal illumination, in the region of the wavelengths from 400nm to 870nm the value of QY changes in the limits 0.65–0.95. With the back illumination, QY is equal to 0.6–

**1**

**2**

**3**

**4**

**400 500 600 700 800 900 1000 1100 1200**

Fig. 24. Spectral distribution of the quantum efficiency 1, 2-frontal illumination; 3, 4-rear

 **(nm)**

1-(=1.0*Ohm*

2-(=4.5*Ohm*

3-(=4.5*Ohm*

4-(=1.0*Ohm*

*cm*)

*cm*)

*cm*)

*cm*)

(a) (b)

Fig. 23. The schematic a) and real b) view of the ITO/nSi BSC

0.8 in the same region of the spectrum (Bruk et al., 2009).

**0.0**

illumination

**0.1 0.2**

**0.3**

**0.4**

**0.5 0.6**

**QY, arb.un.**

**0.7**

**0.8**

**0.9 1.0**

solar cell is presented in Fig. 23.

The I-V load characteristics at AM1.5 spectral distribution and 1000W/m2 illumination are presented in Fig.25.

Fig. 25. The I-V load characteristics and the photoelectric parameters of the elaborated BSC at AM1.5 spectral distribution and 1000W/m2 illumination

The photoelectric parameters of the elaborated BSC have been determined in standard AM1,5 conditions: for the frontal side Voc=0.425V, Jsc=32.63mA/cm2, FF=68.29%, Eff.=9.47%, Rser=2.08Ohm, Rsh=6.7·103Ohm; for the back side Voc=0.392V, Jsc=13.23mA/cm2, FF=69.28%, Eff.=3.6%, Rser=3.40Ohm, Rsh=1.26·104Ohm.

The summary efficiency of the BSC is equal to 13.07%.

#### **5.2 n<sup>+</sup> ITO/SiO2/n/n<sup>+</sup> Si bifacial solar cells with textured surface of Si crystals**

Using the method of n+ITO/SiO2/n/n+Si bifacial solar cells fabrication described in (Simashkevich et al., 2007) with improved parameters in conformity with p.2 of this communication, in (Simashkevich et al., 2011) two types of bifacial solar cells have been obtained which have different profiles of silicon wafer surface (Fig. 26 and Fig. 27).

It is seen from these data that the effected technology optimization allows to increase of the summary efficiency from 13.07% to 15.73% in the case of irregular etching of the silicon surface and to 20.89% in the case of regular etching. The bifaciality ratio also increases from 0.38 up to 0.75.

On the basis of physical parameters of the silicon wafer, ITO layers and of the results of our experiments, the energy band diagram of the n+Si/nSi/SiO2/n+ITO structure was proposed (Simashkevich et al., 2007).

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 327

Fig. 28. Energy band diagram of the bifacial Cu/n+ITO/SiO2/nSi/n+Si/Cu structure

processes take place at the illumination through the rear contact.

the most suitable for the fabrication of SIS structures based solar cells.

**6. Conclusion** 

for cells with area of 8.1cm2.

Fig. 28 shows this energy band diagram at illumination in the short-circuit regime. At the illumination through the frontal contact, the solar radiation is absorbed in the silicon wafer. The light generated carriers are separated by the nSi/SiO2/ITO junction. The BSF of the n+Si/nSi junction facilitate the transport of the carriers to the back contact. The same

SC fabricated on the basis of semiconductor-insulator- semiconductor structures, obtained by deposition of TCO films on the surface of different semiconductor solar materials (Si, InP, CdTe etc) are promising devices for solar energy conversion due to the simplicity of their fabrication and relatively low cost. One of the main advantages of SIS based SC is the elimination of the high temperature diffusion process from the technological chain, which is necessary for obtaining p-n junctions, the maximum temperature at the SIS structure fabrication being not higher than 450oC. The TCO films can be deposited by a variety of techniques among which the spray deposition method is particularly attractive since it is simple, relatively fast and vacuum less. Between different TCO materials, the ITO layers are

Silicon remains the most utilized absorbing semiconductor material for fabrication by spray pyrolysis of such type of SC. The maximum efficiency of ITO/nSi SC is 10-12%, but in the case of textured surface of Si crystals the efficiency reaches more than 15%. ITO/nSi SC with enlarged area up to 48 cm2 have been obtained by the spray method, the efficiency is 10.58%

Fig. 26. Load I-V characteristic of n+ITO/SiO2/n/n+Si BSC with irregular Si surface

Fig. 27. Load I-V characteristic of n+ITO/SiO2/n/n+Si BSC with regular Si surface

Fig. 28. Energy band diagram of the bifacial Cu/n+ITO/SiO2/nSi/n+Si/Cu structure

Fig. 28 shows this energy band diagram at illumination in the short-circuit regime. At the illumination through the frontal contact, the solar radiation is absorbed in the silicon wafer. The light generated carriers are separated by the nSi/SiO2/ITO junction. The BSF of the n+Si/nSi junction facilitate the transport of the carriers to the back contact. The same processes take place at the illumination through the rear contact.

#### **6. Conclusion**

326 Solar Cells – Silicon Wafer-Based Technologies

**Frontal illumination**

**JSC= 34.6mA/cm2**

**Voltage, V**

**Voltage, V**

**UOC= 0.478V FF = 57.4% Eff.= 9.53%**

**Rear illumination JSC= 22.5mA/cm2**

**UOC= 0.461V FF = 59.4% Eff. = 6.20%**

**0.0 0.1 0.2 0.3 0.4 0.5**

**0.0 0.1 0.2 0.3 0.4 0.5**

Fig. 27. Load I-V characteristic of n+ITO/SiO2/n/n+Si BSC with regular Si surface

**Rear illumination JSC= 25.6mA/cm2**

**UOC= 0.458V FF = 76.9% Eff.= 8.98%**

Fig. 26. Load I-V characteristic of n+ITO/SiO2/n/n+Si BSC with irregular Si surface

**Frontal illumination**

**JSC= 34.3mA/cm2**

**UOC= 0.461V FF = 75.0% Eff.= 11.91%**

**0**

**0**

**5**

**10**

**15**

**20**

**Current density, mA/cm2**

**25**

**30**

**35**

**5**

**10**

**15**

**20**

**Current density, mA/cm2**

**25**

**30**

**35**

SC fabricated on the basis of semiconductor-insulator- semiconductor structures, obtained by deposition of TCO films on the surface of different semiconductor solar materials (Si, InP, CdTe etc) are promising devices for solar energy conversion due to the simplicity of their fabrication and relatively low cost. One of the main advantages of SIS based SC is the elimination of the high temperature diffusion process from the technological chain, which is necessary for obtaining p-n junctions, the maximum temperature at the SIS structure fabrication being not higher than 450oC. The TCO films can be deposited by a variety of techniques among which the spray deposition method is particularly attractive since it is simple, relatively fast and vacuum less. Between different TCO materials, the ITO layers are the most suitable for the fabrication of SIS structures based solar cells.

Silicon remains the most utilized absorbing semiconductor material for fabrication by spray pyrolysis of such type of SC. The maximum efficiency of ITO/nSi SC is 10-12%, but in the case of textured surface of Si crystals the efficiency reaches more than 15%. ITO/nSi SC with enlarged area up to 48 cm2 have been obtained by the spray method, the efficiency is 10.58% for cells with area of 8.1cm2.

Solar Cells on the Base of Semiconductor-Insulator-Semiconductor Structures 329

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InP based SIS structures fabricated by deposition of ITO layers onto pInP crystal surfaces have high efficiencies, at the same time they are more simple to fabricate in comparison with diffusion junction cells. The efficiency of ITO/InP solar cells obtained by spray pyrolisis depends on the crystallographic orientation of the InP wafers, The maximum efficiency of 11.6% was obtained in the case of fabrication of ITO/pInP/p+InP structures using InP wafers oriented in the (110) plane. ITO/InP SC, obtained by spray pyrolysis demonstrates radiation stability. After the irradiation of ITO/InP solar cells with an integral proton flux of 1013cm-2, their efficiency decreases by 26%, that is less than in the case of Si and GaAs based solar cells.

A new type of bifacial solar cells n+Si/nSi/SiO2/n+ITO based only on isotype junctions was elaborated and fabricated. It was demonstrated that the simultaneous illumination of both frontal and rear surfaces of the structures allow to obtain a summary current. The technological process of manufacturing such solar cells does not require sophisticated equipment. Bifacial solar cells with summary efficiency of 21% and 65% bifaciality coefficient have been obtained using as an absorbent material of single crystalline silicon with a textured surface.

### **7. Acknowledgment**

The authors would like to acknowledge Drs E.Bobeico and V.Fedorov for carrying out the measurements of some parameters of ITO/nSi based solar cells, Dr. Iu.Usatii for the help in developing the large-area deposition of ITO layers.

We thank the direction of the Institute of Applied Physics of the Academy of Sciences of Moldova for support and creation of favorable conditions for investigations. We thank Dr. Olga Iliasenco for technical assistance.

We also are grateful to those numerous scientists and engineers worldwide whose data have been included in this overview.

#### **8. References**


InP based SIS structures fabricated by deposition of ITO layers onto pInP crystal surfaces have high efficiencies, at the same time they are more simple to fabricate in comparison with diffusion junction cells. The efficiency of ITO/InP solar cells obtained by spray pyrolisis depends on the crystallographic orientation of the InP wafers, The maximum efficiency of 11.6% was obtained in the case of fabrication of ITO/pInP/p+InP structures using InP wafers oriented in the (110) plane. ITO/InP SC, obtained by spray pyrolysis demonstrates radiation stability. After the irradiation of ITO/InP solar cells with an integral proton flux of 1013cm-2, their efficiency decreases by 26%, that is less than in the case of Si and GaAs based

A new type of bifacial solar cells n+Si/nSi/SiO2/n+ITO based only on isotype junctions was elaborated and fabricated. It was demonstrated that the simultaneous illumination of both frontal and rear surfaces of the structures allow to obtain a summary current. The technological process of manufacturing such solar cells does not require sophisticated equipment. Bifacial solar cells with summary efficiency of 21% and 65% bifaciality coefficient have been obtained using as an absorbent material of single crystalline silicon

The authors would like to acknowledge Drs E.Bobeico and V.Fedorov for carrying out the measurements of some parameters of ITO/nSi based solar cells, Dr. Iu.Usatii for the help in

We thank the direction of the Institute of Applied Physics of the Academy of Sciences of Moldova for support and creation of favorable conditions for investigations. We thank Dr.

We also are grateful to those numerous scientists and engineers worldwide whose data have

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solar cells.

with a textured surface.

**7. Acknowledgment** 

developing the large-area deposition of ITO layers.

Olga Iliasenco for technical assistance.

pp.9-19, ISSN 0927-0248

been included in this overview.

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**1. Introduction**

In this chapter, the author explains the present technological and scientific maturity of the field of solar-energy conversion. The author builds on scientific foundations to generalize several upper limits of solar-energy conversion as a function of the geometric-concentration factor. These limits are used to define a high-efficiency regime for the terrestrial conversion of solar-energy. The current world-record efficiency is measured in solar cells composed of three junctions operating in tandem under a geometric-concentration factor of 454 Suns. By illustrating that the current world-record efficiency is clearly within the high-efficiency regime, the author argues that the field of photovoltaic solar-energy conversion is far removed from its infancy. Inasmuch that the world-record efficiency is less than half of the theoretical terrestrial limit, the author argues that there is significant space for scientific innovation. In addition, by noting that the world-record efficiency, which is measured with a tandem solar cell with three junctions operating at 454 Suns, is 9% less than the physical limit of a tandem solar cells with two junctions operating under the same number of Suns, the author makes apparent the potential for improvement to the present technological paradigm. The author concludes that solar-energy science and technology has significantly more challenges

to address and innovations to realize before it may be considered a fully mature field.

The remainder of this chapter is organized as follows. In Section 2, the author describes an ideal *p-n* junction solar cell and distinguishes the solar cell's absorber, its function, and its relation to the other essential components of the solar cell. In Section 3, the author reviews three important approaches that establish upper-limiting efficiencies of solar-energy conversion: the radiation-in-radiation-out approach of Landsberg and Tonge, the omni-colour approach of DeVos, Grosjean, and Pauwels, and the detailed-balance approach of Shockley and Queisser. The detailed-balance approach establishes the maximum-power conversion-efficiency of a single *p-n* junction solar cell in the terrestrial environment as 40.7%. Yet, the omni-colour approach establishes the maximum-power conversion-efficiency of solar energy in the terrestrial environment as 86.8%. In Section 4, the author reviews four approaches for realizing a global efficiency enhancement with respect to the maximum-power conversion-efficiency of a single *p-n* junction solar cell. The current technological paradigm experimentally demonstrates high-efficiencies by using stacks of *p-n* junction solar cells operating in tandem. Other next-generation approaches propose the incorporation of one or more physical phenomena (*e.g.*, multiple transitions, multiple electron-hole pair generation, and hot carriers) to reach high-efficiencies. In Section 5, the author offers concluding remarks.

Michael Y. Levy *Hartsdale, New York*

**Energy Conversion** 

**Maturity of Photovoltaic Solar-**

*U.S.A.*

**15**


## **Maturity of Photovoltaic Solar-Energy Conversion**

Michael Y. Levy *Hartsdale, New York U.S.A.*

#### **1. Introduction**

332 Solar Cells – Silicon Wafer-Based Technologies

Simashkevich, A.; Sherban, D.; Morvillo, P.; Bobeico, E.; Bruk, L. & Usatii, Iu. (2007). Bifacial

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*Physics and Chemistry of Solid State*, Vol.11, No.4, (October 2010), pp. 950-956 Simashkevich, A.V.; Sherban, D.A.; Bruk, L.I., Harea, E.E. & Usatii, Iu. (2011). Efficient

Tarr, N. & Pulfrey, D. (1979). New experimental evidence for minority-carrier. *Appl. Phys.* 

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Usatii, Iu. (2011). Preparation of ITO-Si solar cells with enlarged area and the study of their

Vasu, V. & Aubrahmanyam. A. (1992) Photovoltaic properties of indium tin oxide

Vasu, V.; Subrahmanyam, A.; Kumar, J. & Ramasamy, P. (1993). Spray-pyrolytic-grown

Wishwakarma, S., Rahmatullah R. & Prasad, H.C. (1993). Low cost SnO2:P/SiO2/n-Si

Yamamoto, A.; Yamaguchi, M. & Uemura. C. (1984). High conversion efficiency and high

properties. (in Romanian). *Ph.D. Thesis*, Chisinau, (February 2011)

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*Lett*., V.34, No.4, (February 1979), pp.295-297, ISSN 0003-6951

*Conf.*, ISBN: 3-936338-22-1, Milan, Italy, (September 2007), pp.484-486 Simashkevich, A.; Sherban, D.; Rusu, M.; Bruk, L. & Usatii. Iu. (2009). ITO/nSi solar cells:

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1242

solar cells based on isotype junctions, *Proc. of the 22th European PV Solar Energy* 

voltage dependent charge transport mechanisms, *Proc. of the 24th European Photovoltaic Solar Energy Conference,* pp.2230-2232, ISBN: 3-936338-24-1, Hamburg,

of the mechanism of a current flowing through an ITO/nSi isotype structure. *Surface engineering and applied electrochemistry*, Vol.46, No.1, (February 2010), pp.40-

Transparent Conductive Oxide Layers and Their Application in Solar Energetic.

ITO/nSi solar cells with silicon textured surface. *Elektronnaya Obrabotka Materialov*,

solar cell with antireflection coating of transparent conducting oxide, *Proc of the 2nd World Conf. on PV Solar Energy Conversion*, Vol.1, pp.300-302, ISBN 92-828-5179-6,

(ITO)/silicon junctions prepared by spray pyrolysis - dependence on oxidation time. *Semicond. Sci. and Tech*., Vol.7, No.3, (March 1992), pp.320-323, ISSN 0268-

ITO/InP junctions: effect of tin doping. *Semicond. Sci. Technol*., Vol.8, No.3 (March

(textured) heterojunction solar cells. *J.Phys.D:Appl.Phys*., v.26, No.6, (June 1993),

radiation resistance InP homojunction solar cells. *Appl. Phys. Lett.*, Vol.44, No.6,

In this chapter, the author explains the present technological and scientific maturity of the field of solar-energy conversion. The author builds on scientific foundations to generalize several upper limits of solar-energy conversion as a function of the geometric-concentration factor. These limits are used to define a high-efficiency regime for the terrestrial conversion of solar-energy. The current world-record efficiency is measured in solar cells composed of three junctions operating in tandem under a geometric-concentration factor of 454 Suns. By illustrating that the current world-record efficiency is clearly within the high-efficiency regime, the author argues that the field of photovoltaic solar-energy conversion is far removed from its infancy. Inasmuch that the world-record efficiency is less than half of the theoretical terrestrial limit, the author argues that there is significant space for scientific innovation. In addition, by noting that the world-record efficiency, which is measured with a tandem solar cell with three junctions operating at 454 Suns, is 9% less than the physical limit of a tandem solar cells with two junctions operating under the same number of Suns, the author makes apparent the potential for improvement to the present technological paradigm. The author concludes that solar-energy science and technology has significantly more challenges to address and innovations to realize before it may be considered a fully mature field.

The remainder of this chapter is organized as follows. In Section 2, the author describes an ideal *p-n* junction solar cell and distinguishes the solar cell's absorber, its function, and its relation to the other essential components of the solar cell. In Section 3, the author reviews three important approaches that establish upper-limiting efficiencies of solar-energy conversion: the radiation-in-radiation-out approach of Landsberg and Tonge, the omni-colour approach of DeVos, Grosjean, and Pauwels, and the detailed-balance approach of Shockley and Queisser. The detailed-balance approach establishes the maximum-power conversion-efficiency of a single *p-n* junction solar cell in the terrestrial environment as 40.7%. Yet, the omni-colour approach establishes the maximum-power conversion-efficiency of solar energy in the terrestrial environment as 86.8%. In Section 4, the author reviews four approaches for realizing a global efficiency enhancement with respect to the maximum-power conversion-efficiency of a single *p-n* junction solar cell. The current technological paradigm experimentally demonstrates high-efficiencies by using stacks of *p-n* junction solar cells operating in tandem. Other next-generation approaches propose the incorporation of one or more physical phenomena (*e.g.*, multiple transitions, multiple electron-hole pair generation, and hot carriers) to reach high-efficiencies. In Section 5, the author offers concluding remarks.

On the external surface of both emitters is a metallic contact. The carriers in the contacts are in equilibrium with one another, so where the contact interfaces with the emitter the occupancy of holes and electrons are described by the same Fermi energy. The absolute value of the Fermi energy at the contact of the *n*-type emitter is roughly equal to the absolute value of the quasi-Fermi energy of majority carriers at the interface between the absorber interfaces with the *n*-type emitter. An analog of this statement holds for the contact to the *p*-type emitter. Thus, between the two contacts there is a voltage, *V*, that is proportional to the potential difference *ε*F,C − *ε*F,V as *V* = (*ε*F,C − *ε*F,V) /*q*, where *q* is the elementary charge. Therefore, the chemical energy of each electron-hole pair, *μ*e-h, is converted to electrical energy by a unit pulse of charge current, *q*, at the voltage *V*. In the following subsection, the present author

Maturity of Photovoltaic Solar-Energy Conversion 335

In this section, the present author reviews three distinct approaches to upper-bound the efficiency of solar-energy conversion. In Section 3.1, the present author offers a schematic of a generalized converter and uses the schematic to define the conversion efficiency. In sections 3.2, 3.3, and 3.4, the present author reviews the Landsberg-Tonge limit, the Shockley-Queisser limit, and the omni-colour limit, respectively. In Section 3.5, the present author compares and contrasts these three approaches. Finally, in Section 3.6, the present author draws conclusions regarding the upper-theoretical efficiency of converting solar energy to electricity in the terrestrial environment. The present author concludes that though the efficiency limit of a single *p-n* junction solar cell is large, a significant efficiency enhancement is possible. This is because, in the first approximation, the terrestrial limits of a single *p-n* junction solar cell are 40.7% and 24.0%, whereas those of an omni-colour converter are 86.8% and 52.9% for fully-concentrated and non-concentrated sunlight, respectively.

Figure 2 is a schematic of a generalized energy converter (*c.f.* the converter in

and a rate of heat flow, *Q*˙ , is transmitted to the ambient. Internally, the converter experiences a rate change of energy, *E*˙ , and a rate change of entropy, *S*˙. In addition, the converter, by its

The first-law conversion efficiency, *η*, is defined as the ratio of the useable power over the

Typically, in the science of solar-energy conversion, no more than two radiation flows pump the converter (see Figure 3). Always present is a direct source of radiation from the sun, which is assumed a black body with a surface temperature *T*S, yielding an energy flux, *U*˙ p,S. Sometimes present, depending on the geometric-concentration factor, *C*, is a diffuse source of radiation scattered from the Earth's atmosphere, which is assumed to be a black body with a surface temperature *T*E, yielding an energy flux, *U*˙ p,E. Considering the dilution factor of solar

*η* . <sup>=</sup> *<sup>W</sup>*˙ *E*˙ p

p. Analogously, the converter, which maintains a temperature *T*c, sinks a power

*g*.

, which is linearly related to the solid angle subtended by the sun on

s. Meanwhile, a rate of useable work, *W*˙ , is delivered

. (1)

p, and a rate of

Landsberg & Tonge (1980)). The converter is pumped with a power flow, *E*˙

energy flow pumped into the converter, so that (Landsberg & Tonge, 1980)

reviews various limits describing the efficiency of solar-energy conversion.

**3. Limits to ideal solar-energy conversion**

**3.1 Generalized energy converter**

s, and a rate of entropy flow, *S*˙

2.16 <sup>×</sup> <sup>10</sup>−<sup>5</sup>

own internal processes, generates a rate of entropy, *S*˙

entropy flow, *S*˙

radiation, *D*

flow, *E*˙

#### **2. Ideal** *p-n* **junction solar cell**

In Figure 1, the present author illustrates the ideal electronic structure of a photovoltaic solar cell (Würfel, 2002; Würfel, 2004), a device that converts the energy of radiation into electrical energy. The ideal structure of the solar cell is comprised of several components: an absorber, two emitters and two contacts. The absorber enables photo-chemical conversion, the emitters enable electro-chemical conversion, and the contacts enable useful work to be performed by an external load. In the following paragraphs, the present author describes an ideal solar cell in more detail.

Fig. 1. Ideal structure of a solar cell. Shown is the absorber, which is sandwiched between an *n*-type emitter and a *p*-type emitter. An Ohmic contact is made to each of the emitters. A voltage, *V*, exists between the contacts of the solar cell.

An absorber is in the center of the solar cell. The absorber is a medium whose electronic states form a conduction band and a valence band. The conduction and valence bands are separated by an energetic gap that is characterized by the absence of electronic states. The occupancy of the electronic states of the conduction band and valence band are described by the quasi-Fermi energies *ε*F,C and *ε*F,V, respectively. The absorber is the region of the solar cell where the absorption of photons occurs and where the subsequent photogeneration of electrons and holes takes place. Ideally, each photon with energy greater than that of the energetic gap may generate a single electron-hole pair. In such case, the energy of each photon with energy greater than the bandgap is converted to the chemical energy of an electron-hole pair, *μ*e-h, where *μ*e-h = *ε*F,C − *ε*F,V (Würfel, 2002; Würfel, 2004).

The absorber is sandwiched between two semi-permeable emitters (Würfel, 2002; Würfel, 2004). The emitters are selected to produce an asymmetry in the band structure. The electronegativity and bandgap of the emitter on the right (*i.e.,* the *n*-type emitter) are selected so that the (*i*) electrons largely or completely permeate through and (*ii*) holes largely or completely do not (Würfel, 2002; Würfel, 2004). A small gradient drives the majority carriers (*i.e.*, holes) to the right so that a beneficial current is produced. A large gradient drives minority carriers (*i.e.*, electrons) to the right so that a detrimental current is produced. The latter current is very small, resulting from the relative impermeability of the rightmost emitter to electrons. The emitter on the left is similarly selected, except that it is the holes that permeate through and yield a beneficial current.

2 Will-be-set-by-IN-TECH

In Figure 1, the present author illustrates the ideal electronic structure of a photovoltaic solar cell (Würfel, 2002; Würfel, 2004), a device that converts the energy of radiation into electrical energy. The ideal structure of the solar cell is comprised of several components: an absorber, two emitters and two contacts. The absorber enables photo-chemical conversion, the emitters enable electro-chemical conversion, and the contacts enable useful work to be performed by an external load. In the following paragraphs, the present author describes an ideal solar cell


+

Fig. 1. Ideal structure of a solar cell. Shown is the absorber, which is sandwiched between an *n*-type emitter and a *p*-type emitter. An Ohmic contact is made to each of the emitters. A

An absorber is in the center of the solar cell. The absorber is a medium whose electronic states form a conduction band and a valence band. The conduction and valence bands are separated by an energetic gap that is characterized by the absence of electronic states. The occupancy of the electronic states of the conduction band and valence band are described by the quasi-Fermi energies *ε*F,C and *ε*F,V, respectively. The absorber is the region of the solar cell where the absorption of photons occurs and where the subsequent photogeneration of electrons and holes takes place. Ideally, each photon with energy greater than that of the energetic gap may generate a single electron-hole pair. In such case, the energy of each photon with energy greater than the bandgap is converted to the chemical energy of an electron-hole

The absorber is sandwiched between two semi-permeable emitters (Würfel, 2002; Würfel, 2004). The emitters are selected to produce an asymmetry in the band structure. The electronegativity and bandgap of the emitter on the right (*i.e.,* the *n*-type emitter) are selected so that the (*i*) electrons largely or completely permeate through and (*ii*) holes largely or completely do not (Würfel, 2002; Würfel, 2004). A small gradient drives the majority carriers (*i.e.*, holes) to the right so that a beneficial current is produced. A large gradient drives minority carriers (*i.e.*, electrons) to the right so that a detrimental current is produced. The latter current is very small, resulting from the relative impermeability of the rightmost emitter to electrons. The emitter on the left is similarly selected, except that it is the holes that

*h*ω

valence band

conduction band

μe-h

absorber *<sup>n</sup>*-type

εF,C

emitter

Ohmic contact

**2. Ideal** *p-n* **junction solar cell**

*qV*


+

Ohmic contact

*p*-type emitter

> εF,V

voltage, *V*, exists between the contacts of the solar cell.

pair, *μ*e-h, where *μ*e-h = *ε*F,C − *ε*F,V (Würfel, 2002; Würfel, 2004).

permeate through and yield a beneficial current.

in more detail.

On the external surface of both emitters is a metallic contact. The carriers in the contacts are in equilibrium with one another, so where the contact interfaces with the emitter the occupancy of holes and electrons are described by the same Fermi energy. The absolute value of the Fermi energy at the contact of the *n*-type emitter is roughly equal to the absolute value of the quasi-Fermi energy of majority carriers at the interface between the absorber interfaces with the *n*-type emitter. An analog of this statement holds for the contact to the *p*-type emitter. Thus, between the two contacts there is a voltage, *V*, that is proportional to the potential difference *ε*F,C − *ε*F,V as *V* = (*ε*F,C − *ε*F,V) /*q*, where *q* is the elementary charge. Therefore, the chemical energy of each electron-hole pair, *μ*e-h, is converted to electrical energy by a unit pulse of charge current, *q*, at the voltage *V*. In the following subsection, the present author reviews various limits describing the efficiency of solar-energy conversion.

#### **3. Limits to ideal solar-energy conversion**

In this section, the present author reviews three distinct approaches to upper-bound the efficiency of solar-energy conversion. In Section 3.1, the present author offers a schematic of a generalized converter and uses the schematic to define the conversion efficiency. In sections 3.2, 3.3, and 3.4, the present author reviews the Landsberg-Tonge limit, the Shockley-Queisser limit, and the omni-colour limit, respectively. In Section 3.5, the present author compares and contrasts these three approaches. Finally, in Section 3.6, the present author draws conclusions regarding the upper-theoretical efficiency of converting solar energy to electricity in the terrestrial environment. The present author concludes that though the efficiency limit of a single *p-n* junction solar cell is large, a significant efficiency enhancement is possible. This is because, in the first approximation, the terrestrial limits of a single *p-n* junction solar cell are 40.7% and 24.0%, whereas those of an omni-colour converter are 86.8% and 52.9% for fully-concentrated and non-concentrated sunlight, respectively.

#### **3.1 Generalized energy converter**

Figure 2 is a schematic of a generalized energy converter (*c.f.* the converter in Landsberg & Tonge (1980)). The converter is pumped with a power flow, *E*˙ p, and a rate of entropy flow, *S*˙ p. Analogously, the converter, which maintains a temperature *T*c, sinks a power flow, *E*˙ s, and a rate of entropy flow, *S*˙ s. Meanwhile, a rate of useable work, *W*˙ , is delivered and a rate of heat flow, *Q*˙ , is transmitted to the ambient. Internally, the converter experiences a rate change of energy, *E*˙, and a rate change of entropy, *S*˙. In addition, the converter, by its own internal processes, generates a rate of entropy, *S*˙ *g*.

The first-law conversion efficiency, *η*, is defined as the ratio of the useable power over the energy flow pumped into the converter, so that (Landsberg & Tonge, 1980)

$$
\eta \doteq \frac{\dot{W}}{\dot{E}\_{\text{P}}}.\tag{1}
$$

Typically, in the science of solar-energy conversion, no more than two radiation flows pump the converter (see Figure 3). Always present is a direct source of radiation from the sun, which is assumed a black body with a surface temperature *T*S, yielding an energy flux, *U*˙ p,S. Sometimes present, depending on the geometric-concentration factor, *C*, is a diffuse source of radiation scattered from the Earth's atmosphere, which is assumed to be a black body with a surface temperature *T*E, yielding an energy flux, *U*˙ p,E. Considering the dilution factor of solar radiation, *D* 2.16 <sup>×</sup> <sup>10</sup>−<sup>5</sup> , which is linearly related to the solid angle subtended by the sun on

Solar Illumination

Maturity of Photovoltaic Solar-Energy Conversion 337

Ω

*n p*

thermal conductor

ambient

*Z*

+ -

In arriving at the above inequality, Landsberg and Tonge assume steady-state conditions. Equality holds for the special case where there is no internal entropy generation (*i.e. S*˙

0). The resulting equality is first derived by Patela by considering the exergy of heat radiation (Petela, 1964). The Landsberg-Tonge limit may be extended so as to model the dual sources of the solar geometry (Würfel, 2002). In the case of two black-body sources simultaneously pumping the converter, a derivation similar to that of Landsberg and Tonge

Figure 4 illustrates the Landsberg-Tonge efficiency limit. In Section 3.3, the detailed-balance method of Shockley and Queisser is presented and applied to a single *p-n* junction solar cell.

Shockley and Queisser present a framework to analyze the efficiency limit of solar-energy conversion by a single *p-n* junction (Shockley & Queisser, 1961). They name this limit the detailed-balance limit for it is derived from the notion that, in principle, all recombination

+ (1 − *C D*)

<sup>S</sup> <sup>+</sup> (<sup>1</sup> <sup>−</sup> *C D*) *<sup>T</sup>*<sup>4</sup>

Fig. 3. Cross section of an abstracted *p-n* junction solar cell with spherical symmetry. The exaggerated physical symmetry reinforces the solar geometry, where a solid angle of the solar cell's surface, Ω, is subtended by direct insolation from the sun and the remainder of the hemisphere is subtended by diffuse radiation from the atmosphere. The solid angle may be adjusted by geometrical concentration of the sun's light. The solar cell is maintained at the

ambient temperature, the surface terrestrial temperature, by a thermal conductor.

*<sup>η</sup>* <sup>≤</sup> <sup>1</sup> <sup>−</sup> <sup>4</sup> 3 *T*c *T*p + 1 3 *T*<sup>c</sup> *T*p

<sup>3</sup> *<sup>T</sup>*<sup>c</sup> *<sup>T</sup>*<sup>3</sup> <sup>S</sup> <sup>+</sup> <sup>1</sup> <sup>3</sup> *<sup>T</sup>*<sup>4</sup> c 

(*C D*) *T*<sup>4</sup>

first-law efficiency:

yields a first-law efficiency given as

(*C D*) *T*4 <sup>S</sup> <sup>−</sup> <sup>4</sup>

*η* ≤

**3.3 Shockley-Queisser limit**

*<sup>I</sup> <sup>V</sup>*

<sup>4</sup>

 *T*4 <sup>E</sup> <sup>−</sup> <sup>4</sup>

E

<sup>3</sup> *<sup>T</sup>*<sup>c</sup> *<sup>T</sup>*<sup>3</sup>

<sup>E</sup> <sup>+</sup> <sup>1</sup> <sup>3</sup> *<sup>T</sup>*<sup>4</sup> c 

. (3)

*<sup>g</sup>* =

. (4)

Fig. 2. Generalized schematic diagram of an energy converter. In the radiative limit, the energy flows pumped to and sunk by the converter (*i.e. E*˙ <sup>p</sup> and *E*˙ s) are limited to the radiant energy flux [J m−<sup>2</sup> s−1] pumped to and sunk by the converter: *E*˙ <sup>p</sup> and *E*˙ s, respectively.

the earth (Shockley & Queisser, 1961), and a geometric-concentration factor of solar energy, *C*, which may range between unity and 1/*D* (De Vos, 1992), the total energy flux impinging upon the converter, *E*˙ p, is written with the Stefan-Boltzmann constant, *σ* 5.67 <sup>×</sup> <sup>10</sup>−<sup>8</sup> W/m2/K4 , as

$$\dot{E}\_{\rm P} = \sigma \left[ \mathbb{C} D \, T\_{\rm S}^4 + (1 - \mathbb{C} \, D) \, T\_{\rm E}^4 \right]. \tag{2}$$

Meanwhile, the quantification of the power density generated by the converter depends on the specific details of the converter. As this section only discusses a generalized converter, no further mathematical form of the power density is specified.

Calculating the performance measure by substituting the right-hand side of Equation (1) into the denominator of Equation (2) is different from the manner of calculating the performance measure as done in the detailed-balance work of many references (Bremner et al., n.d.; Brown & Green, 2002a;b; De Vos, 1980; 1992; De Vos & Desoete, 1998; Levy & Honsberg, 2006; Luque & Martí, 2001; Martí & Araújo, 1996; Shockley & Queisser, 1961; Werner, Brendel & Oueisser, 1994). In the latter references, though the particle flux impinging upon the solar cell is given in terms of the dual source, the performance measure is calculated with respect to the energy flux from the sun, *U*˙ p,S. This distorts the performance measure of the device, resulting in efficiencies 1 + <sup>1</sup>−*C D C D <sup>T</sup>*<sup>E</sup> *T*S 4 times those obtained using the first-law efficiency (Levy & Honsberg, 2008a). . In the following subsection, the present author reviews an approach to upper bound the efficiency limit of converting solar energy to useful work.

#### **3.2 Landsberg-Tonge limit**

Landsberg and Tonge present thermodynamic efficiencies for the conversion of solar radiation into work (Landsberg & Tonge, 1980). The converter is pumped with all the radiation emitted from a black body, which maintains a surface temperature *T*p. The converter is also given as a black body, however its temperature is maintained at *T*c. The converter, therefore, sinks black-body radiation associated with this temperature. With the use of two balance equations, for energy and for entropy, Landsberg and Tonge derive the following inequality for the

4 Will-be-set-by-IN-TECH

*Q*

.

. . .

<sup>p</sup> and *E*˙

E  <sup>p</sup> and *E*˙

s) are limited to the radiant

s, respectively.

5.67 <sup>×</sup> <sup>10</sup>−<sup>8</sup> W/m2/K4

times those obtained using

. (2)

 ,

*S*g *T*c

*E*p *, S*<sup>p</sup> *E*s *, S*<sup>s</sup>

Fig. 2. Generalized schematic diagram of an energy converter. In the radiative limit, the

p, is written with the Stefan-Boltzmann constant, *σ*

the earth (Shockley & Queisser, 1961), and a geometric-concentration factor of solar energy, *C*, which may range between unity and 1/*D* (De Vos, 1992), the total energy flux impinging upon

Meanwhile, the quantification of the power density generated by the converter depends on the specific details of the converter. As this section only discusses a generalized converter, no

Calculating the performance measure by substituting the right-hand side of Equation (1) into the denominator of Equation (2) is different from the manner of calculating the performance measure as done in the detailed-balance work of many references (Bremner et al., n.d.; Brown & Green, 2002a;b; De Vos, 1980; 1992; De Vos & Desoete, 1998; Levy & Honsberg, 2006; Luque & Martí, 2001; Martí & Araújo, 1996; Shockley & Queisser, 1961; Werner, Brendel & Oueisser, 1994). In the latter references, though the particle flux impinging upon the solar cell is given in terms of the dual source, the performance measure is calculated with respect to the energy flux from the sun, *U*˙ p,S. This distorts the performance

the first-law efficiency (Levy & Honsberg, 2008a). . In the following subsection, the present author reviews an approach to upper bound the efficiency limit of converting solar energy to

Landsberg and Tonge present thermodynamic efficiencies for the conversion of solar radiation into work (Landsberg & Tonge, 1980). The converter is pumped with all the radiation emitted from a black body, which maintains a surface temperature *T*p. The converter is also given as a black body, however its temperature is maintained at *T*c. The converter, therefore, sinks black-body radiation associated with this temperature. With the use of two balance equations, for energy and for entropy, Landsberg and Tonge derive the following inequality for the

1 + <sup>1</sup>−*C D C D*

 *<sup>T</sup>*<sup>E</sup> *T*S 4 

<sup>S</sup> <sup>+</sup> (<sup>1</sup> <sup>−</sup> *C D*) *<sup>T</sup>*<sup>4</sup>

..

energy flows pumped to and sunk by the converter (*i.e. E*˙

the converter, *E*˙

useful work.

**3.2 Landsberg-Tonge limit**

as

energy flux [J m−<sup>2</sup> s−1] pumped to and sunk by the converter: *E*˙

*E*˙ <sup>p</sup> = *σ CDT*<sup>4</sup>

further mathematical form of the power density is specified.

measure of the device, resulting in efficiencies

*W*

.

Fig. 3. Cross section of an abstracted *p-n* junction solar cell with spherical symmetry. The exaggerated physical symmetry reinforces the solar geometry, where a solid angle of the solar cell's surface, Ω, is subtended by direct insolation from the sun and the remainder of the hemisphere is subtended by diffuse radiation from the atmosphere. The solid angle may be adjusted by geometrical concentration of the sun's light. The solar cell is maintained at the ambient temperature, the surface terrestrial temperature, by a thermal conductor.

first-law efficiency:

$$\eta \le 1 - \frac{4}{3} \frac{T\_{\rm c}}{T\_{\rm P}} + \frac{1}{3} \left(\frac{T\_{\rm c}}{T\_{\rm P}}\right)^4. \tag{3}$$

In arriving at the above inequality, Landsberg and Tonge assume steady-state conditions. Equality holds for the special case where there is no internal entropy generation (*i.e. S*˙ *<sup>g</sup>* = 0). The resulting equality is first derived by Patela by considering the exergy of heat radiation (Petela, 1964). The Landsberg-Tonge limit may be extended so as to model the dual sources of the solar geometry (Würfel, 2002). In the case of two black-body sources simultaneously pumping the converter, a derivation similar to that of Landsberg and Tonge yields a first-law efficiency given as

$$\eta \le \frac{\left(\mathbb{C}\,D\right)\left(T\_{\mathbb{S}}^4 - \frac{4}{3}\,T\_{\mathbb{C}}\,T\_{\mathbb{S}}^3 + \frac{1}{3}\,T\_{\mathbb{C}}^4\right) + \left(1 - \mathbb{C}\,D\right)\left(T\_{\mathbb{E}}^4 - \frac{4}{3}\,T\_{\mathbb{C}}\,T\_{\mathbb{E}}^3 + \frac{1}{3}\,T\_{\mathbb{C}}^4\right)}{\left(\mathbb{C}\,D\right)\left.T\_{\mathbb{S}}^4 + \left(1 - \mathbb{C}\,D\right)\left.T\_{\mathbb{E}}^4\right|}.\tag{4}$$

Figure 4 illustrates the Landsberg-Tonge efficiency limit. In Section 3.3, the detailed-balance method of Shockley and Queisser is presented and applied to a single *p-n* junction solar cell.

#### **3.3 Shockley-Queisser limit**

Shockley and Queisser present a framework to analyze the efficiency limit of solar-energy conversion by a single *p-n* junction (Shockley & Queisser, 1961). They name this limit the detailed-balance limit for it is derived from the notion that, in principle, all recombination

**3.4 Omni-colour limit**

**3.5 Comparative analysis**

and contrasted.

of solar irradiance.

light (Würfel, 2004).

In principle, the detailed-balance method may be applied to omni-colour converters (De Vos, 1980; 1992; De Vos et al., 1982). The omni-colour limit may be derived in terms of either photovoltaic processes (Araújo & Martí, 1994; De Vos, 1980; 1992; De Vos et al., 1982; Würfel, 2004), photothermal processes (De Vos, 1992), or hybrids thereof (De Vos, 1992; Luque & Martí, 1999). In either case, as the number of layers in a stack of photovoltaic converters (Alvi et al., 1976; De Vos, 1992; Jackson, 1955; Loferski, 1976; Wolf, 1960) or in a stack of photothermal converters (De Vos, 1992; De Vos & Vyncke, 1984) approach infinity, the solar-energy conversion efficiencies approach the same limit (De Vos, 1980; 1992; De Vos & Vyncke, 1984) – the omni-colour limit. Figure 4 illustrates the upper-efficiency limit of omni-colour solar-energy conversion. In Section 3.5, the present author compares and

Maturity of Photovoltaic Solar-Energy Conversion 339

In Section 3.2 through Section 3.4, the present author reviews several approaches that quantify the efficiency limits of solar-energy conversion. The aforementioned limits are now compared

All of the limits reviewed in this Section 3 have in common an efficiency limit of zero when the converter's temperature is that of the pump. In addition, several of the limits approach the Carnot limit for the special case where the converter's temperature is absolute zero. These include the Landsberg-Tonge limit and the De Vos-Grosjean-Pauwels limit. At absolute zero the Shockley-Queisser limit is substantially lower (44%) than the Carnot limit. It is interesting to note that the Landsberg-Tonge limit (see Equation 4 on page 5) and the omni-colour limit (De Vos, 1980) both approach unity for regardless of the geometric-concentration factor

The large differences between the Shockley-Queisser limit and the other limits are attributed to the relationship between the energetic gap of the semiconductor comprising the *p-n* junction and the range of photon energies comprising the broadband spectrum of black-body radiation. Sub-bandgap photons do not yield a photovoltaic effect and so do not participate in generating charge current. Meanwhile, the conversion of each supra-bandgap photon uniformly generates a single electron-hole pair at a voltage limited by the bandgap. Therefore, the portion of each supra-bandgap photon's energy in excess of the bandgap does not contribute to useful work. By using an omni-colour converter, the efficiency degradation caused by the relationship between the energetic gap of the semiconductors comprising the tandem stack and the broadband nature of the solar spectrum are eliminated. Therefore, the difference between the De Vos-Grosjean-Pauwels limit and the Landsberg-Tonge limit is attributed to the generation of internal irreversible entropy. Except for the two temperature extremes aforementioned, each layer of the omni-colour converter generates a rate of irreversible entropy resulting from its internal processes. This is so even though each layer of the omni-colour converter operates at its maximum-power point and converts monochromatic

As illustrated by the present author in Figure 4, the efficiency limits reviewed heretofore may be given in descending order as Carnot, Landsberg-Tonge, De Vos-Grosjean-Pauwels, and Shockley-Queisser. Photovoltaic converters may not exceed the De Vos-Grosjean-Pauwels limit for their internal processes are associated with a rate of irreversible internal entropy generation (Markvart, 2007; Würfel, 1982). In Section 3.6, the present author concludes these findings by describing limits to the conversion of solar energy in the terrestrial environment.

contrasts the efficiency limits that are heretofore reviewed.

Fig. 4. Efficiency limits of ideal solar-energy converters as a function of the ratio of the converter's temperature, *T*c, to the pump's temperature, *T*S. Shown are the Landsberg-Tonge closed-form efficiencies of the radiation-in-radiation-out converter, the DeVos-Grosjean-Pauwels analytic efficiencies of the omni-colour converter, and the

Shockley-Queisser numerical efficiencies of the *p-n* junction converter. All efficiencies are for fully-concentrated solar irradiance. As a visual aid, the Carnot efficiencies are presented.

processes may be limited to photo-induced processes and balanced by photo-induced generation processes. Their *ab initio* limit – as opposed to a semi-empirical limit based on factors such as measured carrier lifetimes – represents an upper-theoretical limit above which a single *p-n* junction solar cell may not perform. In addition, it is a reference for experimental measurements of single-junction solar cells in terms of future potential.

In their framework, Shockley and Queisser identify several factors that may degrade the efficiency of energy conversion and ideally allow that the degrading factors are perfectly mitigated. Therefore, in the detailed balance limit it is permissible that:


Figure 4 illustrates the upper-efficiency limit of solar-energy conversion by a single *p-n* solar cell. The Shockley-Queisser model predicts that the the upper limiting efficiency of a *p-n* junction solar cell is 44%. This efficiency limit is valid only when the solar cell's temperature is held to absolute zero. In Section 3.4, the omni-colour limit is presented.

#### **3.4 Omni-colour limit**

6 Will-be-set-by-IN-TECH

Carnot

Landsberg-Tonge

Shockley-Queisser

DeVos-Grosjean-Pauwels

0 0.2 0.4 0.6 0.8 1

 0 1000 2000 3000 4000 5000 6000 Converter temperature, Tc, [K]

Normalized temperature, Tc/TS, [1]

closed-form efficiencies of the radiation-in-radiation-out converter, the

measurements of single-junction solar cells in terms of future potential.

mitigated. Therefore, in the detailed balance limit it is permissible that:

semiconductors band-gap are transmitted into the solar cell is unity,

completely concentrated onto the solar cell (see Figure 3 on page 5).

is held to absolute zero. In Section 3.4, the omni-colour limit is presented.

Fig. 4. Efficiency limits of ideal solar-energy converters as a function of the ratio of the converter's temperature, *T*c, to the pump's temperature, *T*S. Shown are the Landsberg-Tonge

DeVos-Grosjean-Pauwels analytic efficiencies of the omni-colour converter, and the

Shockley-Queisser numerical efficiencies of the *p-n* junction converter. All efficiencies are for fully-concentrated solar irradiance. As a visual aid, the Carnot efficiencies are presented.

processes may be limited to photo-induced processes and balanced by photo-induced generation processes. Their *ab initio* limit – as opposed to a semi-empirical limit based on factors such as measured carrier lifetimes – represents an upper-theoretical limit above which a single *p-n* junction solar cell may not perform. In addition, it is a reference for experimental

In their framework, Shockley and Queisser identify several factors that may degrade the efficiency of energy conversion and ideally allow that the degrading factors are perfectly

• the fractions of recombination and generation events that are coupled to radiative

• the probability that incident photons with energy greater than or equal to the

• the fraction of solid angle subtended by the sun may be unity- *i.e.*, the sun's radiation is

Figure 4 illustrates the upper-efficiency limit of solar-energy conversion by a single *p-n* solar cell. The Shockley-Queisser model predicts that the the upper limiting efficiency of a *p-n* junction solar cell is 44%. This efficiency limit is valid only when the solar cell's temperature

• the probability with which a transmitted photon creates an electron-hole pair is unity, • the probability that an electron-hole pair yields a charge current pulse through an external

processes are both unity,

load is unity, and,

Efficiency,

η, [%] In principle, the detailed-balance method may be applied to omni-colour converters (De Vos, 1980; 1992; De Vos et al., 1982). The omni-colour limit may be derived in terms of either photovoltaic processes (Araújo & Martí, 1994; De Vos, 1980; 1992; De Vos et al., 1982; Würfel, 2004), photothermal processes (De Vos, 1992), or hybrids thereof (De Vos, 1992; Luque & Martí, 1999). In either case, as the number of layers in a stack of photovoltaic converters (Alvi et al., 1976; De Vos, 1992; Jackson, 1955; Loferski, 1976; Wolf, 1960) or in a stack of photothermal converters (De Vos, 1992; De Vos & Vyncke, 1984) approach infinity, the solar-energy conversion efficiencies approach the same limit (De Vos, 1980; 1992; De Vos & Vyncke, 1984) – the omni-colour limit. Figure 4 illustrates the upper-efficiency limit of omni-colour solar-energy conversion. In Section 3.5, the present author compares and contrasts the efficiency limits that are heretofore reviewed.

#### **3.5 Comparative analysis**

In Section 3.2 through Section 3.4, the present author reviews several approaches that quantify the efficiency limits of solar-energy conversion. The aforementioned limits are now compared and contrasted.

All of the limits reviewed in this Section 3 have in common an efficiency limit of zero when the converter's temperature is that of the pump. In addition, several of the limits approach the Carnot limit for the special case where the converter's temperature is absolute zero. These include the Landsberg-Tonge limit and the De Vos-Grosjean-Pauwels limit. At absolute zero the Shockley-Queisser limit is substantially lower (44%) than the Carnot limit. It is interesting to note that the Landsberg-Tonge limit (see Equation 4 on page 5) and the omni-colour limit (De Vos, 1980) both approach unity for regardless of the geometric-concentration factor of solar irradiance.

The large differences between the Shockley-Queisser limit and the other limits are attributed to the relationship between the energetic gap of the semiconductor comprising the *p-n* junction and the range of photon energies comprising the broadband spectrum of black-body radiation. Sub-bandgap photons do not yield a photovoltaic effect and so do not participate in generating charge current. Meanwhile, the conversion of each supra-bandgap photon uniformly generates a single electron-hole pair at a voltage limited by the bandgap. Therefore, the portion of each supra-bandgap photon's energy in excess of the bandgap does not contribute to useful work. By using an omni-colour converter, the efficiency degradation caused by the relationship between the energetic gap of the semiconductors comprising the tandem stack and the broadband nature of the solar spectrum are eliminated. Therefore, the difference between the De Vos-Grosjean-Pauwels limit and the Landsberg-Tonge limit is attributed to the generation of internal irreversible entropy. Except for the two temperature extremes aforementioned, each layer of the omni-colour converter generates a rate of irreversible entropy resulting from its internal processes. This is so even though each layer of the omni-colour converter operates at its maximum-power point and converts monochromatic light (Würfel, 2004).

As illustrated by the present author in Figure 4, the efficiency limits reviewed heretofore may be given in descending order as Carnot, Landsberg-Tonge, De Vos-Grosjean-Pauwels, and Shockley-Queisser. Photovoltaic converters may not exceed the De Vos-Grosjean-Pauwels limit for their internal processes are associated with a rate of irreversible internal entropy generation (Markvart, 2007; Würfel, 1982). In Section 3.6, the present author concludes these findings by describing limits to the conversion of solar energy in the terrestrial environment.

*<sup>η</sup>*|Ter , [%] Converter *<sup>C</sup>* <sup>=</sup> 1/*<sup>D</sup> <sup>C</sup>* <sup>=</sup> <sup>1</sup> †

Maturity of Photovoltaic Solar-Energy Conversion 341

Carnot 95.0 95.0 Landsberg-Tonge 93.3 <sup>a</sup> 72.4 <sup>b</sup> De Vos-Grosjean-Pauwels 86.8 <sup>c</sup> 52.9 <sup>d</sup> Shockley-Queisser 40.7 <sup>e</sup> 24.0 <sup>f</sup> † Listed values are first-law efficiencies that are calculated by including the energy flow absorbed due to direct solar radiation and the energy flow due to diffuse atmospheric radiation. The listed values are likely to be less than what are previously recorded in the literature. See Section 3.1 on page 3 for a more

comprehensive discussion.

and reference (Würfel, 2004).

Table 1. Upper-efficiency limits of the terrestrial conversion of solar energy, *η*|Ter . All efficiencies calculated for a surface solar temperature of 6000 K, a surface terrestrial temperature of 300 K, a solar cell maintained at the surface terrestrial temperature, a geometric dilution factor, *<sup>D</sup>*, of 2.16×10−5, and a geometric-concentration factor, *<sup>C</sup>*, that is

present author.

either 1 (non-concentrated sunlight) or 1/*D* (fully-concentrated sunlight).

a significant efficiency enhancement that is scientifically plausible.

n.d.).

<sup>a</sup> Calculated from Equation (3) on page 5. <sup>b</sup> Calculated from Equation (4) on page 5. <sup>c</sup> Obtained from reference (De Vos, 1980)

<sup>d</sup> Adjusted from the value 68.2% recorded in reference (De Vos, 1980) and independently calculated by the

<sup>e</sup> Obtained from reference (Bremner et al.,

<sup>f</sup> Adjusted from the value 31.0% recorded in reference (Martí & Araújo, 1996).

must have an upper-efficiency limit greater than 24.0.%. Clearly, for physical consistency, the optimized theoretical performance of the high-efficiency proposal must be less than that of the omni-colour solar cell at that geometric concentration factor. Furthermore, the present author asserts that any fabricated solar cell that claims to be a high-efficiency solar cell must demonstrate a global efficiency enhancement with respect to an optimized Shockley-Queisser solar cell. For example, to substantiate a claim of high-efficiency, a solar cell maintained at the terrestrial surface temperature and under a geometric concentration of 240 suns must demonstrate an efficiency greater than 35.7% – the efficiency of an optimized Shockley-Queisser solar cell operating under those conditions. Before moving on to Section 4.2, where the present author reviews the tandem solar cell, the reader is encouraged to view the high-efficiency regime as illustrated in Figure 5. The reader will note that there is

#### **3.6 Terrestrial conversion limits**

Table 1 lists the upper-efficiency limits of the terrestrial conversion of solar energy. As is convention in the science of solar-energy conversion, all efficiencies are calculated for a surface solar temperature of 6000 K, a surface terrestrial temperature of 300 K, and a converter maintained at the surface terrestrial temperature. In addition, the geometric dilution factor is taken as 2.16×10−<sup>5</sup> (De Vos, 1992). For each type of converter listed, the upper- efficiency limit is given for fully-concentrated sunlight and, in some cases, for non-concentrated sunlight. The values listed depend only on the sun's surface temperature, the earth's surface temperature, and the geometric-concentration factor, as opposed to consideration regarding the air mass of the Earth and other secondary phenomena. The present author concludes that though the upper-efficiency limit of a single *p-n* junction solar cell is large, a significant efficiency enhancement is possible. This is true because the terrestrial limits of a single *p-n* junction solar cell is 40.7% and 24.0%, whereas the terrestrial limits of an omni-colour converter is 86.8% and 52.9% for fully-concentrated and non-concentrated sunlight, respectively. In Section 4, the present author defines the notion of high-efficiency approaches to solar-energy conversion and briefly reviews various proposed high-efficiency approaches.

#### **4. High-efficiency approaches**

In this section, Section 4, the present author reviews several distinct approaches for high-efficiency solar cells. In Section 4.1, the present author defines "high-efficiency" in terms of the upper-conversion efficiencies of the Shockley-Queisser model and the De Vos-Grosjean-Pauwels model. In Section 4.2, the present author reviews the current technological paradigm to realize high-efficiency solar cells: stacks of single *p-n* junction solar cells operating in tandem. In sections 4.3, 4.4, and 4.5, the present author reviews three next-generation approaches to realize high-efficiency solar cells: the carrier-multiplication solar cell, the hot-carrier solar cell, and the multiple-transition solar cell, respectively. Finally, in Section 4.6, the present author draws conclusions regarding the justification for researching and developing next-generation approaches. Though stacks of single *p-n* junction solar cells operating in tandem are the only high-efficiency approach with demonstrated high-efficiency performance, the present author concludes that development on a next-generation solar cell is justified in that a (*i*) next-generation solar cells offer a global-efficiency enhancement in themselves and (*i*) also per layer if incorporated in a stack of solar cells operating in tandem. Immediately below in Section 4.1, the present author defines what is meant by high-efficiency performance.

#### **4.1 Global efficiency enhancement**

There are several proposals for high-efficiency solar cells. In this chapter, similar to Anderson in his discussion of the efficiency enhancements in quantum-well solar cells (Anderson, 2002), the present author defines high-efficiency in terms of a global efficiency enhancement. Shown in Figure 5 are the upper-efficiency conversion limits of the single-junction solar cell and the omni-colour solar cell. In Figure 5, the upper-efficiency conversion limits are given as a function of the geometric-concentration factor, *C*. The present author defines "high efficiency" in terms of the numerical data given in Figure 5. The present author asserts that, for any and all geometric concentration factor, a proposal for high-efficiency solar cell must, when optimized, offer an efficiency greater than that of an optimized Shockley-Queisser solar cell at that same geometric-concentration factor. For example, according to the present author's definition, under non-concentrated sunlight a high-efficiency proposal, when optimized, 8 Will-be-set-by-IN-TECH

Table 1 lists the upper-efficiency limits of the terrestrial conversion of solar energy. As is convention in the science of solar-energy conversion, all efficiencies are calculated for a surface solar temperature of 6000 K, a surface terrestrial temperature of 300 K, and a converter maintained at the surface terrestrial temperature. In addition, the geometric dilution factor is taken as 2.16×10−<sup>5</sup> (De Vos, 1992). For each type of converter listed, the upper- efficiency limit is given for fully-concentrated sunlight and, in some cases, for non-concentrated sunlight. The values listed depend only on the sun's surface temperature, the earth's surface temperature, and the geometric-concentration factor, as opposed to consideration regarding the air mass of the Earth and other secondary phenomena. The present author concludes that though the upper-efficiency limit of a single *p-n* junction solar cell is large, a significant efficiency enhancement is possible. This is true because the terrestrial limits of a single *p-n* junction solar cell is 40.7% and 24.0%, whereas the terrestrial limits of an omni-colour converter is 86.8% and 52.9% for fully-concentrated and non-concentrated sunlight, respectively. In Section 4, the present author defines the notion of high-efficiency approaches to solar-energy conversion

In this section, Section 4, the present author reviews several distinct approaches for high-efficiency solar cells. In Section 4.1, the present author defines "high-efficiency" in terms of the upper-conversion efficiencies of the Shockley-Queisser model and the De Vos-Grosjean-Pauwels model. In Section 4.2, the present author reviews the current technological paradigm to realize high-efficiency solar cells: stacks of single *p-n* junction solar cells operating in tandem. In sections 4.3, 4.4, and 4.5, the present author reviews three next-generation approaches to realize high-efficiency solar cells: the carrier-multiplication solar cell, the hot-carrier solar cell, and the multiple-transition solar cell, respectively. Finally, in Section 4.6, the present author draws conclusions regarding the justification for researching and developing next-generation approaches. Though stacks of single *p-n* junction solar cells operating in tandem are the only high-efficiency approach with demonstrated high-efficiency performance, the present author concludes that development on a next-generation solar cell is justified in that a (*i*) next-generation solar cells offer a global-efficiency enhancement in themselves and (*i*) also per layer if incorporated in a stack of solar cells operating in tandem. Immediately below in Section 4.1, the present author defines what is meant by high-efficiency

There are several proposals for high-efficiency solar cells. In this chapter, similar to Anderson in his discussion of the efficiency enhancements in quantum-well solar cells (Anderson, 2002), the present author defines high-efficiency in terms of a global efficiency enhancement. Shown in Figure 5 are the upper-efficiency conversion limits of the single-junction solar cell and the omni-colour solar cell. In Figure 5, the upper-efficiency conversion limits are given as a function of the geometric-concentration factor, *C*. The present author defines "high efficiency" in terms of the numerical data given in Figure 5. The present author asserts that, for any and all geometric concentration factor, a proposal for high-efficiency solar cell must, when optimized, offer an efficiency greater than that of an optimized Shockley-Queisser solar cell at that same geometric-concentration factor. For example, according to the present author's definition, under non-concentrated sunlight a high-efficiency proposal, when optimized,

and briefly reviews various proposed high-efficiency approaches.

**3.6 Terrestrial conversion limits**

**4. High-efficiency approaches**

**4.1 Global efficiency enhancement**

performance.


† Listed values are first-law efficiencies that are calculated by including the energy flow absorbed due to direct solar radiation and the energy flow due to diffuse atmospheric radiation. The listed values are likely to be less than what are previously recorded in the literature. See Section 3.1 on page 3 for a more comprehensive discussion.


Table 1. Upper-efficiency limits of the terrestrial conversion of solar energy, *η*|Ter . All efficiencies calculated for a surface solar temperature of 6000 K, a surface terrestrial temperature of 300 K, a solar cell maintained at the surface terrestrial temperature, a geometric dilution factor, *<sup>D</sup>*, of 2.16×10−5, and a geometric-concentration factor, *<sup>C</sup>*, that is either 1 (non-concentrated sunlight) or 1/*D* (fully-concentrated sunlight).

must have an upper-efficiency limit greater than 24.0.%. Clearly, for physical consistency, the optimized theoretical performance of the high-efficiency proposal must be less than that of the omni-colour solar cell at that geometric concentration factor. Furthermore, the present author asserts that any fabricated solar cell that claims to be a high-efficiency solar cell must demonstrate a global efficiency enhancement with respect to an optimized Shockley-Queisser solar cell. For example, to substantiate a claim of high-efficiency, a solar cell maintained at the terrestrial surface temperature and under a geometric concentration of 240 suns must demonstrate an efficiency greater than 35.7% – the efficiency of an optimized Shockley-Queisser solar cell operating under those conditions. Before moving on to Section 4.2, where the present author reviews the tandem solar cell, the reader is encouraged to view the high-efficiency regime as illustrated in Figure 5. The reader will note that there is a significant efficiency enhancement that is scientifically plausible.

*<sup>η</sup>*|Ter , [%] Converter *<sup>C</sup>* <sup>=</sup> 1/*<sup>D</sup> <sup>C</sup>* <sup>=</sup> <sup>1</sup> †

Infinite-Stack Tandem \* 86.8 <sup>a</sup> 52.9 <sup>b</sup> Eight-Stack Photovoltaic Tandem 77.63 <sup>c</sup> 46.12 <sup>e</sup> Seven-Stack Photovoltaic Tandem 76.22 <sup>c</sup> 46.12 <sup>e</sup> Six-Stack Photovoltaic Tandem 74.40 <sup>c</sup> 44.96 <sup>e</sup> Five-Stack Photovoltaic Tandem 72.00 <sup>c</sup> 43.43 <sup>e</sup> Four-Stack Photovoltaic Tandem 68.66 <sup>c</sup> 41.31 <sup>d</sup> Three-Stack Photovoltaic Tandem 63.747 <sup>c</sup> 38.21 <sup>d</sup> Two-Stack Photovoltaic Tandem 55.80 <sup>c</sup> 33.24 <sup>d</sup> One-Stack Photovoltaic Solar Cell \*\* 40.74 <sup>c</sup> 24.01 <sup>d</sup> † Listed values are first-law efficiencies that are calculated by including the energy flow absorbed due to direct solar radiation and the energy flow due to diffuse atmospheric radiation. The listed values are likely to be less than what are previously recorded in the literature. See Section 3.1 on page 3 for a more comprehensive

Maturity of Photovoltaic Solar-Energy Conversion 343

\* Recorded values are identical to those of the omni-colour converter of Table 1 on page 9. \*\* Recorded values are identical to those of the Shockley-Queisser converter of Table 1 on page 9. <sup>a</sup> Obtained from reference (De Vos, 1980) and independently calculated by the present author. <sup>b</sup> Adjusted from the value 68.2% recorded in reference (De Vos, 1980) and independently

<sup>c</sup> Obtained from reference (Bremner et al., n.d.) and independently calculated by the present author. <sup>d</sup> Adjusted from the values recorded in reference (Martí & Araújo, 1996) and independently calculated by the present author. <sup>e</sup> Calculated independently by the present author. Values are not previously published in the

single-transition single *p-n* junction solar cells operating in tandem. All efficiencies calculated for a surface solar temperature of 6000 K, a surface terrestrial temperature of 300 K, a solar cell maintained at the surface terrestrial temperature, a geometric dilution factor, *D*, of 2.16×10−5, and a geometric-concentration factor, *<sup>C</sup>*, that is either 1 (non-concentrated

1994; Werner, Kolodinski & Queisser, 1994), thus they may be correctly viewed as a high-efficiency approach. These solar cells produce an efficiency enhancement by generating more than one electron-hole pair per absorbed photon via

calculated by the present author.

Table 2. Upper-efficiency limits, *η*|Ter , of the terrestrial conversion of stacks of

discussion.

literature.

sunlight) or 1/*D* (fully-concentrated sunlight).

Fig. 5. The region of high-efficiency solar-energy conversion as a function of the geometric-concentration factor. The high-efficiency region (shaded) is defined as that region offering a global-efficiency enhancement with respect to the maximum single-junction efficiencies (lower edge) and the maximum omni-colour efficiencies (upper edge). The efficiency required to demonstrate a global efficiency enhancement varies as a function of the geometric-concentration factor. For illustrative purposes, the terrestrial efficiencies (see Table 2) of a two-stack tandem solar cell and a five-stack tandem solar cell are given . Finally, for illustrative purposes, the present world-record solar cell efficiency is given (*i.e.*, 41.1% under a concentration of 454 suns (Guter et al., 2009)).

#### **4.2 Tandem solar cell**

The utilization of a stack of *p-n* junction solar cells operating in tandem is proposed to exceed the performance of one *p-n* junction solar cell operating alone (Jackson, 1955). The upper-efficiency limits for *N*-stack tandems (1 ≤ *N* ≤ 8) are recorded in Table 2 on page 11 . As the number of solar cells operating in a tandem stack increases to infinity, the upper-limiting efficiency of the stack increases to the upper-limiting efficiency of the omni-colour solar cell (De Vos, 1980; 1992; De Vos & Vyncke, 1984). This is explained in Section 3.4 on page 7. In practice, solar cells may be integrated into a tandem stack via a vertical architecture or a lateral architecture. An example of a vertical architecture is a monolithic solar cell. Until now, the largest demonstrated efficiency of a monolithic solar cell – or for any solar cell – is the metamorphic solar-cell fabricated by Fraunhofer Institute for Solar Energy Systems (Guter et al., 2009). This tandem is a three-junction metamorphic solar cell and operates with a conversion efficiency of 41.1% under a concentration of 454 suns (Guter et al., 2009). An example of horizontal architectures are the solar cells of references (Barnett et al., 2006; Green & Ho-Baillie, 2010), which utilize spectral-beam splitters (Imenes & Mills, 2004) that direct the light onto their constituent solar cells. The present author now reviews the carrier-multiplication solar cell, the first of three next-generation proposals to be reviewed in this chapter.

#### **4.3 Carrier-multiplication solar cell**

Carrier-multiplication solar cells are theorized to exceed the Shockley-Queisser limit (De Vos & Desoete, 1998; Landsberg et al., 1993; Werner, Brendel & Oueisser, 10 Will-be-set-by-IN-TECH

World Record

geometric-concentration factor. The high-efficiency region (shaded) is defined as that region offering a global-efficiency enhancement with respect to the maximum single-junction efficiencies (lower edge) and the maximum omni-colour efficiencies (upper edge). The efficiency required to demonstrate a global efficiency enhancement varies as a function of the geometric-concentration factor. For illustrative purposes, the terrestrial efficiencies (see Table 2) of a two-stack tandem solar cell and a five-stack tandem solar cell are given . Finally, for illustrative purposes, the present world-record solar cell efficiency is given (*i.e.*, 41.1%

The utilization of a stack of *p-n* junction solar cells operating in tandem is proposed to exceed the performance of one *p-n* junction solar cell operating alone (Jackson, 1955). The upper-efficiency limits for *N*-stack tandems (1 ≤ *N* ≤ 8) are recorded in Table 2 on page 11 . As the number of solar cells operating in a tandem stack increases to infinity, the upper-limiting efficiency of the stack increases to the upper-limiting efficiency of the omni-colour solar cell (De Vos, 1980; 1992; De Vos & Vyncke, 1984). This is explained in Section 3.4 on page 7. In practice, solar cells may be integrated into a tandem stack via a vertical architecture or a lateral architecture. An example of a vertical architecture is a monolithic solar cell. Until now, the largest demonstrated efficiency of a monolithic solar cell – or for any solar cell – is the metamorphic solar-cell fabricated by Fraunhofer Institute for Solar Energy Systems (Guter et al., 2009). This tandem is a three-junction metamorphic solar cell and operates with a conversion efficiency of 41.1% under a concentration of 454 suns (Guter et al., 2009). An example of horizontal architectures are the solar cells of references (Barnett et al., 2006; Green & Ho-Baillie, 2010), which utilize spectral-beam splitters (Imenes & Mills, 2004) that direct the light onto their constituent solar cells. The present author now reviews the carrier-multiplication solar cell, the first of three

Carrier-multiplication solar cells are theorized to exceed the Shockley-Queisser limit (De Vos & Desoete, 1998; Landsberg et al., 1993; Werner, Brendel & Oueisser,

Omni-colour Five Junction Two Junction Single Junction

10<sup>0</sup> 101 10<sup>2</sup> 103 10<sup>4</sup>

under a concentration of 454 suns (Guter et al., 2009)).

next-generation proposals to be reviewed in this chapter.

**4.3 Carrier-multiplication solar cell**

Concentration factor, C, [suns]

Fig. 5. The region of high-efficiency solar-energy conversion as a function of the

High-Efficiency Regime

**4.2 Tandem solar cell**

Efficiency,

η |Ter , [%]


† Listed values are first-law efficiencies that are calculated by including the energy flow absorbed due to direct solar radiation and the energy flow due to diffuse atmospheric radiation. The listed values are likely to be less than what are previously recorded in the literature. See Section 3.1 on page 3 for a more comprehensive discussion.


Table 2. Upper-efficiency limits, *η*|Ter , of the terrestrial conversion of stacks of single-transition single *p-n* junction solar cells operating in tandem. All efficiencies calculated for a surface solar temperature of 6000 K, a surface terrestrial temperature of 300 K, a solar cell maintained at the surface terrestrial temperature, a geometric dilution factor, *D*, of 2.16×10−5, and a geometric-concentration factor, *<sup>C</sup>*, that is either 1 (non-concentrated sunlight) or 1/*D* (fully-concentrated sunlight).

1994; Werner, Kolodinski & Queisser, 1994), thus they may be correctly viewed as a high-efficiency approach. These solar cells produce an efficiency enhancement by generating more than one electron-hole pair per absorbed photon via

justify the claim that the multiple-transition solar cell is a high-efficiency approach. Resulting from internal current constraints and voltage constraints, the upper-efficiency limit of the multi-transition solar cell is asserted to be less than that of the De Vos-Grosjean-Pauwels converter (Brown & Green, 2002b; 2003). That said, it has been shown (Levy & Honsberg, 2009) that the absorption characteristic of multiple-transition solar cells may lead to both incomplete absorption and absorption overlap (Cuadra et al., 2004). Either of these

Maturity of Photovoltaic Solar-Energy Conversion 345

In Section 4.1, the present author defined the high-efficiency regime of a solar cell. In Sections 4.2-4.5, the present author reviewed several approaches that are proposed to exceed the Shockley-Queisser limit and reach towards De Vos-Grosjean-Pauwels limit. Of all the approaches, only a stack of *p-n* junctions operating in tandem has experimentally demonstrated an efficiency greater than the Shockley-Queisser limit. The current world-record efficiency is 41.1% for a tandem solar cell operating at 454 suns (Guter et al.,

The fact that the experimental efficiency of solar-energy conversion by a photovoltaic solar cell has surpassed Shockley-Queisser limit is a major scientific and technological accomplishment. This accomplishment demonstrates that the field of solar energy science and technology is no longer in its infancy. However, as may be seen from Figure 5 on page 10 there is still significant space for further maturation of this field. Foremost, the present world record is less than half of the terrestrial limit (86.8%). Reaching closer to the terrestrial limit will require designing solar cells that operate under significantly larger geometric concentration factors and designing tandem solar cells with more junctions. That said, there is significant room for improvement even with respect to the present technologic paradigm used to obtain the world record. The world-record experimental conversion efficiency of 41.1% is recorded for a solar cell composed of three-junctions operating in tandem under 454 suns. Yet, this experimental efficiency is fully 9 percentage points and 16 percentage points less than the theoretical upper limit of a solar cell composed of a two-junction tandem and three-junction tandem (i.e., 50.1%), respectively, operating in tandem at 454 suns (i.e., 50.1%) and 16 percentage points less than the theoretical upper limit of a solar cell composed of three-junctions (i.e., 57.2%) operating at

The author begins this chapter by reviewing the operation of an idealized single-transition, single *p-n* junction solar cell. The present author concludes that though the upper-efficiency limit of a single *p-n* junction solar cell is large, a significant efficiency enhancement is possible. This is so because the terrestrial limits of a single *p-n* junction solar cell is 40.7% and 24.0%, whereas the terrestrial limits of an omni-colour converter is 86.8% and 52.9% for fully-concentrated and non-concentrated sunlight, respectively. There are several high-efficiency approaches proposed to bridge the gap between the single-junction limit and the omni-colour limit. Only the current technological paradigm of stacks of single *p-n* junctions operating in tandem experimentally demonstrates efficiencies with a global efficiency enhancement. The fact that any solar cells operates with an efficiency greater than the Shockley-Queisser limit is a major scientific and technological accomplishment, which demonstrates that the field of solar energy science and technology is no longer in its infancy. That being said, the differences between the present technological record (41.1%) and

phenomena would significantly diminish the efficiencies of these solar cells.

2009). The significance of this is now more deeply explored.

454 suns. The author now offers concluding remarks.

**4.6 Comparative analysis**

**5. Conclusions**

inverse-Auger processes (Werner, Kolodinski & Queisser, 1994) or via impact-ionization processes (Kolodinski et al., 1993; Landsberg et al., 1993). The efficiency enhancement is calculated by several authors (Landsberg et al., 1993; Werner, Brendel & Oueisser, 1994; Werner, Kolodinski & Queisser, 1994). Depending on the assumptions, the upper limit to terrestrial conversion of solar energy using the carrier-multiple solar cell is 85.4% (Werner, Brendel & Oueisser, 1994) or 85.9% (De Vos & Desoete, 1998). Though the carrier-multiple solar cell is close to the upper-efficiency limit of the De Vos-Grosjean-Pauwels solar cell, the latter is larger than the former because the former is a two-terminal device. The present author now reviews the hot-carrier solar cell, the second of three next-generation proposals to be reviewed in this chapter.

#### **4.4 Hot-carrier solar cell**

Hot-carrier solar cells are theorized to exceed the Shockley-Queisser limit (Markvart, 2007; Ross, 1982; Würfel et al., 2005), thus they may be correctly viewed as a high-efficiency approach. These solar cells generate one electron-hole pair per photon absorbed. In describing this solar cell, it is assumed that carriers in the conduction band may interact with themselves and thus equilibrate to the same chemical potential and same temperature (Markvart, 2007; Ross, 1982; Würfel et al., 2005). The same may be said about the carriers in the valence band (Markvart, 2007; Ross, 1982; Würfel et al., 2005). However, the carriers do not interact with phonons and thus are thermally insulated from the absorber. Resulting from a mono-energetic contact to the conduction band and a mono-energetic contact to the valence band, it may be shown that (*i*), the output voltage may be greater than the conduction-to-valence bandgap and that (*ii*) the temperature of the carriers in the absorber may be elevated with respect to the absorber. The efficiency enhancement is calculated by several authors (Markvart, 2007; Ross, 1982; Würfel et al., 2005). Depending on the assumptions, the upper-conversion efficiency of any hot-carrier solar cell is asserted to be 85% (Würfel, 2004) or 86% (Würfel et al., 2005). The present author now reviews the multiple-transition solar cell, the third of three next-generation proposals to be reviewed in this chapter.

#### **4.5 Multiple-transition solar cell**

The multi-transition solar cell is an approach that may offer an improvement to solar-energy conversion as compared to a single *p-n* junction, single-transition solar cell (Wolf, 1960). The multi-transition solar cell utilizes energy levels that are situated at energies below the conduction band edge and above the valence band edge. The energy levels allow the absorption of a photon with energy less than that of the conduction-to-valence band gap. Wolf uses a semi-empirical approach to quantify the solar-energy conversion efficiency of a three-transition solar cell and a four-transition solar cell (Wolf, 1960). Wolf calculates an upper-efficiency limit of 51% for the three-transition solar cell and 65% four-transition solar cell (Wolf, 1960).

Subsequently, as opposed to the semi-empirical approach of Wolf, the detailed-balance approach is applied to multi-transition solar cells (Luque & Martí, 1997). The upper-efficiency limit of the three-transition solar cell is now established at 63.2 (Brown et al., 2002; Levy & Honsberg, 2008b; Luque & Martí, 1997). In addition, the upper-conversion efficiency limits of *N*-transition solar cells are examined (Brown & Green, 2002b; 2003). Depending on the assumptions, the upper-conversion efficiency of any multi-transition solar cell is asserted to be 77.2% (Brown & Green, 2002b) or 85.0% (Brown & Green, 2003). These upper-limits justify the claim that the multiple-transition solar cell is a high-efficiency approach. Resulting from internal current constraints and voltage constraints, the upper-efficiency limit of the multi-transition solar cell is asserted to be less than that of the De Vos-Grosjean-Pauwels converter (Brown & Green, 2002b; 2003). That said, it has been shown (Levy & Honsberg, 2009) that the absorption characteristic of multiple-transition solar cells may lead to both incomplete absorption and absorption overlap (Cuadra et al., 2004). Either of these phenomena would significantly diminish the efficiencies of these solar cells.

#### **4.6 Comparative analysis**

12 Will-be-set-by-IN-TECH

inverse-Auger processes (Werner, Kolodinski & Queisser, 1994) or via impact-ionization processes (Kolodinski et al., 1993; Landsberg et al., 1993). The efficiency enhancement is calculated by several authors (Landsberg et al., 1993; Werner, Brendel & Oueisser, 1994; Werner, Kolodinski & Queisser, 1994). Depending on the assumptions, the upper limit to terrestrial conversion of solar energy using the carrier-multiple solar cell is 85.4% (Werner, Brendel & Oueisser, 1994) or 85.9% (De Vos & Desoete, 1998). Though the carrier-multiple solar cell is close to the upper-efficiency limit of the De Vos-Grosjean-Pauwels solar cell, the latter is larger than the former because the former is a two-terminal device. The present author now reviews the hot-carrier solar cell, the second of three next-generation

Hot-carrier solar cells are theorized to exceed the Shockley-Queisser limit (Markvart, 2007; Ross, 1982; Würfel et al., 2005), thus they may be correctly viewed as a high-efficiency approach. These solar cells generate one electron-hole pair per photon absorbed. In describing this solar cell, it is assumed that carriers in the conduction band may interact with themselves and thus equilibrate to the same chemical potential and same temperature (Markvart, 2007; Ross, 1982; Würfel et al., 2005). The same may be said about the carriers in the valence band (Markvart, 2007; Ross, 1982; Würfel et al., 2005). However, the carriers do not interact with phonons and thus are thermally insulated from the absorber. Resulting from a mono-energetic contact to the conduction band and a mono-energetic contact to the valence band, it may be shown that (*i*), the output voltage may be greater than the conduction-to-valence bandgap and that (*ii*) the temperature of the carriers in the absorber may be elevated with respect to the absorber. The efficiency enhancement is calculated by several authors (Markvart, 2007; Ross, 1982; Würfel et al., 2005). Depending on the assumptions, the upper-conversion efficiency of any hot-carrier solar cell is asserted to be 85% (Würfel, 2004) or 86% (Würfel et al., 2005). The present author now reviews the multiple-transition solar cell, the third of three next-generation proposals to be reviewed in

The multi-transition solar cell is an approach that may offer an improvement to solar-energy conversion as compared to a single *p-n* junction, single-transition solar cell (Wolf, 1960). The multi-transition solar cell utilizes energy levels that are situated at energies below the conduction band edge and above the valence band edge. The energy levels allow the absorption of a photon with energy less than that of the conduction-to-valence band gap. Wolf uses a semi-empirical approach to quantify the solar-energy conversion efficiency of a three-transition solar cell and a four-transition solar cell (Wolf, 1960). Wolf calculates an upper-efficiency limit of 51% for the three-transition solar cell and 65% four-transition solar

Subsequently, as opposed to the semi-empirical approach of Wolf, the detailed-balance approach is applied to multi-transition solar cells (Luque & Martí, 1997). The upper-efficiency limit of the three-transition solar cell is now established at 63.2 (Brown et al., 2002; Levy & Honsberg, 2008b; Luque & Martí, 1997). In addition, the upper-conversion efficiency limits of *N*-transition solar cells are examined (Brown & Green, 2002b; 2003). Depending on the assumptions, the upper-conversion efficiency of any multi-transition solar cell is asserted to be 77.2% (Brown & Green, 2002b) or 85.0% (Brown & Green, 2003). These upper-limits

proposals to be reviewed in this chapter.

**4.4 Hot-carrier solar cell**

this chapter.

cell (Wolf, 1960).

**4.5 Multiple-transition solar cell**

In Section 4.1, the present author defined the high-efficiency regime of a solar cell. In Sections 4.2-4.5, the present author reviewed several approaches that are proposed to exceed the Shockley-Queisser limit and reach towards De Vos-Grosjean-Pauwels limit. Of all the approaches, only a stack of *p-n* junctions operating in tandem has experimentally demonstrated an efficiency greater than the Shockley-Queisser limit. The current world-record efficiency is 41.1% for a tandem solar cell operating at 454 suns (Guter et al., 2009). The significance of this is now more deeply explored.

The fact that the experimental efficiency of solar-energy conversion by a photovoltaic solar cell has surpassed Shockley-Queisser limit is a major scientific and technological accomplishment. This accomplishment demonstrates that the field of solar energy science and technology is no longer in its infancy. However, as may be seen from Figure 5 on page 10 there is still significant space for further maturation of this field. Foremost, the present world record is less than half of the terrestrial limit (86.8%). Reaching closer to the terrestrial limit will require designing solar cells that operate under significantly larger geometric concentration factors and designing tandem solar cells with more junctions. That said, there is significant room for improvement even with respect to the present technologic paradigm used to obtain the world record. The world-record experimental conversion efficiency of 41.1% is recorded for a solar cell composed of three-junctions operating in tandem under 454 suns. Yet, this experimental efficiency is fully 9 percentage points and 16 percentage points less than the theoretical upper limit of a solar cell composed of a two-junction tandem and three-junction tandem (i.e., 50.1%), respectively, operating in tandem at 454 suns (i.e., 50.1%) and 16 percentage points less than the theoretical upper limit of a solar cell composed of three-junctions (i.e., 57.2%) operating at 454 suns. The author now offers concluding remarks.

#### **5. Conclusions**

The author begins this chapter by reviewing the operation of an idealized single-transition, single *p-n* junction solar cell. The present author concludes that though the upper-efficiency limit of a single *p-n* junction solar cell is large, a significant efficiency enhancement is possible. This is so because the terrestrial limits of a single *p-n* junction solar cell is 40.7% and 24.0%, whereas the terrestrial limits of an omni-colour converter is 86.8% and 52.9% for fully-concentrated and non-concentrated sunlight, respectively. There are several high-efficiency approaches proposed to bridge the gap between the single-junction limit and the omni-colour limit. Only the current technological paradigm of stacks of single *p-n* junctions operating in tandem experimentally demonstrates efficiencies with a global efficiency enhancement. The fact that any solar cells operates with an efficiency greater than the Shockley-Queisser limit is a major scientific and technological accomplishment, which demonstrates that the field of solar energy science and technology is no longer in its infancy. That being said, the differences between the present technological record (41.1%) and

Guter, W., Schöne, J., Philipps, S. P., Steiner, M., Siefer, G., Wekkeli, A., Welser, E., Oliva,

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sound physical models indicates significant room to continue to enhance the performance of solar-energy conversion.

#### **6. Acknowledgments**

The author acknowledges the support of P. L. Levy during the preparation of this manuscript.

#### **7. References**


14 Will-be-set-by-IN-TECH

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**6. Acknowledgments**

*in Photovoltaics* .

**7. References**


**16** 

*Tunisia* 

**Application of the Genetic Algorithms for** 

**Identifying the Electrical Parameters of** 

 *1Laboratoire C3S, Ecole Supérieure des Sciences et Techniques de Tunis,* 

*2Laboratoire de Photovoltaïque, Centre de Recherches et des Technologies de l'Energie,* 

The determination of model parameters plays an important role in solar cell design and fabrication, especially if these parameters are well correlated to known physical phenomena. A detailed knowledge of the cell parameters can be an important way for the control of the solar cell manufacturing process, and may be a mean of pinpointing causes of degradation of the performances of panels and photovoltaic systems being produced. For this reason, the model parameters identification provides a powerful tool in the optimization of solar cell

The algorithms for determining model parameters in solar cells, are of two types: those that make use of selected parts of the characteristic (Chan et al., 1987; Charles et al., 1981; Charles et al., 1985; Dufo-Lopez and Bernal-Agustin, 2005; Enrique et al., 2007) and those that employ the whole characteristic (Haupt and Haupt, 1998; Bahgat et al., 2004; Easwarakhanthan et al., 1986). The first group of algorithms involves the solution of five equations derived from considering select points of an current-voltage (I-V) characteristic, e.g. the open-circuit and short-circuit coordinates, the maximum power points and the slopes at strategic portions of the characteristic for different level of illumination and temperature. This method is often much faster and simpler in comparison to curve fitting. However, the disadvantage of this approach is that only selected parts of the characteristic are used to determine the cell parameters. The curve fitting methods offer the advantage of taking all the experimental data in consideration. Conversely it has the disadvantage of artificial solutions. The nonlinear fitting procedure is based on the minimisation of a not convex criterion, and using traditional deterministic optimization algorithms leads to local minima solutions. To overcome this problem, the nonlinear least square minimization technique can be computed with global search approaches such Genetic Algorithms (GAs) (Haupt and Haupt, 1998; Sellami et al., 2007; Zagrouba et al., 2010) strategy, increasing the probability of obtaining the best minimum value

In this chapter, we propose a numerical technique based on GAs to identify the electrical parameters of photovoltaic (PV) solar cells, modules and arrays. These parameters are, respectively, the photocurrent (Iph), the saturation current (Is), the series resistance (Rs), the

**1. Introduction** 

performance.

of the cost function in very reasonable time.

**PV Solar Generators** 

*Technopole de Borj-Cédria,* 

Anis Sellami1 and Mongi Bouaïcha2


## **Application of the Genetic Algorithms for Identifying the Electrical Parameters of PV Solar Generators**

Anis Sellami1 and Mongi Bouaïcha2

 *1Laboratoire C3S, Ecole Supérieure des Sciences et Techniques de Tunis, 2Laboratoire de Photovoltaïque, Centre de Recherches et des Technologies de l'Energie, Technopole de Borj-Cédria, Tunisia* 

#### **1. Introduction**

16 Will-be-set-by-IN-TECH

348 Solar Cells – Silicon Wafer-Based Technologies

Werner, J. H., Kolodinski, S. & Queisser, H. (1994). Novel optimization principles and

Wolf, M. (1960). Limitations and possibilities for improvement of photovoltaic solar energy

Würfel, P. (2004). Thermodynamics of solar energy converters, *in* A. Martí & A. Luque

Würfel, P., Brown, A. S., Humphrey, T. E. & Green, M. A. (2005). Particle conservation in the

Würfel, P. (1982). The chemical potential of radiation, *Journal of Physics C* 15: 3867–85. Würfel, P. (2002). Thermodynamic limitations to solar energy conversion, *Physica E*

hot-carrier solar cell, *Progress in Photovoltaics* 13(4): 277–85.

*Institute of Radio Engineers*, Vol. 48, pp. 1246–63.

14(1-2): 18–26.

Philadelphia, chapter 3, p. 57.

efficiency limits for semiconductor solar cells, *Physical Review Letters* 72(24): 3851–4.

converters. Part I: Considerations for Earth's surface operation, *Proceedings of the*

(eds), *Next Generations Photovoltaics*, Institute of Physics Publishing, Bristol and

The determination of model parameters plays an important role in solar cell design and fabrication, especially if these parameters are well correlated to known physical phenomena. A detailed knowledge of the cell parameters can be an important way for the control of the solar cell manufacturing process, and may be a mean of pinpointing causes of degradation of the performances of panels and photovoltaic systems being produced. For this reason, the model parameters identification provides a powerful tool in the optimization of solar cell performance.

The algorithms for determining model parameters in solar cells, are of two types: those that make use of selected parts of the characteristic (Chan et al., 1987; Charles et al., 1981; Charles et al., 1985; Dufo-Lopez and Bernal-Agustin, 2005; Enrique et al., 2007) and those that employ the whole characteristic (Haupt and Haupt, 1998; Bahgat et al., 2004; Easwarakhanthan et al., 1986). The first group of algorithms involves the solution of five equations derived from considering select points of an current-voltage (I-V) characteristic, e.g. the open-circuit and short-circuit coordinates, the maximum power points and the slopes at strategic portions of the characteristic for different level of illumination and temperature. This method is often much faster and simpler in comparison to curve fitting. However, the disadvantage of this approach is that only selected parts of the characteristic are used to determine the cell parameters. The curve fitting methods offer the advantage of taking all the experimental data in consideration. Conversely it has the disadvantage of artificial solutions. The nonlinear fitting procedure is based on the minimisation of a not convex criterion, and using traditional deterministic optimization algorithms leads to local minima solutions. To overcome this problem, the nonlinear least square minimization technique can be computed with global search approaches such Genetic Algorithms (GAs) (Haupt and Haupt, 1998; Sellami et al., 2007; Zagrouba et al., 2010) strategy, increasing the probability of obtaining the best minimum value of the cost function in very reasonable time.

In this chapter, we propose a numerical technique based on GAs to identify the electrical parameters of photovoltaic (PV) solar cells, modules and arrays. These parameters are, respectively, the photocurrent (Iph), the saturation current (Is), the series resistance (Rs), the

Application of the Genetic Algorithms

is the ideality factor. (Charles et al., 1985)

**3. Classical optimization algorithms** 

distances separating experimental Ii and predicted data I(Vi,):

Gsh=1/Rsh, Iph, n and Is.

ith point among m data points.

for Identifying the Electrical Parameters of PV Solar Generators 351

the number of parameters is augmented by 2 for the second diode. Consequently, the unicity of the solution is affected. However, precise experiments taking into account different physical phenomena contributing to the electronic transport are suitable to identify all the conduction modes. The single one diode model used here is rather simple, efficient and sufficiently accurate for process optimization and system design tasks. In photovoltaic, the output power of a solar module and a solar array is generally dependant of the electrical characteristics of the poor cell in the module, and the electrical characteristics of the poor module in an array. To skip this difficulty, electrical parameters of all cells forming a photovoltaic module should be very close each one to the other. For a photovoltaic array, all solar modules forming it should also have similar electrical characteristics. Consequently, the one diode model can also be applied to fit solar modules and arrays if we ensure that the cell to cell and the module to module variations are not important (Easwarakhanthan et al., 1986). It should be noted, however, that the parameters determined by the one diode model will lose somewhat their physical meaning in the case of solar modules and arrays. Consequently, the precision of each fitting approach will be certainly better in the case of solar cells than that of

solar modules, which itself, should be more accurate than that of solar arrays.

Under these assumptions, results could be very acceptable with a good accuracy, and in replacement of expression (1), we will use the I-V relation given by expression (2), where n

> *s th V RI nV <sup>s</sup> ph s*

*V RI I I Ie*

Using expression (2) and the GAs, we can determine values of the electrical parameters Rs,

The error criterion which used in classical curve fitting is based on the sum of the squared

1 <sup>2</sup> S( ) ( ,) *m*

*I IV*

Where = (Iph,Is,n,Rs,Gsh), Ii and Vi are respectively the measured current and voltage at the

The equation (3) is implicit in I and one way of simplifying the computation of I(Vi,) is to

( ) ( ,) 1 ( ) ( ) *i si <sup>i</sup> ph s sh i s i th V RI IV I I Exp G V RI nV*

The equation (4) is nonlinear. Hence, the resulting set of normal equations F()=0, derived from multivariate calculus will be non linear and no exact solution can be found. To obtain

 

*i*

substitute Ii and Vi in equation (3). Hence, we obtain the following equation:

(3)

*i i*

 

1

*sh*

(2)

(4)

*R*

shunt resistance (Rsh) and the ideality factor (n). The manipulated data are provided from experimental I-V acquisition process. The one diode type approach is used to model the AM1.5 I-V characteristic of the solar cell. To extract electrical parameters, the approach is formulated as a non convex optimization problem. The GAs approach was used as a numerical technique in order to overcome problems involved in the local minima in the case of non convex optimization criteria.

This chapter is organized as follows: Firstly, we present the classical one-diode equivalent circuit and discuss its validity to model solar modules and arrays. Then, we expose the limitations of the classical optimization algorithms for parameters extraction. Next, we describe the detailed steps to be followed in the application of GAs for determining solar PV generators parameters. Finally, we show the procedure of extracting the coordinates (Vm,Im) of the maximum power point (MPP) from the identified parameters.

#### **2. The one diode model**

The I-V characteristic of a solar cell under illumination can be derived from the Schottky diffusion model in a PN junction. In Fig. 1, we give the scheme of the equivalent electrical circuit of a solar cell under illumination for both cases; the double diode model and the one diode model.

Fig. 1. Scheme of the equivalent electrical circuit of an illuminated solar cell: (a) the double diode model, and (b) the one diode model.

A rigorous and complete expression of the I-V characteristic of an illuminated solar cell that describes the complete transport phenomena is given by: (Sze, 1982)

$$I = I\_{ph} - I\_{s1} \left[ e^{\frac{V + R\_S l}{V\_{th}}} - 1 \right] - I\_{s2} \left[ e^{\frac{V + R\_S l}{2V\_{th}}} - 1 \right] - \frac{V + R\_S l}{R\_{th}} \tag{1}$$

Where Iph is the photocurrent, Is1 and Is2 are the saturation currents of diodes D1 and D2, respectively. Rs is the series resistance, Rsh is the shunt resistance and Vth is the thermal voltage. However, it is well established that value of Is2 is generally 10-6 times lesser than that one of Is1. For this reason, it is well suitable to restrict ourselves to the one diode model.

In addition, despite the fact that the double diode model can take into account all the conduction modes, which is likely for physical interpretation, it may generate many difficulties. Hence, in this case, the accuracy of the fitting related to the value of the ending cost of the objective function, which corresponds to the admitted absolute minimum can be improved (Ketter et al., 1975). However, the physical meaning of the solution is lost, since

shunt resistance (Rsh) and the ideality factor (n). The manipulated data are provided from experimental I-V acquisition process. The one diode type approach is used to model the AM1.5 I-V characteristic of the solar cell. To extract electrical parameters, the approach is formulated as a non convex optimization problem. The GAs approach was used as a numerical technique in order to overcome problems involved in the local minima in the case

This chapter is organized as follows: Firstly, we present the classical one-diode equivalent circuit and discuss its validity to model solar modules and arrays. Then, we expose the limitations of the classical optimization algorithms for parameters extraction. Next, we describe the detailed steps to be followed in the application of GAs for determining solar PV generators parameters. Finally, we show the procedure of extracting the coordinates

The I-V characteristic of a solar cell under illumination can be derived from the Schottky diffusion model in a PN junction. In Fig. 1, we give the scheme of the equivalent electrical circuit of a solar cell under illumination for both cases; the double diode model and the one

I 

V

Iph

Fig. 1. Scheme of the equivalent electrical circuit of an illuminated solar cell: (a) the double

A rigorous and complete expression of the I-V characteristic of an illuminated solar cell that

�����

���� � 1� � �����

D 

���

Rsh

(b)

Rs

(1)

I 

V 

��� � 1� � ��� ��

Where Iph is the photocurrent, Is1 and Is2 are the saturation currents of diodes D1 and D2, respectively. Rs is the series resistance, Rsh is the shunt resistance and Vth is the thermal voltage. However, it is well established that value of Is2 is generally 10-6 times lesser than that one of Is1. For this reason, it is well suitable to restrict ourselves to the one diode model. In addition, despite the fact that the double diode model can take into account all the conduction modes, which is likely for physical interpretation, it may generate many difficulties. Hence, in this case, the accuracy of the fitting related to the value of the ending cost of the objective function, which corresponds to the admitted absolute minimum can be improved (Ketter et al., 1975). However, the physical meaning of the solution is lost, since

describes the complete transport phenomena is given by: (Sze, 1982)

�����

����� � ��� ��

Rsh

Rs

(Vm,Im) of the maximum power point (MPP) from the identified parameters.

of non convex optimization criteria.

**2. The one diode model** 

D1 D2 

diode model, and (b) the one diode model.

(a)

diode model.

Iph

the number of parameters is augmented by 2 for the second diode. Consequently, the unicity of the solution is affected. However, precise experiments taking into account different physical phenomena contributing to the electronic transport are suitable to identify all the conduction modes. The single one diode model used here is rather simple, efficient and sufficiently accurate for process optimization and system design tasks. In photovoltaic, the output power of a solar module and a solar array is generally dependant of the electrical characteristics of the poor cell in the module, and the electrical characteristics of the poor module in an array. To skip this difficulty, electrical parameters of all cells forming a photovoltaic module should be very close each one to the other. For a photovoltaic array, all solar modules forming it should also have similar electrical characteristics. Consequently, the one diode model can also be applied to fit solar modules and arrays if we ensure that the cell to cell and the module to module variations are not important (Easwarakhanthan et al., 1986). It should be noted, however, that the parameters determined by the one diode model will lose somewhat their physical meaning in the case of solar modules and arrays. Consequently, the precision of each fitting approach will be certainly better in the case of solar cells than that of solar modules, which itself, should be more accurate than that of solar arrays.

Under these assumptions, results could be very acceptable with a good accuracy, and in replacement of expression (1), we will use the I-V relation given by expression (2), where n is the ideality factor. (Charles et al., 1985)

$$I = I\_{ph} - I\_s \left[ e^{\frac{V + R\_s I}{nV\_{sh}}} - 1 \right] - \frac{V + R\_s I}{R\_{sh}} \tag{2}$$

Using expression (2) and the GAs, we can determine values of the electrical parameters Rs, Gsh=1/Rsh, Iph, n and Is.

#### **3. Classical optimization algorithms**

The error criterion which used in classical curve fitting is based on the sum of the squared distances separating experimental Ii and predicted data I(Vi,):

$$\mathbf{S}(\boldsymbol{\theta}) = \sum\_{i=1}^{m} \left[ I\_i - I(V\_{i\prime}, \boldsymbol{\theta}) \right]^2 \tag{3}$$

Where = (Iph,Is,n,Rs,Gsh), Ii and Vi are respectively the measured current and voltage at the ith point among m data points.

The equation (3) is implicit in I and one way of simplifying the computation of I(Vi,) is to substitute Ii and Vi in equation (3). Hence, we obtain the following equation:

$$I(V\_{i\prime}, \theta) = I\_{ph} - I\_s \left[ \exp\left(\frac{(V\_i + R\_s I\_i)}{nV\_{\text{fl}}}\right) - 1\right] - G\_{sh} \left(V\_i + R\_s I\_i\right) \tag{4}$$

The equation (4) is nonlinear. Hence, the resulting set of normal equations F()=0, derived from multivariate calculus will be non linear and no exact solution can be found. To obtain

Application of the Genetic Algorithms

**Current (A)**

**Current (A)**

for Identifying the Electrical Parameters of PV Solar Generators 353

Fig. 2. Comparison between the experimental I-V characteristic and the fitted curve for a 57

**Voltage (V)**

**-0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6**

I exp I fit

I exp I fit

Fig. 3. Comparison between the experimental I-V characteristic and the fitted curve for a 57

**Voltage (V)**

**-0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6**

In order to analyse the effect of the initialized parameters n and Rs on the minimization of

Fig. 5 depicts the evolution of the objective function in regard to the initial value of N parameters (N varies from 1 up to 2). The initial value of Rs is fixed, and the minima are represented by dots joined just more clearness. We remark that the initial value of N parameters decides on the type of minimum whether it is absolute (case Ninit=1.5) or relative (the other cases). We note that the search trajectory is a set of parabolic arcs confirming the

mm diameter solar cell. The initial value of n and Rs are: n=1; Rs=0

**-0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8**

mm diameter solar cell. The initial value of n and Rs are: n=2; Rs=0

**-0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8**

fact that:

the error criterion, we have fixed one of them and we have varied the other.


an approximation of the exact solution, we use Newton's method. The Newton functional iteration procedure evolves from:

$$\left[\theta\_k\right] = \left[\theta\_{k-1}\right] - \left[f(\theta\_{k-1})\right]^{-1} \left[F(\theta\_{k-1})\right] \tag{5}$$

Where J[] is the Jacobean matrix

Although, using Newton's Method, the initializing step of the five parameters plays a prominent part in the identification and determines drastically the convergence. There is a net difficulty in initializing the fitting parameters, which can be overcome by performing a procedure based on a reduced non-linear least-squares technique in which only two parameters have to be initialized. The electrical parameters are grouped in two classes: the series resistance Rs and the diode quality factor n for the first one and the shunt resistance Rsh, the photocurrent Iph and the saturation current is for the second one.

The model is highly non-linear for the first class, if n and Rs were fixed, the model would have a linear behaviour in regard to the second class. So that theses parameters are estimated by linear regression (Chan et al., 1987). Keeping theses three parameters constant, the model will be non-linear in regard to the first class of parameters. The objective function S() will be minimized with respect to n and Rs. The two non-linear equations resulting from multivariate calculus are solved also by Newton's method, the iterations for n and Rs are continued till the relative accuracy for each of them becomes less then 0,1%. The steps are then repeated with the new determined values of n and Rs, till the relative difference between two consecutive values of S computed soon after each linear regression, becomes smaller than a relative error which depends on the accuracy of the measured data.

The intention of the initializing procedure is to reduce from five to two the number of parameters that have to be initialized; a result of this first step is to have five starting values of the parameters within the domain of convergence. The feature of this set of values obtained from the first step is:


To overcome the undesired oscillations and an eventual overflow which results from the Newton step choice, the algorithm uses a step adjustment procedure at each iteration. The modified Newton functional iteration procedure evolves from:

$$\left[\theta\_k\right] = \left[\theta\_{k-1}\right] - \lambda \left[f(\theta\_{k-1})\right]^{-1} \left[F(\theta\_{k-1})\right] \tag{6}$$

The Newton steps are continued until the successively computed parameters are found to change by less than 0.0001%. At this end, Dichotomies method is used to solve the implicit equation (3).

This algorithm is tested for a number of samples of solar cells and for many configurations of initial values, it has been demonstrated that it converges in few seconds. The number of bugs resulting from overflows is scarce. Dead lock events do not exceed 3% for all the cells that are performed. The results of the fitted curve and experimental data for a 57 mm diameter silicon solar cell are presented in Fig. 2, Fig. 3 and Fig. 4.

The results show that for Fig. 4, the algorithm finds the absolute minimum with the desired accuracy (less than 0.3%). However, the initialized parameters in Fig. 2 and Fig. 3 allow the algorithm to converge to local minimums.

an approximation of the exact solution, we use Newton's method. The Newton functional

 <sup>1</sup> 11 1 () () *kk k k*

 

Although, using Newton's Method, the initializing step of the five parameters plays a prominent part in the identification and determines drastically the convergence. There is a net difficulty in initializing the fitting parameters, which can be overcome by performing a procedure based on a reduced non-linear least-squares technique in which only two parameters have to be initialized. The electrical parameters are grouped in two classes: the series resistance Rs and the diode quality factor n for the first one and the shunt resistance

The model is highly non-linear for the first class, if n and Rs were fixed, the model would have a linear behaviour in regard to the second class. So that theses parameters are estimated by linear regression (Chan et al., 1987). Keeping theses three parameters constant, the model will be non-linear in regard to the first class of parameters. The objective function S() will be minimized with respect to n and Rs. The two non-linear equations resulting from multivariate calculus are solved also by Newton's method, the iterations for n and Rs are continued till the relative accuracy for each of them becomes less then 0,1%. The steps are then repeated with the new determined values of n and Rs, till the relative difference between two consecutive values of S computed soon after each linear regression, becomes

The intention of the initializing procedure is to reduce from five to two the number of parameters that have to be initialized; a result of this first step is to have five starting values of the parameters within the domain of convergence. The feature of this set of values


To overcome the undesired oscillations and an eventual overflow which results from the Newton step choice, the algorithm uses a step adjustment procedure at each iteration. The

> <sup>1</sup> 1 11 () () *kk k k*

The Newton steps are continued until the successively computed parameters are found to change by less than 0.0001%. At this end, Dichotomies method is used to solve the implicit

This algorithm is tested for a number of samples of solar cells and for many configurations of initial values, it has been demonstrated that it converges in few seconds. The number of bugs resulting from overflows is scarce. Dead lock events do not exceed 3% for all the cells that are performed. The results of the fitted curve and experimental data for a 57 mm

The results show that for Fig. 4, the algorithm finds the absolute minimum with the desired accuracy (less than 0.3%). However, the initialized parameters in Fig. 2 and Fig. 3 allow the

 

*J F* (6)

 

smaller than a relative error which depends on the accuracy of the measured data.

modified Newton functional iteration procedure evolves from:

diameter silicon solar cell are presented in Fig. 2, Fig. 3 and Fig. 4.

algorithm to converge to local minimums.

   

*J F* (5)

Rsh, the photocurrent Iph and the saturation current is for the second one.

iteration procedure evolves from:

Where J[] is the Jacobean matrix

obtained from the first step is:

are sufficiently accurate.

equation (3).

**Voltage (V)**

Fig. 2. Comparison between the experimental I-V characteristic and the fitted curve for a 57 mm diameter solar cell. The initial value of n and Rs are: n=1; Rs=0

Fig. 3. Comparison between the experimental I-V characteristic and the fitted curve for a 57 mm diameter solar cell. The initial value of n and Rs are: n=2; Rs=0

In order to analyse the effect of the initialized parameters n and Rs on the minimization of the error criterion, we have fixed one of them and we have varied the other.

Fig. 5 depicts the evolution of the objective function in regard to the initial value of N parameters (N varies from 1 up to 2). The initial value of Rs is fixed, and the minima are represented by dots joined just more clearness. We remark that the initial value of N parameters decides on the type of minimum whether it is absolute (case Ninit=1.5) or relative (the other cases). We note that the search trajectory is a set of parabolic arcs confirming the fact that:


Application of the Genetic Algorithms

**The objective function: Sum of**

**squared errors (x1,00E-03)**

**0 0,5 1 1,5 2 2,5 3 3,5 4**

Fig. 6. Search path of the absolute minimum in n plans.

minimum which is the lowest and the real solution.

**4. Application of the genetic algorithms** 

Vi in Eq. (2). Hence, we obtain Eq. (8).

Where exp

for Identifying the Electrical Parameters of PV Solar Generators 355

value of n parameter. Therefore, the initial value of Rs is tacked to be arbitrary within an

For each combination of (Rs initial, n initial), the algorithm converges to a minimum which can be relative or absolute. We stress on the fact that theoretically there is no way to predict the nature of the minimum (absolute or relative) for non linear models when we use Newton method. When the initial value of the n parameter is sampled linearly in the interval of its natural variation from 1 to 2 (Fig. 5), we have excluded, in such manner, the influence of the initial conditions. We obtain a set of minima; we deduce the absolute

To numerically carry out the electrical parameters of the solar generators (cell and module), from the measured I-V curves, we fit the theoretical expression given in equation (2) to the experimental one. The fitting procedure is based on the use of the genetic algorithms (GAs). The error criterion in the nonlinear fitting procedure is based on the sum of the squared difference between the theoretical and experimental current values. As a consequence, the cost function to be minimized is given by (Easwarakhanthan et al., 1986; Phang et al., 1986):

exp 2

*<sup>i</sup> I* is the measured current at the Vi bias, = (Iph, Is, Rs, Gsh, n) is the set of parameters

(7)

(8)

N=1 N=1,5 N=2

[ ( , )]

*i i*

(V ) ( , ) exp 1 ( ) *i s i ph s sh i s q RI IV I I G V RI nKT*

1

*I IV*

to carry out, m the number of considered data points and I(Vi,) is the predicted current. Eq. (2) is implicit in I; one way of simplifying the computation of I(Vi,) is to substitute Ii and

*i* 

*m*

interval witch take into consideration the physical proprieties of this parameter.

**Initial value of Rs parameter**

**1,00E-06 1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01**


Fig. 6 gives the evolution of the objective function with the initial value of Rs (the initial value of Rs varies from 10-6 to 0.1 ); the initial value of n is fixed. We deduce that the starting value of Rs, has, practically no influence on the minimum in comparison with the effect of the initial

**Voltage (V)**

Fig. 4. Comparison between the experimental I-V characteristic and the fitted curve for a 57 mm diameter solar cell. The initial value of n and Rs are: n=1,5; Rs=0,001

Fig. 5. Search path of the absolute minimum in Rs plans.

Fig. 6 gives the evolution of the objective function with the initial value of Rs (the initial value of Rs varies from 10-6 to 0.1 ); the initial value of n is fixed. We deduce that the starting value of Rs, has, practically no influence on the minimum in comparison with the effect of the initial

Fig. 4. Comparison between the experimental I-V characteristic and the fitted curve for a 57

**Voltage (V)**

**Initial value of N parameter**

**1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2**

**-0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6**

I exp

I fit

mm diameter solar cell. The initial value of n and Rs are: n=1,5; Rs=0,001

Rs=0 Rs=0,003 Rs=0,05

 

**-0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8**

**Current (A)**

 **The objective function: Sum of**

**squared errors (x1,00E-03)**

**0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5**

Fig. 5. Search path of the absolute minimum in Rs plans.


Fig. 6. Search path of the absolute minimum in n plans.

value of n parameter. Therefore, the initial value of Rs is tacked to be arbitrary within an interval witch take into consideration the physical proprieties of this parameter.

For each combination of (Rs initial, n initial), the algorithm converges to a minimum which can be relative or absolute. We stress on the fact that theoretically there is no way to predict the nature of the minimum (absolute or relative) for non linear models when we use Newton method. When the initial value of the n parameter is sampled linearly in the interval of its natural variation from 1 to 2 (Fig. 5), we have excluded, in such manner, the influence of the initial conditions. We obtain a set of minima; we deduce the absolute minimum which is the lowest and the real solution.

#### **4. Application of the genetic algorithms**

To numerically carry out the electrical parameters of the solar generators (cell and module), from the measured I-V curves, we fit the theoretical expression given in equation (2) to the experimental one. The fitting procedure is based on the use of the genetic algorithms (GAs). The error criterion in the nonlinear fitting procedure is based on the sum of the squared difference between the theoretical and experimental current values. As a consequence, the cost function to be minimized is given by (Easwarakhanthan et al., 1986; Phang et al., 1986):

$$\mathcal{X} = \sum\_{i=1}^{m} \left[ I\_i^{\text{exp}} - I(V\_{i'}, \theta) \right]^2 \tag{7}$$

Where exp *<sup>i</sup> I* is the measured current at the Vi bias, = (Iph, Is, Rs, Gsh, n) is the set of parameters to carry out, m the number of considered data points and I(Vi,) is the predicted current. Eq. (2) is implicit in I; one way of simplifying the computation of I(Vi,) is to substitute Ii and Vi in Eq. (2). Hence, we obtain Eq. (8).

$$I(V\_i, \theta) = I\_{ph} - I\_s \left[ \exp\left(\frac{q(V\_i + R\_s I)}{nKT}\right) - 1\right] - G\_{sh} \text{ ( $V\_i + R\_s I$ )}\tag{8}$$

Application of the Genetic Algorithms

between the two parents.

individuals (chromosomes).

model, the roulette wheel procedure, etc.

for Identifying the Electrical Parameters of PV Solar Generators 357

The very common operators used in GAs are selection, reproduction and mutation (Haupt and Haupt, 1998; Sellami et al., 2007; Zagrouba et al., 2010), which are described as follows: 1. *Selection:* This procedure is applied to select chromosomes that participate in the reproduction process to give birth to the next generation. Only the best chromosomes are retained for the next generation of the algorithm, while the bad ones are discarded. There are several methods of this process, including the elitist model, the ranking

2. *Reproduction/pairing*: This procedure takes two selected chromosomes from a current generation (parents) and crosses them to obtain two individuals for the new generation (offspring's). There are several types of crossing, but the simplest methods choose arbitrary one or more points (parameters) in the chromosome of each parent to mark as crossover points. Then the parameters between these points are merely swapped

In our case, each parent is represented by a chromosome containing five parameters. The paring is performed by crossing one, two, three, four and five parameters between the two parents, leading to obtain from these two parents a new generation of 25

3. *Mutation*: It consists of introducing changes in some genes (parameters) of a chromosome in a population. This procedure is performed by GAs to explore new solutions. Random mutations alter a small percentage of the population (mutation rate) except for the best chromosomes. A mutation rate between 1% and 20% often works well. If the mutation rate is above 20%, too many good parameters can be mutated, and then the algorithm stalls. In our case, mutation was applied to all parameters of 4% of chromosomes number. Note that the new value of each parameter should be in the [lo,hi] corresponding interval. Consequently, after paring, mutated parameters are

The used GA program is a homemade. We developed it on Matlab environment, for both PV cell, module and array. For flexibility, we choose to develop this program instead of

Current-Voltage characteristic under AM1.5 illumination was performed using the cell tester CT 801 from Pasan (Pasan, 2004). This cell tester includes in the same compact architecture a single-flash xenon light source, an automatic sliding contact frame, a test chuck with interchangeable plates to fit any cell configuration, a calibrated reference cell, and a Panel-PC type computer. To become a fully featured cell testing unit, it needs to be connected to an external electronic load and flash generator, itself included in a 19" 6U rack. Its single-flash technology gives a negligible heating of the cell, in the tenths of a degree range, much lower than continuous-light testers, so an accurate I-V curve determination can be achieved (Pasan, 2004). In Fig. 8, we give the plot of the I-V curve of a multicrystalline

To determine the cell parameters, we use equation (2) and the I-V curve of Fig. 8. Obtained

In general, the time-convergence of the algorithm is influenced by the choice of the IPOP. If coordinates of the absolute minimum of the cost function in the parameter's space are unknown, initial invidious (IPOP) were generated randomly. The latter were chosen

results are compared to those obtained by the Pasan cell tester software version V3.0.

engaged to ensure that the parameters space is explored in new regions.

using Genetic Algorithms and Direct Search Toolbox of Matlab.

**4.1 Identification of the electrical parameters of the solar cell** 

silicon solar cell having a surface area of 4 cm2.

( ). [ , ] *i o ipop par o IPOP h l random N N l* (9)

Fig. 7. Flow chart of the genetic algorithms.

Where:

Nipop is the initial number of chromosomes in IPOP,

Npar is the number of parameters in the chromosome (Npar = 5 in our case),

lo and hi are respectively the lowest and the highest values of parameters Is, Iph, Rs, Rsh and n.

In Fig. 7, we give the flow chart of the GAs. The chromosome here is the vector containing the five parameters Iph, Is, Rs, Gsh, and n. The initial population (IPOP) of chromosomes is a matrix given by Eq. (9): (Easwarakhanthan et al., 1986)


Define: - Parameters (Is, Iph, Rs ,Rsh ,n)

Create Initial Population (IPOP)

Evaluate cost

Select mate

Reproduce

Mutate

Test of convergence

Stop

Fig. 7. Flow chart of the genetic algorithms.

Nipop is the initial number of chromosomes in IPOP,

matrix given by Eq. (9): (Easwarakhanthan et al., 1986)

Npar is the number of parameters in the chromosome (Npar = 5 in our case),

lo and hi are respectively the lowest and the highest values of parameters Is, Iph, Rs, Rsh

In Fig. 7, we give the flow chart of the GAs. The chromosome here is the vector containing the five parameters Iph, Is, Rs, Gsh, and n. The initial population (IPOP) of chromosomes is a

Where:

and n.

$$IPOP = (h\_i - l\_o).random[N\_{ipop}, N\_{par}] + l\_o \tag{9}$$

The very common operators used in GAs are selection, reproduction and mutation (Haupt and Haupt, 1998; Sellami et al., 2007; Zagrouba et al., 2010), which are described as follows:


In our case, each parent is represented by a chromosome containing five parameters. The paring is performed by crossing one, two, three, four and five parameters between the two parents, leading to obtain from these two parents a new generation of 25 individuals (chromosomes).

3. *Mutation*: It consists of introducing changes in some genes (parameters) of a chromosome in a population. This procedure is performed by GAs to explore new solutions. Random mutations alter a small percentage of the population (mutation rate) except for the best chromosomes. A mutation rate between 1% and 20% often works well. If the mutation rate is above 20%, too many good parameters can be mutated, and then the algorithm stalls. In our case, mutation was applied to all parameters of 4% of chromosomes number. Note that the new value of each parameter should be in the [lo,hi] corresponding interval. Consequently, after paring, mutated parameters are engaged to ensure that the parameters space is explored in new regions.

The used GA program is a homemade. We developed it on Matlab environment, for both PV cell, module and array. For flexibility, we choose to develop this program instead of using Genetic Algorithms and Direct Search Toolbox of Matlab.

#### **4.1 Identification of the electrical parameters of the solar cell**

Current-Voltage characteristic under AM1.5 illumination was performed using the cell tester CT 801 from Pasan (Pasan, 2004). This cell tester includes in the same compact architecture a single-flash xenon light source, an automatic sliding contact frame, a test chuck with interchangeable plates to fit any cell configuration, a calibrated reference cell, and a Panel-PC type computer. To become a fully featured cell testing unit, it needs to be connected to an external electronic load and flash generator, itself included in a 19" 6U rack. Its single-flash technology gives a negligible heating of the cell, in the tenths of a degree range, much lower than continuous-light testers, so an accurate I-V curve determination can be achieved (Pasan, 2004). In Fig. 8, we give the plot of the I-V curve of a multicrystalline silicon solar cell having a surface area of 4 cm2.

To determine the cell parameters, we use equation (2) and the I-V curve of Fig. 8. Obtained results are compared to those obtained by the Pasan cell tester software version V3.0.

In general, the time-convergence of the algorithm is influenced by the choice of the IPOP. If coordinates of the absolute minimum of the cost function in the parameter's space are unknown, initial invidious (IPOP) were generated randomly. The latter were chosen

Application of the Genetic Algorithms

using GAs method.


0

Experimental Theoretical

0.02

0.04

0.06

I (A)

0.08

0.1

0.12

0.14

cell.

for Identifying the Electrical Parameters of PV Solar Generators 359

differs of 1% for Rsh. However, value of Rs obtained with the Pasan software is 7.5 times that one obtained with GAs. Regarding the good fitting result in Fig. 9, and taking into account that the Rs effect on the I-V curve is in general observed for voltages near the Voc value, one can argue that the output value of Rs obtained with GAs is reasonable, but no conclusion can be

Fig. 9. Adjustment of the theoretical I-V curve of the solar cell's to the experimental one

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

V (V)

Fig. 10. Mean and minimum values of the function versus generation number of the solar

done on the Rs value given by the Pasan software since no fitting is presented.

Fig. 8. Experimental I-V curve of the solar cell performed with the Pasan machine.

uniformly between the highest and the lowest value of each parameter. In this work, the first generation was started with 145 (537824) chromosomes as the initial population (IPOP), where 5 is the number of parameters to be identified. Each parameter in a chromosome has a lowest (lo) and a highest (hi) value. Since the interval between lo and hi contains an infinite number of values, we started in the simulation with different values such as 200, 100, 50, 25, 15, 10 and 5. We remark that simulation results are similar for all values 200, 100, 50, 25, 15 and 14. For values less than 14, the algorithm leads to a relatively high value of the cost function.

After determining the cost function for each chromosome, we apply a selection in IPOP (Select mate): only a family of good chromosomes that corresponds to good values of the cost was kept for the pairing (reproduce) and the others (bad) were killed. To ensure that the parameters space is suitably explored, a mutation of 4% in the chromosomes was operated (mutate). At the end of the algorithm, the convergence was tested. If the result (last value of ) does not give satisfaction compared to a predefined cost minimum (=0.000270 A2), all below steps are repeated in the second generation and so on. The fitting result is plot in Fig. 9. As we can see, theoretical curve fits very well experimental results.

 In Fig. 10, we plot the mean and the minimum values of the cost function with respect to the generation number. One can notice that beyond the third generation, the cost function becomes stable in a relative good minimum. The minimum value of the cost function was found to be equal to 0.000256 A2 and was reached after five generations. According to this relatively good value, one can assume that the GAs are very suitable for the estimation of the electrical parameters via the fitting method. In table 1, we compare the electrical parameters resulting from the use of the GAs-based fitting procedure, with those given by the Pasan cell tester software. Hence, the minimization problem is of five parameters (Iph, Is, Rs, Rsh, n), which is a hard problem in fitting procedures. As presented in table 1, the Pasan software gives only estimations of three parameters (Iph, Rs, Rsh) from the five unknown ones. The saturation current Is and the ideality factor n are not performed. In contrast, using the GAs method, we can estimate values of Is and n in addition to the other three parameters (Iph, Rs, Rsh). Obtained values' using the Pasan software and GAs method are identical for Iph and

Fig. 8. Experimental I-V curve of the solar cell performed with the Pasan machine.

function.

uniformly between the highest and the lowest value of each parameter. In this work, the first generation was started with 145 (537824) chromosomes as the initial population (IPOP), where 5 is the number of parameters to be identified. Each parameter in a chromosome has a lowest (lo) and a highest (hi) value. Since the interval between lo and hi contains an infinite number of values, we started in the simulation with different values such as 200, 100, 50, 25, 15, 10 and 5. We remark that simulation results are similar for all values 200, 100, 50, 25, 15 and 14. For values less than 14, the algorithm leads to a relatively high value of the cost

After determining the cost function for each chromosome, we apply a selection in IPOP (Select mate): only a family of good chromosomes that corresponds to good values of the cost was kept for the pairing (reproduce) and the others (bad) were killed. To ensure that the parameters space is suitably explored, a mutation of 4% in the chromosomes was operated (mutate). At the end of the algorithm, the convergence was tested. If the result (last value of ) does not give satisfaction compared to a predefined cost minimum (=0.000270 A2), all below steps are repeated in the second generation and so on. The fitting result is plot in Fig.

 In Fig. 10, we plot the mean and the minimum values of the cost function with respect to the generation number. One can notice that beyond the third generation, the cost function becomes stable in a relative good minimum. The minimum value of the cost function was found to be equal to 0.000256 A2 and was reached after five generations. According to this relatively good value, one can assume that the GAs are very suitable for the estimation of the electrical parameters via the fitting method. In table 1, we compare the electrical parameters resulting from the use of the GAs-based fitting procedure, with those given by the Pasan cell tester software. Hence, the minimization problem is of five parameters (Iph, Is, Rs, Rsh, n), which is a hard problem in fitting procedures. As presented in table 1, the Pasan software gives only estimations of three parameters (Iph, Rs, Rsh) from the five unknown ones. The saturation current Is and the ideality factor n are not performed. In contrast, using the GAs method, we can estimate values of Is and n in addition to the other three parameters (Iph, Rs, Rsh). Obtained values' using the Pasan software and GAs method are identical for Iph and

9. As we can see, theoretical curve fits very well experimental results.

differs of 1% for Rsh. However, value of Rs obtained with the Pasan software is 7.5 times that one obtained with GAs. Regarding the good fitting result in Fig. 9, and taking into account that the Rs effect on the I-V curve is in general observed for voltages near the Voc value, one can argue that the output value of Rs obtained with GAs is reasonable, but no conclusion can be done on the Rs value given by the Pasan software since no fitting is presented.

Fig. 9. Adjustment of the theoretical I-V curve of the solar cell's to the experimental one using GAs method.

Fig. 10. Mean and minimum values of the function versus generation number of the solar cell.

Application of the Genetic Algorithms

one, using Gas.

number (case of PV solar modules).

0.5

1

1.5

Cost

2

2.5

3

results of this minimization are shown in Table 2.

0

Experimental Theoretical

0.5

1

1.5

I(A)

2

2.5

for Identifying the Electrical Parameters of PV Solar Generators 361

In the case of the used PV module, the GAs-based fitting procedure of the theoretical I-V curve to the experimental one (achieved using the PV module tester shown in Fig. 11) gives a minimum value around 0.0676 A2 and was reached after only seven generations. The

Fig. 12. Adjustment of the theoretical I-V curve of the PV solar module to the experimental

0 2 4 6 8 10 12 14 16 18 20

Voltage V(V)

Min-cost Mean-cost

Fig. 13. The mean and the minimum values of the standard deviation versus generation

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>0</sup>

Generation number


Table 1. Comparison between the electrical parameters determined using GAs and those given by the Pasan CT 801 software in the case of the used solar cell.

#### **4.2 Determination of the PV module parameters**

For the module characterization, we use a homemade solar module tester. The system takes advantage of the quick response time of PV devices by illuminating and characterising the samples within a few milliseconds. The tester measures the complete I-V curve of the PV module by using a capacitor load (Sellami et al., 1998). In the meantime, it measures the illumination level, the temperature, the voltage and its corresponding current in order to minimize the quantification errors coming from ADC and DAC conversion. Data are then transferred to the computer that calculates the efficiency, the short circuit current, the open circuit voltage and the fill factor. The bloc diagram of the PV module tester is given in Fig. 11. We used a commercial 50 Wp PV module manufactured by ANIT-Italy. Testing was performed at 44°C and 873 W/m2 illuminations.

Fig. 11. Block diagram of the PV module tester.

The adjustment of the theoretical I-V curve of the PV module to the experimental one using GAs, and the mean and the minimum values of the cost function versus generation number are given in Fig. 12 and 13, respectively. In this simulation (PV module), we choose 125 chromosomes as IPOP and the predefined cost minimum is =0.0700 A2.

**Electrical parameters Pasan CT 801 Genetic Algorithms**  Is (A) Not performed 1.2170 10-2 Iph (A) 0.1360 0.1360 Rs (Ω) 0.2790 0.0363 Rsh (Ω) 99999 99050 *n* Not performed 1.0196

Table 1. Comparison between the electrical parameters determined using GAs and those

For the module characterization, we use a homemade solar module tester. The system takes advantage of the quick response time of PV devices by illuminating and characterising the samples within a few milliseconds. The tester measures the complete I-V curve of the PV module by using a capacitor load (Sellami et al., 1998). In the meantime, it measures the illumination level, the temperature, the voltage and its corresponding current in order to minimize the quantification errors coming from ADC and DAC conversion. Data are then transferred to the computer that calculates the efficiency, the short circuit current, the open circuit voltage and the fill factor. The bloc diagram of the PV module tester is given in Fig. 11. We used a commercial 50 Wp PV module manufactured by ANIT-Italy. Testing was

> **Photovoltaic module**

**Vv<sup>+</sup> Vv - Vi <sup>+</sup> Vi -**

**Electronic load**

**DAC**

**R**

**C**

The adjustment of the theoretical I-V curve of the PV module to the experimental one using GAs, and the mean and the minimum values of the cost function versus generation number are given in Fig. 12 and 13, respectively. In this simulation (PV module), we choose

125 chromosomes as IPOP and the predefined cost minimum is =0.0700 A2.

**ADC ADC ADC ADC**

**Industrial interface card / Computer**

**Illumination Voltage Current**

given by the Pasan CT 801 software in the case of the used solar cell.

**4.2 Determination of the PV module parameters** 

performed at 44°C and 873 W/m2 illuminations.

**Sensor Reference cell**

Fig. 11. Block diagram of the PV module tester.

**Temperature**

In the case of the used PV module, the GAs-based fitting procedure of the theoretical I-V curve to the experimental one (achieved using the PV module tester shown in Fig. 11) gives a minimum value around 0.0676 A2 and was reached after only seven generations. The results of this minimization are shown in Table 2.

Fig. 12. Adjustment of the theoretical I-V curve of the PV solar module to the experimental one, using Gas.

Fig. 13. The mean and the minimum values of the standard deviation versus generation number (case of PV solar modules).

Application of the Genetic Algorithms

powers.

**5. Conclusion** 

algorithms.

**6. References** 

obtained using a professional machine (Pasan CT 801).

for Identifying the Electrical Parameters of PV Solar Generators 363

Obtained results in the case of the PV cell using the Pasan software and the GAs are nearly identical. However, in the case of the PV module, our homemade system is able to measure I-V characteristics, but it is not equipped with sophisticated software to give the electrical characteristics of the module. Consequently, the measured I-V curve of the module is analysed only with the GAs method, and no comparison is performed as shown in table 3. The credibility of obtained results with the PV module is extrapolated from that one of the PV solar cell, where obtained results with the GAs technique are compared to those

**Cell** (using GAs) 0.137 0.571 0.078 **Cell** (using Pasan software V 3.0) 0.131 0.565 0.074 *Module (using GAs)* 2.120 14.200 30.104 Table 3. MPP's coordinates of the solar cell and the solar module and their corresponding

This chapter has studied the extraction of solar generators' (cell and module) parameters from the I-V characteristics under illumination. The main problem that has been addressed is the accuracy of the determined parameters with curve fitting by using optimisation

In this work, we proposed the genetic algorithms to extract PV solar cells electrical parameters. The determination of these parameters using experimental data was formulated in the form of a non convex optimization problem. The curve fitting by the Newton algorithm, conducts to less satisfactory results, which depend on the initial conditions leading to local minima solutions. We thus used the genetic algorithms (GAs) as an optimization tool in order to increase the probability to reach the global minima solutions. The algorithm for the identification of solar modules electrical parameters can be extended to multi-diode model. Furthermore, we can use a minimisation criterion based on the area difference between the experimental and theoretical characteristics. Moreover, hybrid algorithms which combine heuristic solutions as GAs and PSO (Particle Swarm

Bahgat, A. B. G., Helwa, N.H., Ahamd, G.E., El Shenawy, E.T., 2004. Estimation of the

Chan, Daniel S. H,. Phang, Jacob C. H., 1987, Analytical Methods for the extraction of Solar-

Charles, J. P., Abdelkrim, M., Muoy, Y. H., Mialhe, P., 1981. A practical method of analysis of the current voltage characteristics of solar cells. Solar cells, 4, p.169-178.

maximum power and normal operating power of a photovoltaic module by neural

Cell Single- and Double-Diode Model Parameters from I-V Characteristics, IEEE

Optimisation) with deterministic methods can be a powerful tool in the future.

Transactions on Electron Devices, Vol. ED-34, N°2, p. 286-293.

networks. Ren. Energy 29 (3), 443–457.

**Iopt (A) Uopt (V) MPP (W)** 


Table 2. Electrical parameters of the PV module obtained with GAs.

#### **4.3 Determination of the Maximum Power Point**

In order to extract the maximum available power from a PV cell, it is necessary to use it (the cell) at its maximum power point (MPP). Several MPP methods, such as perturbation, fuzzy control, power–voltage differentiation and on-line method have been reported (Dufo-Lopez and Bernal-Agustin, 2005; Bahgat et al., 2004; Yu et al., 2004). These control methods have drawbacks in stability and response time in the case when solar illumination changes abruptly. A direct MPP method using PV model parameters was introduced in (Yu et al., 2004). However, the validity of obtained result depends on the accuracy of the model parameters; i.e. the criterion for parameters extraction is not convex, and the traditional deterministic optimization algorithm used in (Yu et al., 2004) leads to local minima solutions. Indeed, in our case, we use the GAs, which belongs to heuristic solutions that represent a trade-off between solution quality and time. The GAs have a stochastic search procedure in nature, they usually outperform gradient based techniques in getting close to the global minima and hence avoid being trapped in local ones.

A derivative of the output power P with respect to the output voltage V is equal to zero at MPP.

$$\frac{dP}{dV} = I - V \left[ \frac{q}{nkT} \left( I\_{ph} + I\_s - I - \frac{V + R\_s I}{R\_{sh}} \right) + \frac{1}{R\_{sh}} \right] = 0$$

$$\left[ \frac{qR\_s}{1 + \frac{qR\_s}{nkT} \left( I\_{ph} + I\_s - I - \frac{V + R\_s I}{R\_{sh}} \right) + \frac{R\_s}{R\_{sh}}} \right] = 0 \tag{10}$$

If the parameters of the equivalent circuit model are given, MPP is obtained by solving Eq. (10) using standard numerical non-linear method. This can be easily achieved with the optimisation Toolbox of MATLAB software.

In table 3, we give the current and voltage values corresponding to the Maximum Power Points (MPP) obtained using Eq. (10) and the electrical parameters given in tables 1 and 2 identified by the GAs. The output results in the case of the solar cell are compared to those provided by the Pasan software. In the case of the cell (table 3), one can notice that our GAs simulations results differ at least by 5.3% from those given by the Pasan software. In general, the well used procedure to estimate the MPP in cell and module testers is based on the selection of the maximum power from an experimental set of current-voltage multiplication. The accuracy of this statistical approach depends on the precision of the experimental data, which should surround the real value of the MPP. However, our approach presents two advantages; first, it is based on Eq. (10), which is free of these experimental constrains. Secondly, Eq. (10) itself, uses the identified electrical parameters extracted by the GAs that belong to a sophisticated global search method.

Obtained results in the case of the PV cell using the Pasan software and the GAs are nearly identical. However, in the case of the PV module, our homemade system is able to measure I-V characteristics, but it is not equipped with sophisticated software to give the electrical characteristics of the module. Consequently, the measured I-V curve of the module is analysed only with the GAs method, and no comparison is performed as shown in table 3. The credibility of obtained results with the PV module is extrapolated from that one of the PV solar cell, where obtained results with the GAs technique are compared to those obtained using a professional machine (Pasan CT 801).


Table 3. MPP's coordinates of the solar cell and the solar module and their corresponding powers.

### **5. Conclusion**

362 Solar Cells – Silicon Wafer-Based Technologies

**Electrical parameters Values (GAs)**  Is (A) 8.1511 10-6 Iph (A) 2.4901 Rs (Ω) 0.9539 Rsh (Ω) 196.4081 *n* 60.4182

In order to extract the maximum available power from a PV cell, it is necessary to use it (the cell) at its maximum power point (MPP). Several MPP methods, such as perturbation, fuzzy control, power–voltage differentiation and on-line method have been reported (Dufo-Lopez and Bernal-Agustin, 2005; Bahgat et al., 2004; Yu et al., 2004). These control methods have drawbacks in stability and response time in the case when solar illumination changes abruptly. A direct MPP method using PV model parameters was introduced in (Yu et al., 2004). However, the validity of obtained result depends on the accuracy of the model parameters; i.e. the criterion for parameters extraction is not convex, and the traditional deterministic optimization algorithm used in (Yu et al., 2004) leads to local minima solutions. Indeed, in our case, we use the GAs, which belongs to heuristic solutions that represent a trade-off between solution quality and time. The GAs have a stochastic search procedure in nature, they usually outperform gradient based techniques in getting close to

A derivative of the output power P with respect to the output voltage V is equal to zero at

*<sup>s</sup> ph s*

*<sup>q</sup> V RI I II*

If the parameters of the equivalent circuit model are given, MPP is obtained by solving Eq. (10) using standard numerical non-linear method. This can be easily achieved with the

In table 3, we give the current and voltage values corresponding to the Maximum Power Points (MPP) obtained using Eq. (10) and the electrical parameters given in tables 1 and 2 identified by the GAs. The output results in the case of the solar cell are compared to those provided by the Pasan software. In the case of the cell (table 3), one can notice that our GAs simulations results differ at least by 5.3% from those given by the Pasan software. In general, the well used procedure to estimate the MPP in cell and module testers is based on the selection of the maximum power from an experimental set of current-voltage multiplication. The accuracy of this statistical approach depends on the precision of the experimental data, which should surround the real value of the MPP. However, our approach presents two advantages; first, it is based on Eq. (10), which is free of these experimental constrains. Secondly, Eq. (10) itself, uses the identified electrical parameters

*dP nkT R R*

*dV qR V RI R I II*

*<sup>s</sup> s s ph s*

*nkT R R*

1

*sh sh*

*sh sh*

0

(10)

Table 2. Electrical parameters of the PV module obtained with GAs.

the global minima and hence avoid being trapped in local ones.

1

extracted by the GAs that belong to a sophisticated global search method.

*I V*

optimisation Toolbox of MATLAB software.

MPP.

**4.3 Determination of the Maximum Power Point** 

This chapter has studied the extraction of solar generators' (cell and module) parameters from the I-V characteristics under illumination. The main problem that has been addressed is the accuracy of the determined parameters with curve fitting by using optimisation algorithms.

In this work, we proposed the genetic algorithms to extract PV solar cells electrical parameters. The determination of these parameters using experimental data was formulated in the form of a non convex optimization problem. The curve fitting by the Newton algorithm, conducts to less satisfactory results, which depend on the initial conditions leading to local minima solutions. We thus used the genetic algorithms (GAs) as an optimization tool in order to increase the probability to reach the global minima solutions.

The algorithm for the identification of solar modules electrical parameters can be extended to multi-diode model. Furthermore, we can use a minimisation criterion based on the area difference between the experimental and theoretical characteristics. Moreover, hybrid algorithms which combine heuristic solutions as GAs and PSO (Particle Swarm Optimisation) with deterministic methods can be a powerful tool in the future.

#### **6. References**


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Dufo-Lopez, Rodolfo, Bernal-Agustin, José L., 2005, Design and control strategies of PV-

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Enrique, J.M., Durán, E., Sidrach-de-Cardona, M., Andújar, J.M., 2007. Theoretical

Ikegami, T., Maezono, T., Nakanishi, F., Yamagata, Y., Ebihara, K., 2001. Estimation of

operation of PV system. Solar Energy Materials & Solar Cells, 67, 389-395. Ketter, Robert L., Prawel, Sherwood P., 1975. "Modern methods of engineering

Phang, Jacob C.H., Chan, S.H. Daniel., 1986. A review of curve fitting error criteria for solar

Sellami, A., Ghodbane, F., Andoulsi, R., Ezzaouia, H., 1998. An electrical performance tester

Sellami, A., Zagrouba, M., Bouaïcha, M., Bessaïs, B., Meas. Sci. Technol. 18 (2007) 1472–1476.

Yu, G.J., Jung, Y.S., Choi, J.Y., Kim, G.S., 2004. A novel two-mode MPPT control algorithm based on comparative study of existing algorithms. Sol. Energy 76, 455–463.

for PV modules. Proc. WREC (Florence, Italy) vol 3, pp 1717–1720.

Zagrouba, M., Sellami, A., Bouaïcha, M., Solar Energy Solar Energy 84 (2010) 860–866.

Diesel systems using genetic algorithms. Sol. Energy, 79, 33–46.

Haupt, R. L., Haupt, S. E., 1998. Practical Genetic Algorithms (New York: Wiley).

State Electronics, Vol. 28, N°8, p. 807-820.

computation"; Mac Graw-Hill book company. Pasan Cell Tester CT 801 operating manual., 2004, (www. pasan.ch).

cell I-V characteristics. Solar cells, 18, p.1-12.

Sze, S. M., ''Physics of Semiconductors Devices'', 2nd edition (1982).

Solar Energy, Vol.4, p.1-12.

1, Pages 31-38.

single and double exponential models for I-V characterization of solar cells. Solid-

algorithm for determining the solar cell parameters with microcomputers. Int. J.

assessment of the maximum power point tracking efficiency of photovoltaic facilities with different converter topologies. Solar Energy, Volume 81, Issue

equivalent circuit parameters of PV module and its application to optimal

### *Edited by Leonid A. Kosyachenko*

The third book of four-volume edition of 'Solar Cells' is devoted to solar cells based on silicon wafers, i.e., the main material used in today's photovoltaics. The volume includes the chapters that present new results of research aimed to improve efficiency, to reduce consumption of materials and to lower cost of wafer-based silicon solar cells as well as new methods of research and testing of the devices. Light trapping design in c-Si and mc-Si solar cells, solar-energy conversion as a function of the geometric-concentration factor, design criteria for spacecraft solar arrays are considered in several chapters. A system for the micrometric characterization of solar cells, for identifying the electrical parameters of PV solar generators, a new model for extracting the physical parameters of solar cells, LBIC method for characterization of solar cells, non-idealities in the I-V characteristic of the PV generators are discussed in other chapters of the volume.

Photo by PhonlamaiPhoto / iStock

Solar Cells - Silicon Wafer-Based Technologies

Solar Cells

Silicon Wafer-Based Technologies

*Edited by Leonid A. Kosyachenko*