**6. Top cell (AlAs/GaAs)**

Modeling of the top region may be performed in two ways, by considering the equivalent circuit of the device and/or by solving for excess carriers and subsequent electric currents and current densities in the solid state. In this brief outline we are considering the first

High Efficiency Solar Cells via Tuned Superlattice Structures: Beyond 42.2% 333

cell is a bulk (e.g. GaAs/AlAs cell) and the bottom is a superlattice-based pin cell optimized at long wavelengths. Such devices offer efficiency increase by acting simultaneously: top unit near 20% and bottom unit near 30% (when they operate on their own) lead to structures (quantum cells) with overall efficiencies in excess of 35% (under one sun and with recombination effects and scattering included). As seen in Figure 5 below, the superlattice approach offers a tool for capturing solar photons at desired wavelengths with the appropriate quantum mechanical tuning. In other words, ground eigen-states in quantum

wells match specific wavelengths (corresponding to photons with the same energy);

Fig. 6. Regions of the solar spectrum covered by the superlattice cell and the top cell (visible). The superlattice can be tuned at ~1 eV. Dashed arrows indicate region of feasible

As seen from the figure above, almost full spectrum absorption can be achieved with materials that absorb at desired photon energies. Specifically, visible photons may be absorbed by means of a GaAs/AlAs bulk cell, and IR radiation absorption can be achieved via GaAs (1.42 eV) and Ge (0.67 eV) respectively with superlattice or superlattice sections tuned at desired wavelengths. The n-region of the pin cell can be selected to be Ge in the bulk, ensuring absorption at the tail of the solar spectrum (for Ge: wavelength absorbed at = 1.24/0.67 = 1.85 m, see last arrow in the figure above). How is the current formed in the superlattice layer? The answer hides in the quantum nature of this region: quantum wells quantized the energy of the captured electrons (and light and heavy holes in the valence band); photo-excited electrons escape thermionically from the wells and form excess current in the conduction band. On the other hand, incident IR photons are expected to be absorbed in the MQW area. Projected excess carrier population (electrons with recombination

absorption from the superlattice region

approach by starting from the basic illuminated diode equation and adopting standard results regarding maximum power, short circuit current and open-circuit voltage values. Starting from the fundamental solar cell equation, we can derive maximum power conditions:

$$I\_m = \frac{\beta V\_m}{1 + \beta V\_m} I\_L \tag{20}$$

Where Im, Vm are maximum current and voltage values, and where = q (kT)-1. And

$$V\_m = V\_{oc} - \frac{1}{\beta} \ln(1 + \beta V\_m) \tag{21}$$

Efficiency (as power out over power in) is shown to be:

$$\eta = \frac{P\_o}{P\_u} = \frac{I\_L V\_{oc}}{P\_u} \left[ 1 - (\frac{V\_m}{V\_{oc}}) \frac{\ln(\beta V\_n)}{\beta V\_n} \right] \tag{22}$$

It is clear from (22) that the quantity in brackets is the fill factor (FF) of the device which is found based on maximum voltage values and open circuit voltage:

$$FF = 1 - \frac{\ln(\frac{V\_n}{kT})}{\left(\frac{V\_{oc}}{kT}\right)} = 1 - \frac{\ln(\beta V\_n)}{\beta V\_{oc}}\tag{23}$$

Highly efficient solar cells have been found to have open-circuit voltages within a range from 1 to 1.08V. The table below indicates how open circuit voltage controls maximum voltage (voltage at maximum power point). Assuming short circuit current at 30mA/cm2, under one-sun (100mW/cm2), the efficiency is depicted below by Table 1:


Table 1. Open circuit and maximum voltages, Fill Factor (FF) and collection efficiency (300 Kelvin). The cell is the top AlAs/GaAs that serves as a window to the solar flux.

It is of advantage to suggest an undoped GaAs-Ge multi-quantum well (MQW) in a standard pin-design, namely, p-intrinsic (MQW)-n geometry that includes lattice-matched GaAs and Ge layers in the intrinsic region of the PV device. This formation could offer the advantage of 1eV absorption (at the appropriate quantum well width), without compromises in device transport properties, such as mobility or conductivity. GaAs-based layers provide (a) high mobility and absorption values and (b) a chance for fine-tuning of the *optical gap* with *specific solar photon wavelength*. Recently, high efficiency cell designs have been proposed where two pn cells are grown in tandem (series connection), where the top

approach by starting from the basic illuminated diode equation and adopting standard results regarding maximum power, short circuit current and open-circuit voltage values. Starting from the fundamental solar cell equation, we can derive maximum power

1

Where Im, Vm are maximum current and voltage values, and where = q (kT)-1.

Efficiency (as power out over power in) is shown to be:

found based on maximum voltage values and open circuit voltage:

under one-sun (100mW/cm2), the efficiency is depicted below by Table 1:

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

<sup>1</sup> ln(1 ) *VV V m oc*

ln( ) 1( ) *o L oc <sup>m</sup> <sup>m</sup> in in oc m P IV V V PP V V*

ln( ) ln( ) 1 1

*oc oc*

It is clear from (22) that the quantity in brackets is the fill factor (FF) of the device which is

( )

*m*

Highly efficient solar cells have been found to have open-circuit voltages within a range from 1 to 1.08V. The table below indicates how open circuit voltage controls maximum voltage (voltage at maximum power point). Assuming short circuit current at 30mA/cm2,

Voc(V) Vm(V) FF (%) (%) 1.02 0.926 0.907 27.75 1.03 0.938 0.906 27.99 1.04 0.948 0.905 28.23 1.05 0.958 0.904 28.50

It is of advantage to suggest an undoped GaAs-Ge multi-quantum well (MQW) in a standard pin-design, namely, p-intrinsic (MQW)-n geometry that includes lattice-matched GaAs and Ge layers in the intrinsic region of the PV device. This formation could offer the advantage of 1eV absorption (at the appropriate quantum well width), without compromises in device transport properties, such as mobility or conductivity. GaAs-based layers provide (a) high mobility and absorption values and (b) a chance for fine-tuning of the *optical gap* with *specific solar photon wavelength*. Recently, high efficiency cell designs have been proposed where two pn cells are grown in tandem (series connection), where the top

Table 1. Open circuit and maximum voltages, Fill Factor (FF) and collection efficiency (300 Kelvin). The cell is the top AlAs/GaAs that serves as a window to the solar flux.

*V kT <sup>V</sup> FF <sup>V</sup> <sup>V</sup> kT*

*m*

> > *m*

(23)

*m m L m*

(20)

(22)

(21)

conditions:

And

cell is a bulk (e.g. GaAs/AlAs cell) and the bottom is a superlattice-based pin cell optimized at long wavelengths. Such devices offer efficiency increase by acting simultaneously: top unit near 20% and bottom unit near 30% (when they operate on their own) lead to structures (quantum cells) with overall efficiencies in excess of 35% (under one sun and with recombination effects and scattering included). As seen in Figure 5 below, the superlattice approach offers a tool for capturing solar photons at desired wavelengths with the appropriate quantum mechanical tuning. In other words, ground eigen-states in quantum wells match specific wavelengths (corresponding to photons with the same energy);

Fig. 6. Regions of the solar spectrum covered by the superlattice cell and the top cell (visible). The superlattice can be tuned at ~1 eV. Dashed arrows indicate region of feasible absorption from the superlattice region

As seen from the figure above, almost full spectrum absorption can be achieved with materials that absorb at desired photon energies. Specifically, visible photons may be absorbed by means of a GaAs/AlAs bulk cell, and IR radiation absorption can be achieved via GaAs (1.42 eV) and Ge (0.67 eV) respectively with superlattice or superlattice sections tuned at desired wavelengths. The n-region of the pin cell can be selected to be Ge in the bulk, ensuring absorption at the tail of the solar spectrum (for Ge: wavelength absorbed at = 1.24/0.67 = 1.85 m, see last arrow in the figure above). How is the current formed in the superlattice layer? The answer hides in the quantum nature of this region: quantum wells quantized the energy of the captured electrons (and light and heavy holes in the valence band); photo-excited electrons escape thermionically from the wells and form excess current in the conduction band. On the other hand, incident IR photons are expected to be absorbed in the MQW area. Projected excess carrier population (electrons with recombination

High Efficiency Solar Cells via Tuned Superlattice Structures: Beyond 42.2% 335

above 38% with latest threshold at 41.1% (Fraunhofer Institute, Germany). Currently, a cell that will operate above the 40% threshold is in target, with ultimate target the efficiency at or near 50%. The cell design is based on a p-i-n bulk device model with three distinct areas, two of which are complete PV-heterostructures on their own; in other words, these two regions could *stand alone* as *two independent solar cell structures with quite acceptable performance* (of the order of 21% and more as it has been demonstrated by our group recently). The power output of the PV composite device is a function of the individual power outputs from each sub-cell in the PV unit. On the other hand, triple junction solar cells seem to lead the way to high efficiency photovoltaics especially in the area of concentrated photovoltaics (CPV), where small cell area and therefore less material (hence lower material costs) may lead to high PV performance. The latter are triple junctions of lattice-matched and non-lattice matched III-V heterostructures with two tunnel junctions

Fully develop a theoretical model of PV composite PV devices by first principle calculations and computations based on realistic device parameters; propose a composite PV structure with two major cells: a triple junction and multi-layer tuned cell, with the prospect of high efficiency near 50%. Modeling tools include several established math software packages. Seek for a composite photovoltaic device that combines properties of direct-gap crystalline semiconductors and absorption in the entire spectrum, mainly in the visible and in the infrared (NIR/IR) wavelength ranges, and which is configured as a two-part solar cell: a top triple junction and a multi-layer p-i-n bottom unit tailored to IR infrared wavelengths. The solar spectrum (a 6,000 oK, see in Figure 5) offers the option of finding suitable band gaps for highest absorption. Material selection shows a blue shift in the absorption via wide gap materials as shown (AlAs). Low gap materials offer wavelength matching in the IR range (note the dashed arrows indicating optical gaps corresponding to various wavelengths. It is of advantage to exploit quantum wells grown on n-type or low-doped substrates.

Fig. 7. Tuned quantum wells at 1eV solar photons: shown are energy levels and optical gap

1-eV and optical gap

**GaAs** 

**Holes** 

**Electrons** 

between the layers.

increase

**7. Suggestions for modeling** 

included) is of the order of 1012 to 1013 cm-2 per eigen-state. Thermionic current density values have been found to be near order of 30mA/cm2 and open-circuit voltage values above 1V, at one sun. Overall (for a composite cell see figure 3) collection efficiency values are initially projected well in excess of 35%, which is a key for immediate improvement to even higher collection efficiency. Total current density is dominated by the lowest of the two sub-cell currents, and open-circuit voltage values are the sum of the two sub-cell Voc values. Total current from the bottom cell is the sum of thermionic and nearest neighbor hopping currents. Preliminary results reach estimates of efficiencies from each of the two (latticematched) sub-cells in excess of 21% per cell (predicted synergy of the two sub-cells in excess of 40%). Loss mechanisms at interfaces and quantum wells and their role in overall efficiency determination will also be included. Advantages of the design are:


Heterostructure and (most recently) multijunction solar devices exhibit better performance in transport properties, when compared to bulk solar cells: especially in quantum well devices, photo-excitation causes carrier accumulation in discrete energy levels, with subsequent escape to the conduction band (minus recombination losses) via standard mechanisms such as tunneling, thermal escape or nearest neighbor hopping conduction. Full spectrum absorption and triple junction solar cells have become key factors for high efficiency collection in PV structures of various geometries. Most recently, successful photovoltaic device (PV) designs have shown high efficiency values well above 30%, and efficiency levels in excess of 40% have been reached by means of triple junction metamorphic solar cells and under high sun concentration (good candidate for concentrated PV or CPV). Multijunction solar cells offer a great advantage over their bulk counterparts: by incorporating lattice-matched alloys, one may succeed in designing a device with more than one energy gaps thus increasing the number of absorbed solar photons. During the last decade, various groups have modeled and developed *multijunction* solar cells in order to increase overall collection efficiencies. Emphasis has been given in two types of PV devices (a) lattice-matched solar cells and (b) metamorphic (lattice-mismatched) solar cells. In particular, III-V multijunction solar cells have shown the greatest progress in overall efficiency. The broader impact of this project is a new design proposal for high efficiency solar cells. The target is to exceed 45% collection efficiency for very efficient photovoltaic devices. It is more than clear that once such a cell is realized, the field of concentration photovoltaics (CPV) will benefit greatly: solar cells with (a) record high efficiency values (b) under several hundred suns (Fresnel optics at 500+ suns) and (c) small in size (low area hence less material) is already attracting interest for mass production in many places in the world. In recent years, it has been proposed by us a new design for a high efficiency and lattice-matched solar cell (HESC), where both visible and infrared portions of the solar spectrum are absorbed according to the structure's geometric material arrangement: simultaneous absorption of both short and long wavelengths. In this on-going research enterprise, the synergy between a highly efficient triple junction cell and a highly efficient superlattice or a multi-quantum well region, is presented as a new and innovative way for further efficiency increase. It is well established by now, that triple junction solar cells are exceeding the upper threshold of collection efficiency to ever higher levels, namely above 38% with latest threshold at 41.1% (Fraunhofer Institute, Germany). Currently, a cell that will operate above the 40% threshold is in target, with ultimate target the efficiency at or near 50%. The cell design is based on a p-i-n bulk device model with three distinct areas, two of which are complete PV-heterostructures on their own; in other words, these two regions could *stand alone* as *two independent solar cell structures with quite acceptable performance* (of the order of 21% and more as it has been demonstrated by our group recently). The power output of the PV composite device is a function of the individual power outputs from each sub-cell in the PV unit. On the other hand, triple junction solar cells seem to lead the way to high efficiency photovoltaics especially in the area of concentrated photovoltaics (CPV), where small cell area and therefore less material (hence lower material costs) may lead to high PV performance. The latter are triple junctions of lattice-matched and non-lattice matched III-V heterostructures with two tunnel junctions between the layers.
