**7. Intermediate band solar cells based on quantum dot nanostructures**

In the previous section, we summarized how the operating voltage of nano-enhanced absorb‐ ers can be enhanced by suppressing the radiative dark current. In this section we will focus on the application of three dimensional quantum dot nanostructures in photovoltaics to increase the current output. Luque *et al*. [32] proposed that forming an intermediate band in a single junction photovoltaic cell can drastically enhance the energy conversion efficiency of the cell. The enhancement in efficiency is due to increased infrared light absorption via optical upconversion. This type of internally up-converting PV device is known as an intermediate band solar cell (IBSC). Figure 13 shows the band diagram of a PV cell with an intermediate band. This configuration will enable the absorption of two additional sub-bandgap photons in addition to one above bandgap photon. With proper design, the ultimate open circuit voltage should not be affected by the insertion of the intermediate band. Instead, the open circuit voltage will be equal to the separation between valance and conduction band quasi Fermi levels of the wider bandgap host material, independent of the intermediate band material, i.e Voc = μCV/q. Based on the IBSC theory, a maximum efficiency is possible when the host material bandgap is 1.93 eV with an intermediate band located at 0.7 eV. Semiconductor quantum dots (QDs) are perhaps the best choice to create an intermediate band in a single-junction solar cell due to the inherent tunability of their shape, size, and quantum confinement properties. For an IBSC to work properly, the QD system being used must satisfy certain conditions in terms of bandgaps and band alignments [32].

Many attempts have been made to realize IBSCs based upon QD nanostructures. Initially, QD systems such as InAs, InGaAs, and GaSb dots with GaAs as host material have been studied.

InAs and InGaAs QDs in GaAs exhibit a type I band alignment, while GaSb QDs in GaAs have a type II band alignment. In type I QDs, both electrons in the conduction band and holes in the valence band are confined. In type II QDs, only one type of carriers is confined, for example, in GaSb QDs only holes are confined and electrons are delocalized. Compared to Type I QDs, Type II QD systems offer advantages with longer carrier life times. But in GaSb QDs the high effective mass of holes puts the hole energy levels close to each other and making it difficult to achieve an intermediate band. This makes InAs/GaAs system more appropriate to demon‐ strate the operation of IBSC. So far, QDs used for IBSC study have been grown using a selfassembly process known as the Stranski–Krastanov (S-K) growth method. Molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD) systems are generally used to synthesize such QDs. InAs QDs grown using on GaAs are typically 5-7 nm tall and 25-30 nm wide with QD density ranging from 1010 – 1011 cm-2. Figure 14 shows the atomic force microscope (AFM) image of InAs QDs grown on GaAs and its distribution. The width of the intermediate band (∆ΕIB) formed by QD depends on the QD distribution. Larger QD distribu‐ tion leads to higher ∆ΕIB. Levy *et al*. calculated that highest cell efficiency results when ∆ΕIB ~ 825 meV [33]. material, independent of the intermediate band material, i.e Voc=CV/q. Based on the IBSC theory, a maximum efficiency is possible when the host material bandgap is 1.93 eV with an intermediate band located at 0.7 eV. Semiconductor quantum dots (QDs) are perhaps the best choice to create an intermediate band in a single-junction solar cell due to the inherent tunability of their shape, size, and quantum confinement properties. For an IBSC to work properly, the QD system being used must satisfy certain conditions in terms of bandgaps and band alignments [32]. Many attempts have been made to realize IBSCs based upon QD nanostructures. Initially, QD systems such as InAs, InGaAs, and GaSb dots with GaAs as host material have been studied. InAs and InGaAs QDs in GaAs exhibit a type I band alignment, while GaSb QDs in GaAs have a type II band alignment. In type I QDs, both electrons in the conduction band and holes in the valence band are confined. In type II QDs, only one type of carriers is confined, for example, in GaSb QDs only holes are confined and electrons are delocalized. Compared to Type I QDs, Type II QD systems offer advantages with longer carrier life times. But in GaSb QDs the high effective mass of holes puts the hole energy levels close to each otherand making it difficult to achieve an intermediate band. This makes InAs/GaAs system more

**VII. INTERMEDIATE BAND SOLAR CELLS BASED ON QUANTUM DOT NANOSTRUCTURES** 

In the previous section, we summarized how the operating voltage of nano-enhanced absorbers can be enhanced by suppressing the radiative dark current. In this section we will focus on the application of three dimensional quantum dot nanostructures in photovoltaics to increase the current output. Luque *et al*. [32] proposed that forming an intermediate band in a single junction photovoltaic cell can drastically enhance the energy conversion efficiency of the cell. The enhancement in efficiency is due to increased infrared light absorption via optical up-conversion. This type of internally up-converting PV deviceis known as an intermediate band solar cell (IBSC). Figure 13 shows the band diagram of a PV cell with an intermediate band. This configuration will enable the absorption of two additional sub-bandgap photons in addition to one above bandgap photon. With proper design, the ultimate open circuit voltage should

large. Step-graded structures could also potentially alter the strain profile in the well, and strain in quantum wells has been found to result in a non-isotropic radiation profile that may reduce overall radiative recombination losses [31]. The non-isotropic radiation profile resulting from strain is in many ways similar to that resulting from a reduction in the refractive index of the barrier material, and while potentially beneficial, would seem unlikely to account for the 2x

Step-graded structures may also provide a means of minimizing the overall recombination losses in quantum well solar cells. Faster escape rates can potentially be obtained by employing a step-graded compositional profile to allow photogenerated carriers to readily hop out of the InGaAs well [19], as illustrated in Figure 10. Enhanced extraction of hot carriers from the absorber region of a photovoltaic device has been suggested as a potential mechanism for reducing radiation losses and increasing efficiency [8]. Hot carrier effects can result in a large reduction in the radiative recombination, potentially reducing the B-coefficient by many orders of magnitude – see Figure 12 (b). Even a small effective carrier temperature difference of less than 1 kT is projected to result in more than a 2x reduction in the radiative dark current. Hot carrier effects can potentially be further enhanced by optimizing device design and employing

**7. Intermediate band solar cells based on quantum dot nanostructures**

In the previous section, we summarized how the operating voltage of nano-enhanced absorb‐ ers can be enhanced by suppressing the radiative dark current. In this section we will focus on the application of three dimensional quantum dot nanostructures in photovoltaics to increase the current output. Luque *et al*. [32] proposed that forming an intermediate band in a single junction photovoltaic cell can drastically enhance the energy conversion efficiency of the cell. The enhancement in efficiency is due to increased infrared light absorption via optical upconversion. This type of internally up-converting PV device is known as an intermediate band solar cell (IBSC). Figure 13 shows the band diagram of a PV cell with an intermediate band. This configuration will enable the absorption of two additional sub-bandgap photons in addition to one above bandgap photon. With proper design, the ultimate open circuit voltage should not be affected by the insertion of the intermediate band. Instead, the open circuit voltage will be equal to the separation between valance and conduction band quasi Fermi levels of the wider bandgap host material, independent of the intermediate band material, i.e Voc = μCV/q. Based on the IBSC theory, a maximum efficiency is possible when the host material bandgap is 1.93 eV with an intermediate band located at 0.7 eV. Semiconductor quantum dots (QDs) are perhaps the best choice to create an intermediate band in a single-junction solar cell due to the inherent tunability of their shape, size, and quantum confinement properties. For an IBSC to work properly, the QD system being used must satisfy certain conditions in terms

Many attempts have been made to realize IBSCs based upon QD nanostructures. Initially, QD systems such as InAs, InGaAs, and GaSb dots with GaAs as host material have been studied.

reduction in dark current observed in step-graded structures.

optical concentration [8].

264 Solar Cells - New Approaches and Reviews

of bandgaps and band alignments [32].

**Figure 13:**Schematic showing the bands involved in an intermediate band photovoltaic cell. The intermediate band is located between the conduction and valence bands of a barrier material. The open circuit voltage of this ideal cell is equal to the separation between the conduction and valence band quasi Fermi levels EFC and EFV. There are three transitions – valence band to conduction band, valence band to intermediate band, and intermediate band to **Figure 13.** Schematic showing the bands involved in an intermediate band photovoltaic cell. The intermediate band is located between the conduction and valence bands of a barrier material. The open circuit voltage of this ideal cell is equal to the separation between the conduction and valence band quasi Fermi levels EFC and EFV. There are three tran‐ sitions – valence band to conduction band, valence band to intermediate band, and intermediate band to conduction band – that contribute to the photocurrent.

19 conduction band – that contribute to the photocurrent. A typical QD, due to its small size, has a small absorption cross section for incident photons. Due to this fact, a large number of QD layers need to be stacked together to provide sufficient sub-bandgap photon absorption. These layers are separated by a barrier material also known as a spacer. To accommodate a large number of dot layers in a given intrinsic region thickness, very thin spacers are used. However, the accumulated strain due to stacking the thin spacer layers leads to the formation of defects and dislocations in the system. Figure 15 shows the high resolution TEM image of ten layers of InAs QDs on GaAs. A thin 15 nm spacer, which is not enough to de-couple strain between two successive dot layers, leads to dislocation formation. To avoid such effects due to QD stacking, a technique known as strain compensation has been adopted. In this technique, a tensile material with respect to both barrier and QD materials is inserted between two successive QD layers. GaP and GaAsN are widely used strain compensation materials for the InAs/GaAs system. appropriate to demonstrate the operation of IBSC. So far, QDs used for IBSC study have been grown

using a self-assembly process known as the Stranski–Krastanov (S-K) growth method. Molecular beam

Figure 16 shows a schematic illustrating the strain compensation process in a multi-layer QD system. In order to compensate the strain accumulated during the stacking process, a material with smaller lattice constant with respect to the buffer layers is introduced between two successive QD layers. This process reduces the effects caused by the strain buildup. The strain compensation material and its thickness should be selected such that the total elastic strain in the system is less than a critical value. The total elastic strain (Etotal) depends on the number of QD stacks (N), spacer thickness (tspacer) and the average strain (< *ε*⊥ >) in each QD layer, i.e Etotal < N. tspacer. < *ε*⊥ >. For example, the use of a 4 monolayer (ML) thick GaP strain compensation layer relieves ~36% of the compressive strain in the InAs/GaAs material system [34]. To achieve good quality material, either the spacer should be thick enough so that the successive QD layers are strain de-coupled, or strain compensation layers must be employed. Strain compensation has been successfully implemented in photonic devices such as lasers and photovoltaic cells [29, 35-38]. epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD) systems are generally used to synthesize such QDs. InAs QDs grown using on GaAs are typically 5-7 nm tall and 25-30 nm wide with QD density ranging from 1010 – 1011 cm-2. Figure 14 shows the atomic force microscope (AFM) image of InAs QDs grown on GaAs and its distribution. The width of the intermediate band (IB) formed by QD depends on the QD distribution. Larger QD distribution leads to higher IB. Levy *et al*. calculated that highest cell efficiency results when IB ~ 825 meV [33]. A typical QD, due to its small size, has a small absorption cross section for incident photons. Due to this fact, a large number of QD layers need to be stacked together to provide sufficient sub-bandgap photon absorption. These layers are separated by a barrier material also known as a spacer. To accommodate a large number of dot layers in a given intrinsic region thickness, very thin spacers are used. However, the accumulated strain due to stacking the thin spacer layers leads to the formation of defects and dislocations in the system. Figure 15 shows the high resolution TEM image of ten layers of InAs QDs on GaAs. A thin 15 nm spacer, which is not enough to de-couple strain between two successive dot layers, leads to dislocation formation. To avoid such effects due to QD stacking, a technique known as strain compensation has been adopted. In this technique, a tensile material with respect to both barrier and QD materials is inserted between two successive QD layers. GaP and GaAsN are widely used strain compensation materials for the InAs/GaAs system. Figure 16 shows a schematic illustrating the strain compensation process in a multi-layer QD system. In

order to compensate the strain accumulated during the stacking process, a material with smaller lattice constant with respect to the buffer layers is introduced between two successive QD layers. This process

strain driven process, a variation in QD size is expected. The FWHM of the distribution can be reduced with careful optimization of growth conditions. **Figure 14.** (a) Atomic force microscope image of InAs/GaAs QDs grown via the Stranski–Krastanov growth mode us‐ ing MBE, and b) the resulting QD height distribution. As the formation of these QD is a strain driven process, a varia‐ tion in QD size is expected. The FWHM of the distribution can be reduced with careful optimization of growth conditions.

**Figure 14: a)** Atomic force microscope image of InAs/GaAs QDs grown via the Stranski–Krastanov growth mode using MBE, and **b)** the resulting QD height distribution. As the formation of these QD is a

layers leads to the formation of defects and dislocations in the system. Figure 15 shows the high resolution TEM image of ten layers of InAs QDs on GaAs. A thin 15 nm spacer, which is not enough to de-couple strain between two successive dot layers, leads to dislocation formation. To avoid such effects due to QD stacking, a technique known as strain compensation has been adopted. In this technique, a tensile material with respect to both barrier and QD materials is inserted between two successive QD layers. GaP and GaAsN are widely used strain

Figure 16 shows a schematic illustrating the strain compensation process in a multi-layer QD system. In order to compensate the strain accumulated during the stacking process, a material with smaller lattice constant with respect to the buffer layers is introduced between two successive QD layers. This process reduces the effects caused by the strain buildup. The strain compensation material and its thickness should be selected such that the total elastic strain in the system is less than a critical value. The total elastic strain (Etotal) depends on the number of QD stacks (N), spacer thickness (tspacer) and the average strain (< *ε*⊥ >) in each QD layer, i.e Etotal < N. tspacer. < *ε*⊥ >. For example, the use of a 4 monolayer (ML) thick GaP strain compensation layer relieves ~36% of the compressive strain in the InAs/GaAs material system [34]. To achieve good quality material, either the spacer should be thick enough so that the successive QD layers are strain de-coupled, or strain compensation layers must be employed. Strain compensation has been successfully implemented in photonic

appropriate to demonstrate the operation of IBSC. So far, QDs used for IBSC study have been grown using a self-assembly process known as the Stranski–Krastanov (S-K) growth method. Molecular beam epitaxy (MBE) and metal organic chemical vapor deposition (MOCVD) systems are generally used to synthesize such QDs. InAs QDs grown using on GaAs are typically 5-7 nm tall and 25-30 nm wide with QD density ranging from 1010 – 1011 cm-2. Figure 14 shows the atomic force microscope (AFM) image of InAs QDs grown on GaAs and its distribution. The width of the intermediate band (IB) formed by QD depends on the QD distribution. Larger QD distribution leads to higher IB. Levy *et al*. calculated that

A typical QD, due to its small size, has a small absorption cross section for incident photons. Due to this fact, a large number of QD layers need to be stacked together to provide sufficient sub-bandgap photon absorption. These layers are separated by a barrier material also known as a spacer. To accommodate a large number of dot layers in a given intrinsic region thickness, very thin spacers are used. However, the accumulated strain due to stacking the thin spacer layers leads to the formation of defects and dislocations in the system. Figure 15 shows the high resolution TEM image of ten layers of InAs QDs on GaAs. A thin 15 nm spacer, which is not enough to de-couple strain between two successive dot layers, leads to dislocation formation. To avoid such effects due to QD stacking, a technique known as strain compensation has been adopted. In this technique, a tensile material with respect to both barrier and QD materials is inserted between two successive QD layers. GaP and GaAsN are widely used strain

Figure 16 shows a schematic illustrating the strain compensation process in a multi-layer QD system. In order to compensate the strain accumulated during the stacking process, a material with smaller lattice constant with respect to the buffer layers is introduced between two successive QD layers. This process

21

**Figure 14: a)** Atomic force microscope image of InAs/GaAs QDs grown via the Stranski–Krastanov growth mode using MBE, and **b)** the resulting QD height distribution. As the formation of these QD is a strain driven process, a variation in QD size is expected. The FWHM of the distribution can be reduced

**Figure 14.** (a) Atomic force microscope image of InAs/GaAs QDs grown via the Stranski–Krastanov growth mode us‐ ing MBE, and b) the resulting QD height distribution. As the formation of these QD is a strain driven process, a varia‐ tion in QD size is expected. The FWHM of the distribution can be reduced with careful optimization of growth

5 10 15 20 25 QD Height (nm)

**(19.31.5) nm**

**8%**

compensation materials for the InAs/GaAs system.

266 Solar Cells - New Approaches and Reviews

devices such as lasers and photovoltaic cells [29, 35-38].

200nm

**a) b)** 

with careful optimization of growth conditions.

800nm

conditions.

compensation materials for the InAs/GaAs system.

highest cell efficiency results when IB ~ 825 meV [33].

**Figure 15.** Cross-sectional TEM image of 10 stacks of InAs/GaAs QD grown by MOCVD with 15 nm spacers. In this structure, the use of thin spacer layers results in formation of unwanted dislocations [34].

**Figure 16.** Schematic showing the implementation of strain compensation in a QD structure. Self-assembled QDs are formed due to compressive strain between QD and buffer materials. During the process of stacking QD layers, a mate‐ rial with smaller lattice constant (tensile with respect to buffer) is inserted between two successive QD layers to avoid strain induced effects.

Figure 17 shows a strain-compensated GaAs *p*-*i*-*n* photovoltaic cell in which 3 layers of InAs QD layers with a 29 nm GaAs spacer are inserted [38]. A 4 ML GaP strain compensation layer between two successive QD layers is also included here. One can easily study the affect of strain compensation by measuring PL from the stacked QD samples (transmission electron

**Figure 17.** Schematic representation of an InAs/GaAs quantum dot photovoltaic device stucture with 3 QD layers that employ 4 ML GaP layers for strain compensation [38].

microscope and atomic force microscope also help in such study but are more destructive, expensive and time consuming). The PL measurements conducted on QDs alone are presented in Figure 18. The sample without GaP strain compensation has poor PL emission compared to that of the sample with strain compensation. This is indicative of poor material quality and increased defect density. PL from the sample without stain compensation also shows a bimodal distribution which indicates a large variation in dot size due to strain.

The electrical characteristics of QD photovoltaic cells with and without strain compensation have been studied via current-voltage (I-V) and quantum efficiency measurements. The I-V characteristics of InAs/GaAs QD PV cell structures (Figure 17) are compared in Figure 19. It is evident from the figure that the cell without strain compensation performs poorly when compared to other cells. In this study, three different GaP strain compensation schemes are chosen, i.e. 2 ML, 4 ML and 2ML+2ML (with 5 nm GaAs in between). It is observed from the data that both 4ML and 2ML+2ML samples behave in similar ways with the latter showing slightly better current. This observation is also supported by EQE data shown in Figure 20. The devices with QDs in their active regions show an extended photoresponse compared to the device without QDs. For a higher number of QD layers in the PV cell, a careful optimization of strain compensation layers is needed. Though this I-V data shows a drop in VOC with the insertion of QDs in the PV cells, it is possible to develop QD cells with minimal voltage drop. Bailey *et al*. have demonstrated that by carefully tuning the QD and strain compensation material thicknesses, the VOC can approach 1 V, comparable to that of the GaAs control cell [39].

**Figure 18.** Photoluminescence spectra from 3 layers of stacked InAs QDs with (circles) and without (solid) strain com‐ pensation layers. It is obvious from these spectrums that including proper strain compensation layers improves the material quality.

microscope and atomic force microscope also help in such study but are more destructive, expensive and time consuming). The PL measurements conducted on QDs alone are presented in Figure 18. The sample without GaP strain compensation has poor PL emission compared to that of the sample with strain compensation. This is indicative of poor material quality and increased defect density. PL from the sample without stain compensation also shows a bimodal

**Figure 17.** Schematic representation of an InAs/GaAs quantum dot photovoltaic device stucture with 3 QD layers that

The electrical characteristics of QD photovoltaic cells with and without strain compensation have been studied via current-voltage (I-V) and quantum efficiency measurements. The I-V characteristics of InAs/GaAs QD PV cell structures (Figure 17) are compared in Figure 19. It is evident from the figure that the cell without strain compensation performs poorly when compared to other cells. In this study, three different GaP strain compensation schemes are chosen, i.e. 2 ML, 4 ML and 2ML+2ML (with 5 nm GaAs in between). It is observed from the data that both 4ML and 2ML+2ML samples behave in similar ways with the latter showing slightly better current. This observation is also supported by EQE data shown in Figure 20. The devices with QDs in their active regions show an extended photoresponse compared to the device without QDs. For a higher number of QD layers in the PV cell, a careful optimization of strain compensation layers is needed. Though this I-V data shows a drop in VOC with the insertion of QDs in the PV cells, it is possible to develop QD cells with minimal voltage drop. Bailey *et al*. have demonstrated that by carefully tuning the QD and strain compensation material thicknesses, the VOC can approach 1 V, comparable to that of the GaAs control cell [39].

distribution which indicates a large variation in dot size due to strain.

employ 4 ML GaP layers for strain compensation [38].

268 Solar Cells - New Approaches and Reviews

Figure 19. Current-voltage characteristics of InAs/GaAs QD photovoltaic cell with 3 QD layers. GaP has been used for compensating strain. A 2ML+2ML GaP with 5 ML separation provides best compensation **Figure 19.** Current-voltage characteristics of InAs/GaAs QD photovoltaic cells with 3 QD layers. GaP has been used for compensating strain. A 2ML+2ML GaP with 5 ML separation provides best compensation.

**Figure 20.** External quantum efficiency characteristics of photovoltaic cells fabricated with and without strain compen‐ sation layers. Clearly, the devices with strain compensation outperform the device without compensation.
