Inverted Metamorphic III – V Triple-Junction Solar Cell with a 1 eV CuInSe 2 Bottom Subcell

(1 eV) which can be grown on a GaAs substrate in an inverted manner using epitaxial lift-off techniques. To lattice-match epitaxial CuInSe 2 to Ga(In)As, a compositionally graded buffer region composed of GaxIn1−xP is used. The modeling and simulation of the device include the effects of threading dislocations on minority carrier lifetimes in the metamorphic buffer and bottom subcell active region. Studies focus on device performance under standard testing conditions and concentrated illumination.The results are compared to a reference latticemismatched 3J composed ofGaInP (1.9 eV)/Ga(In)As (1.4 eV)/GaInAs (1 eV) and to a latticematched 3J composed of GaInP (1.9 eV)/Ga(In)As (1.4 eV)/Ge (0.67 eV).The advantage of CuInSe 2 is its higher absorption coefficient, which requires only 1 μm of active material compared to 4 μm of GaInAs in the bottom subcell of the reference lattice mismatched cell. The proposed design reaches an efficiency of 32.6% under 1 sun illumination at 300K with 10 cm threading dislocations and 39.6% at 750 suns.


Introduction
The area of research and development in photovoltaic device technologies has led to significant increases in power conversion efficiencies from 17% to 44.4% since 1983 [1].The example of current state-of-the-art triplejunction solar cells (3Js) composed of III-V semiconductor materials is the bandgap engineered lattice matched (LM) Ga 0.44 In 0.56 P/Ga 0.92 In 0.08 As/Ge solar cell.This cell has achieved efficiencies greater than 40% under concentrated illumination [2] despite a nonoptimal bandgap of the germanium bottom subcell leading to a significant overproduction of photocurrent and thereby limiting the device's efficiency.
For more ideal current matching, a metamorphic lattice mismatched (LMM) 3J design composed of GaInP (1.9 eV)/Ga(In)As (1.4 eV)/Ga 0.7 In 0.3 As (1.0 eV) has been proposed [2], where the Ge bottom subcell has been replaced with the LMM ternary alloy Ga 0.7 In 0.3 As (hereafter referred to as GaInAs).To maintain high crystalline material quality, the device requires an inverted growth on a GaAs substrate such that the formation of threading dislocations resulting from the LMM induced strain is confined within a compositionally graded buffer (CGB) region located away from the active regions of the middle and top subcells [3,4].Epitaxial lift-off techniques of the active regions of the device from the GaAs substrate also allow for the reuse of the substrate which further reduces the costs associated with this complex 3J design architecture.
Here we suggest a similar approach to integrate a lower cost epitaxial material CuIn 1−x Ga x Se 2 (CIGS) as a bottom subcell in a 3J, as shown in Figure 1.To reach the desired bandgap of 1.0 eV for the bottom cell, the stoichiometry of the CIGS subcell must be close to  = 0 or -CuInSe 2 , with ∼25% Cu.The proposed epitaxial growth methods of chalcopyrite CuInSe 2 on a GaAs substrate with (001) orientation follow the methods described by Liao and Rockett using a hybrid cosputtering and coevaporation technique using two magnetron sputterers [5], whereas standard metalorganic chemical vapor deposition techniques are adopted for the III-V semiconductors.The design of the 3J is outlined in   Figure 2 and consists of a top GaInP subcell, with the middle Ga(In)As and bottom CuInSe 2 subcells interconnected by tunnel junctions (TJ).The aim of this paper is to investigate the potential benefits of this material system as the third subcell of a 3J for concentrated photovoltaic (CPV) applications using TCAD Sentaurus by Synopsys version vG-2012 (Mountain View, California) [6].As demonstrated in this paper, a key advantage of replacing the GaInAs (1 eV) as bottom subcell with CuInSe 2 with the same bandgap is a reduction of ∼20% in total cell material thickness, and the cheaper cost of the chalcopyrite elements compared to GaInAs.This work is a continuation of our numerical modeling work on CIGS solar cells [7].
The paper is outlined as follows.Section 2 discusses the growth considerations of integrating III-V and I-III-VI semiconductors, including details of the proposed structure.Section 3 outlines the important properties of the relevant materials and describes models of CGB region and the GaInAs/CuInSe 2 interface based on threading dislocations and surface recombination, respectively.Section 4 then focuses on the simulation results of the proposed 3J under both standard testing conditions and concentrated illumination at 300 K.The simulation results are compared to the aforementioned LMM and LM 3Js, whose structures are described in Sections 2.2 and 2.3 respectively.Section 5 then gives the conclusions and implications of this study.

Structures
2.1.CuInSe 2 3J.The growth of epitaxial CuInSe 2 on GaAs has been demonstrated previously in the literature for photovoltaic applications [9,10] and in an effort to improve the understanding of the fundamental properties of epitaxial CuInSe 2 [11,12].In [10], a CuInSe 2 single junction solar cell epitaxially grown on a GaAs substrate was reported to achieve an efficiency of 6.3%.A possible reason for the low power conversion efficiency reported is the lattice mismatch between GaAs and CIG  , which induced the interdiffusion of Ga into CIG  .This resulted in a strong increase in Ga content near GaAs/CIGS interface.The quality of CIGS with such stoichiometries has been argued to induce significant levels of nonradiative recombination as a result of defects with a wide range of energies within the bandgap [8,[13][14][15] region composed of III-V semiconductors to lattice match GaAs to CuInSe 2 .
A candidate for the CGB material is the ternary alloy Ga x In 1−x As based on its ability to be grown with high quality as demonstrated in the LMM GaInP/Ga(In)As/Ge cell [3].However, it would not be optically transparent for the CuInSe 2 subcell in the proposed 3J cell.The quaternary alloy AlInGaAs has been also discussed as a CGB [16]; however, it has been shown to be difficult to grow with high quality, and the optical and electrical properties for this material have not been thoroughly reported in the literature.Therefore, the proposed bottom CuInSe 2 subcell design consists of an n-type CGB region composed of the high bandgap material Ga x In 1−x P. The growth of 7 layers of a Ga x In 1−x P CGB region has been successfully demonstrated in a 3J with misfit dislocations localized within the CGB region with densities below 1 × 10 6 cm −2 [4].A 1 m overshooting layer composed of Ga 0.25 In 0.75 P was grown on the 7 CGB layers for the active region of the bottom subcell to remain nearly defect free [17].
The details of the structure are outlined in Figure 2, and the relevant material lattice constants are depicted in Figure 3 as a function of their respective molar fractions [18].The structure consists of a top GaInP (1.9 eV) subcell in an n-i-p homojunction configuration with the higher bandgap quaternary alloy (Al 1−x Ga x ) 0.51 In 0.49 P forming front and back surface fields (FSF and BSF, resp.).A high bandgap Al 0.3 Ga 0.7 As/Al 0.3 Ga 0.7 As tunnel junction (TJ) then interconnects the top subcell to an Ga(In) As n-i-p subcell [19,20].Similarly, an Al 0.3 Ga 0.7 As/GaAs TJ interconnects the middle GaInAs to the Ga x In 1−x P CGB layers (as described above) followed by a bottom n-p heterojunction.The bottom subcell in the proposed design would consist of n-In 0.3 Ga 0.7 As and a p-type base composed of CuInSe 2 with a CuInSe 2 back surface field equivalently doped to 1 × 10 18 cm −3 ; the doping of CuInSe 2 to such levels has been demonstrated previously [11].A selective wet etch and lift-off technique can be used to detach the GaAs substrate from the top GaInP subcell using hydrofluoric acid by dissolving an AlAs release layer (see Figure 1) [21].The stack of III-V semiconductor layers including the CuInSe 2 bottom subcell can be bonded to a deposited on a flexible handle prior to lift off for subsequent solar cell device fabrication and processing using standard photolithography and metal deposition techniques.A highly doped GaAs cap layer is used to make an ohmic top contact with the top subcell and an Au/Ti bottom contact for contacting to the CuInSe 2 subcell.A dual layered broadband antireflection coating (ARC) composed of MgF 2 /TiO x is deposited on the structure to minimize incident light reflection (0.1 m/0.06m thick resp.).

GaInAs LMM 3J.
The reference LMM 3J is composed of GaInP (1.9 eV)/Ga(In)As (1.4 eV)/GaInAs (1 eV) and is identical to the structure in Figure 2 with the exception of the bottom subcell active region which is composed of Ga 0.7 In 0.3 As (1 eV) with a 4 m base for current matching.The BSF composed of Ga 0.25 In 0.75 P is used, since a highly doped GaInAs BSF resulted in a poor FF of the device under high concentration.The top and middle subcell base thicknesses are optimized to obtain the highest efficiency, and the top subcell bandgap is set to 1.9 eV.The details of the CGB are also identical to Figure 2 to allow for a better device comparison to the CuInSe 2 3J.

Ge LM 3J.
Similarly, the LM design composed of GaInP (1.9 eV)/Ga(In)As (1.4 eV)/Ge(0.67eV) is identical to Figure 2 for the top and middle subcells with the exception of their base thicknesses (based on current matching).Furthermore, no CGB is required for the bottom Ge subcell.Instead, the Ge subcell is composed of a Ga 0.99 In 0.01 As buffer layer followed by a Ga 0.51 In 0.49 P FSF and a Ge homojunction on a Ge substrate.

Numerical Model
3.1.Model.The semiconductor simulation software TCAD Sentaurus is used to specify the 3J structure of interest and solve the set of coupled differential equations consisting of Poisson's equation and the electron and hole currentcontinuity equations with thermionic emission as boundary conditions for heterointerfaces.These equations consider generation computed using the transfer matrix method, and radiative, Shockley-Read-Hall and Auger recombination using standard recombination formalisms [6]; surface recombination is implemented at the relevant heterointerfaces and is discussed in more detail in Section 3.3.The tunnel junctions are modeled based on [19,20].Details on the numerical modeling environment and its applications to 3J can be found elsewhere [7,19,20,22,23].

Material Properties.
The most important properties for CIGS and Ga x In 1−x P as a function of molar fraction include (1) the bandgap and electron affinity at room temperature, (2) the optical properties in terms of refractive index and  1, where a molar fraction-dependent expression for carrier mobilities is developed for GaInP based on interpolation schemes for  = 0, 0.51, and 1 using data from [30].The material properties for the remaining III-V semiconductor materials can be found elsewhere [23], with the specific data for GaInAs obtained from the literature for bandgap [35], electron affinity [35], effective density of states [18], carrier mobilities [30], optical data based on interpolation between GaAs [34] and InAs [36], and lastly, minority carrier recombination lifetimes for radiative [37], for Shockley-Read-Hall [38], and for Auger [18].It is assumed that carrier mobilities are not significantly influenced by threading dislocations for densities below 10 8 cm −2 [39].A closeup of the bottom subcell is shown in Figure 4(b) which shows 7 CGB layers and the overshoot layer based on [17].The background doping of the CGB is set to 5 × 10 15 cm −3 as a representation of a realistic unintentional background doping, although the device shows no dependence on this doping level under standard testing conditions.The mesh density in these layers is set to be sufficiently large to resolve the appropriate current transport phenomena.Minimal band offsets are present at the GaInAs/CuInSe 2 interface due to the similar electron affinities and bandgaps based on typical heterostructure band alignment considerations.No bandgap narrowing is considered in the model for CuInSe 2 .

Modeling the Compositionally Graded Buffer
The effects of threading dislocations on current transport are also considered in the model by effectively modifying the minority carrier Shockley-Read-Hall (SRH) lifetimes parameterized by the threading dislocation density (TDD), as described in [40] and adopted in [41] to model a III-V semiconductor based 3J grown on a Si substrate.The modified SRH lifetime can be expressed as where  is the diffusion coefficient which considers the doping dependent mobility of the material through the Einstein relation,  SRH is the doping-dependent SRH recombination lifetime with no TDD affects (see Table 1), and [TDD] is the threading dislocation density in units of cm −2 .In both CuInSe 2 and LMM 3J structures, the effects of TDDs are considered in both the CGB (TDD CGB ) and the active region of bottom cell (TDD bot ).Since LM 3J is lattice matched it is assumed that there is minimal formation of TDD in this structure.The effective lifetimes for carriers in CuInSe 2 and for GaInAs are illustrated in Figure 5 as a function of TDD, where a threshold density is defined as one which reduces the effective lifetime by a factor of 2. Lastly, each interface of the complete structure considers surface recombination which is parameterized using a surface recombination velocity (SRV) according to the standard interface recombination formalism [6].Lattice matched interfaces are assumed to have SRV < 10 3 cm/s due to minimal strain and ideal growth conditions.However, the quality of the CGB is expected to affect the GaInAs/CuInSe 2 interface quality, and a SRV is also associated with this interface.To reduce the parameter space of this study and to target an ideal yet realistic lattice matched interface quality, a fixed surface recombination velocity of 10 3 cm/s is implemented for the GaInAs/CuInSe 2 interface of the CuInSe 2 3J and for the GaInAs/GaInAs interface of the LMM 3J.However, note that the interface recombination occurring within the CGB region is not important since majority carriers dominate the transport.TDD in the bottom subcell.The TDD CGB is fixed to 10 6 cm −2 although this has no influence on the performance of the device because transport is a majority carrier phenomenon.For comparison, the J-V characteristics for the simulated LM and LMM 3Js are also included, the latter calculated with TDD CGB = 10 6 cm −2 and a TDD bot = 10 5 cm −2 in the active bottom subcell to outline near-ideal characteristics.The AM1.5D spectrum is normalized to 1000 W cm −2 scaled from the ASTM G173-03.

Simulation Results
The EQE of the top GaInP subcell has a comparable albeit high response in the UV to other published data [42], with its squareness in the long wavelength range attributed to its optically thick base.The absorption range of the top subcell is limited by the bandgap close to 650 nm (  = 1.9 eV).The high response in the UV is due primarily to surface recombination at the top interfaces of the GaInP subcell (∼10 6 cm/s), in agreement with Haas et al. [29].Dopingdependent SRH minority carrier lifetime parameters can provide further calibration of the top subcell EQE in terms of agreement with experiment.The n-i-p design of the top subcell coupled to the low reflectivity of the ARC allows for a large carrier collection probability, or in other words, a magnitude in EQE (>90%).Similarly, the middle Ga(In)As subcell EQE is large in magnitude due to its n-i-p design and low reflectivity.Its EQE is nonzero primarily in the wavelength range of 650 to 880 nm and corresponds to the bandgaps of GaInP (1.9 eV) and Ga(In)As (1.4 eV).One can observe the minimal current sharing between the top and middle subcells.However, the middle subcell base is designed to share photons with the bottom CuInSe 2 subcell to enhance the overall device fill factor since the CuInSe 2 individual subcell's FF is low (69%).Only 1 m of active CuInSe 2 is required to obtain a photocurrent of 15 mA/cm 2 and drops for larger base thicknesses due to etalon effects within this subcell.The EQE of the bottom CuInSe 2 sub-cell ranges from the Ga(In)As bandgap and its own (1.0 eV).As the TDD bot is increased beyond a threshold density of 10 6 cm −2 , the EQE of the CuInSe 2 subcell decreases as it is the only subcell affected.It degrades by up to 30% absolute in the long wavelength region as seen in Figure 6(a) for a TDD bot = 10 7 cm −2 .This drop corresponds to half the minority carrier lifetime (see Figure 5).
Interestingly, one can notice on the J-V curves outlined in Figure 6(b) that the  sc of CuInSe 2 3J remains constant for increasing TDD bot up to 10 7 cm −2 .The lack of degradation of this metric is due to the shunt-like behavior of the CuInSe 2 subcell in reverse bias.The photocurrent of  Figure 6: (a) Simulated EQE and (b) J-V characteristics of the CuInSe 2 3J for increasing levels of TDD bot in the bottom subcell at 1000 W/m 2 intensity and 300 K; a fixed TDD CGB of 10 6 cm −2 is adopted with SRV of 10 3 cm/s at the relevant CGB interfaces.The J-V characteristics of the LMM and LM devices are shown for comparison, with the LMM device having a TDD bot = 10 5 cm −2 in the active region but a TDD CGB = 10 6 cm −2 .the device is thus maintained for increasing TDD bot with a significant degradation in both  oc and FF as a result of the bottom subcell being internally reverse biased.The increased SRH recombination occurring in the bottom subcells of the CuInSe 2 and LMM 3J designs as the TDD bot increase also strongly impacts their respective performance metrics due to the shorter minority carrier lifetime (see Section 3.3).Though not included, the EQE of the LMM device degrades in a similar fashion to the CuInSe 2 3J for increasing TDD bot .The performance metrics of each design are summarized in Table 2 for a fixed TDD bot of 10 6 cm −2 .Figures 7(a)-7(d) illustrate the J-V metrics ( sc ,  oc , FF and ) for the CuInSe 2 3J compared to those of the LMM and LM 3J devices as a function of TDD bot .The results for the LM 3J J-V metrics are constant as a function of TDD bot since no TDD is considered in the structure assuming ideal strain management.The photocurrent of the CuInSe 2 3J demonstrates a deterioration of 1.9% absolute over the complete range of TDD bot studied, in agreement with the results from Figure 6(b).Comparatively, the photocurrent of the LMM device degrades 16.7% since its bottom GaInAs subcell does not have the same shunt-like behavior as the CuInSe 2 subcell.The LM device has a 1.8% higher photocurrent than the other two 3Js since there is less current sharing to the Ge subcell.On the other hand, the CuInSe 2 and LMM 3Js have a higher top subcell bandgap for more optimal current matching considerations in an effort to maximize each device's fill factor.
With respect to the open circuit voltage, Figure 7(b) illustrates a strong degradation for both the CuInSe 2 and LMM 3Js beyond their respective threshold densities of 10 6 cm −2 and 3 × 10 4 cm −2 , since the SRH recombination increases inversely with the minority carrier lifetime (see Figure 5).The respective threshold TDDs are primarily dependent on the bulk SRH lifetime of the material.For the CuInSe 2 3J, increasing the TDD bot from 10 6 cm −2 to 7 × 10 7 cm −2 results in a 5.8% absolute drop in  oc , whereas the LMM device's  oc degrades by 9.3% from 10 4 cm −2 to 7 × 10 7 cm −2 .For the same TDD bot of 10 6 cm −2 , the LMM 3J has a  oc that is 3.1% higher than the CuInSe 2 3J device and 11% higher than the LM 3J device (see Table 2).
The FF and  of both devices are constant up to each device's respective threshold TDD bot , after which these metrics begin to degrade significantly as observed in Figures 7(c)-7(d).Interestingly, the LMM 3J illustrates two TDD bot ranges where the FF decreases at different rates.These two ranges correspond to the two threshold densities for the electron and hole minority carrier lifetimes as illustrated in Figure 5.The FF of the CuInSe 2 is the lowest of all devices over all TDD bot explored, whereas the FF of the LM 3J is the highest.Under standard testing conditions, the proposed 3J composed of CuInSe 2 has the potential of converting the AM1.5D incident spectrum to electricity with an efficiency of 32.7% at 300 K with a FF of 80.7%, a photocurrent of 14.0 mA/cm 2 , and an open circuit voltage of 2.89 V if there are no threading dislocations.If the threading dislocations in the bottom subcell reach a density of 10 6 cm −2 , the efficiency of this cell drops to 31.7% with FF of 79%.Comparatively, the LMM 3J can perform up to 34.5% assuming a TDD bot of 10 6 cm −2 , whereas the LM 3J reaches 33.0% as it is free from any TDD effects (see Table 2).The benefits of replacing a Ge subcell with an epitaxial CuInSe 2 subcell would thus enable a comparable efficiency at 1 sun operation compared to the LM device.With respect to the LMM device; however, a reduction in efficiency is observed due to the low FF of the CuInSe 2 subcell compared to the GaInAs subcell.This could be improved with a longer minority carrier lifetime in CuInSe 2 .However, an advantage of both the CuInSe 2 and LMM devices over the LM device is the reuse of the GaAs substrate for epitaxial growth through the exploitation of the aforementioned epitaxial liftoff process.For the case of the CuInSe 2 device, the growth process requires two chambers.

Performance under Concentrated Illumination.
The simulated device  oc , FF, and efficiency are illustrated in Figures 8(a)-8(c) for the three aforementioned 3Js under concentrated illumination up to  = 3000 suns where the temperature is kept fixed at 300 K.No contact series resistance is modeled in the simulation.The TDD parameters of each 3J are set to TDD CGB = 10 6 cm −2 and TDD bot = 10 5 cm −2 as an ideal scenario of optimized epitaxial growth with minimal formation of threading dislocations.The  sc of each 3J is not shown here as it is linear as a function of .As expected based on the results of Figures 6(b) and 7(b), the  oc is largest for the LMM 3J over all concentrations with  oc = 3.6 V at  = 1000.Comparatively, the LM 3J has the smallest  oc (3.2 V at  = 1000), and the  oc for the CuInSe 2 based 3J is only 2.7% lower than the LMM device at 1000 suns.
The FF for each of the 3Js is illustrated in Figure 8(b) and demonstrates trends that agree with those of Figure 7  the lowest of all three devices since CuInSe 2 subcell has the lowest individual subcell photocurrent and second lowest FF (69%).Lastly, the efficiency of the 3Js shown in Figure 7(c) illustrates much higher performance of the LMM 3J over the LM and CuInSe 2 3Js with a maximum efficiency of 44% under 750 suns' illumination.The LM and CuInSe 2 3Js peak at 40.5% and 39.6% for 750 suns, respectively.Although the efficiency of each 3J begins to degrade close to 1000 suns due to intrinsic semiconductor series resistance effects, the CuInSe 2 device degrades the least up to 3000 suns and surpasses the performance of the LM device.The results of Figure 8 imply that all three of the 3Js explored in this study may have difficulty operating under concentrated illuminations of over 1000x in CPV systems.This represents an inherent limitation in FF and efficiency as a function of concentration based on tunnel junction and intrinsic semiconductor resistances.It is also important to note that the properties of epitaxial quality CuInSe 2 have been much less studied experimentally than III-V materials.Further work may result in improved material quality and therefore a higher 3J performance due to improvements in both  oc and FF.Lastly, the simulated LMM performance does not quite reach nor surpass the world record [42] for a number of reasons.The primary one involves the conservative minority carrier lifetimes assumed in the modeling.Another reason is the possible beneficial effects of photon recycling within each subcell and luminescent coupling between subcells, both of which are not considered in the model.Other reasons include improvements in the ARC design (materials and layer thicknesses) and improvements in each subcell design such as graded doping layers.

Conclusions
The simulated performance metrics of the GaInAs LMM 3J, the Ge LM 3J, and the proposed CuInSe 2 3J are studied up to concentration ratios of 3000 suns at 300 K.For the LMM and CuInSe 2 3J designs, the modeling takes into account the effects of threading dislocations on minority carrier lifetimes in the bottom subcell.Although the bandgap combination of the CuInSe 2 3J is more optimal than the LM 3J, their performances are comparable as a result of the low fill factor of CuInSe 2 3J cell.With respect to their respective bottom subcells, it is especially important to note that the Ge subcell FF (63%) is lower than the CuInSe 2 subcell FF (69%).This emphasizes the need for a substantially higher photocurrent in the 3J's subcell with the lowest FF.Overall, the LMM 3J clearly outperforms the LM 3J and the CuInSe 2 3J, achieving an efficiency of 44% under 750 suns concentration as compared to 40.5% and 39.6%, respectively.The main reasons for this higher performance are the LMM 3J's GaInAs subcell FF of 80% and its higher  oc .However, a strong advantage of the CuInSe 2 3J is the reduction of III-V semiconductor material over the LMM 3J by around 20%, leading to a lower cost of the cell.

2 InternationalFigure 1 :
Figure 1: Proposed (a) growth sequence and (b) final design of the inverted metamorphic GaInP/Ga(In)As/CuInSe 2 structure after a selective wet etch of an AlAs release layer.
Region and the Relevant Interface.The energy band diagram of the complete CuInSe 2 3J structure simulated at equilibrium is shown in Figure 4(a).The structure of the cell consisting of the top GaInP subcell, middle InGaAs subcell, layers of Ga x In 1−x P CGB, and overshoot layer (marked in gray) as well as bottom subcell (InGaAs emitter and CuInSe 2 base) are denoted above the band diagram.

4. 1 . 2 2 Ga 0 . 7 Figure 4 :
Figure 4: (a) Simulated energy band diagram of the GaInP/Ga(In)As/CuInSe 2 3J under illumination conditions and (b) a closeup of the energy band diagram at the compositionally graded buffer region composed of GaInP including the overshoot layer and the CuInSe 2 based bottom subcell including a highly doped CuInSe 2 back surface field (BSF).

7 2 Figure 5 :
Figure 5: Minority carrier lifetimes in CuInSe 2 and GaInAs as a function of threading dislocation densities (TDD).A threshold density of 8.4 × 10 6 cm −2 for CuInSe 2 can be observed based on the reduction of the lifetime by a factor of 2 (marked by light gray rectangle), whereas the threshold is closer to 2.6 × 10 4 cm −2 for electrons in GaInAs (marked by dark gray rectangle).

Figure 7 :
Figure 7: Simulated (a)  sc , (b)  oc , (c) FF and (d)  as a function of threading dislocation densities TDD bot in the active region of the bottom subcell with TDD CGB = 10 6 c −2 m and surface recombination velocities of 1 × 10 3 cm/s at the GaInAs/CuInSe 2 interface as well as each CGB interface, illuminated by the AM1.5D spectrum (1000 W/m 2 ) at 300 K.The light and dark gray regions indicate the threshold level of TDD bot for the CuInSe 2 and LMM devices, respectively, for a reduction in minority carrier lifetime by a factor of 2.

Figure 8 :
Figure 8: Simulated (a)  oc , (b) FF, and (c) efficiency of the CuInSe 2 3J at 300 K as a function of the concentrated illumination ratio () for TDD bot = 10 5 cm −2 and surface recombination velocities of 10 3 cm/s.The simulated data is compared to the predicted performance of the LMM 3J with the same TDD and to the LM 3J.
Ga 0.27 In 0.73 P CGB-7 n-Ga 0.22 In 0.78 P overshoot n-Ga 0.25 In 0.75 P n-GaInAs buffer n-Ga 0.51 In 0.49 P CGB-1 n-Ga 0.47 In 0.53 P CGB-2 n-Ga 0.43 In 0.57 P CGB-3 n-Ga 0.39 In 0.61 P CGB-4 n-Ga 0.35 In 0.65 P CGB-5 n-Ga 0.31 In 0.69 P CGB-6 n- [8]o avoid the formation of Ga rich CIGS, we propose to introduce a CGB Ga x Se 2 , Ga x In 1−x P, and Ga x In 1−x As based on[8].

Table 1 :
[32]rial properties for CuIn 1− Ga  Se 2 and Ga  In 1− P.ParameterModel for CuIn 1− Ga  Se 2 Model for Ga  In 1− P The radiative recombination coefficient  rad for CIGS is set to 10 −14 cm 3 /s such that the material is dominated by non-radiative processes.For GaInP in the CGB region,  rad is assumed constant over molar fraction based on data for Ga 0.51 In 0.49 P[32]since the CGB region is a majority carrier region, and thus the recombination in these layers is not relevant to device performance.In any event, SRH recombination would dominate due to the effects of threading dislocations.The parameters adopted in the simulations for CIGS and GaInP are summarized in Table

Table 2 :
Simulated current-voltage metrics of the 3Js of interest under 1000 W/m 2 and at 300 K with TDD CGB and TDD bot of 10 6 cm −2 .
.The LM 3J has the largest device FF due to the bottom Ge subcell having the highest photocurrent compensating for its low individual FF of 63%.The LMM 3J has the second largest FF since it has the second highest bottom subcell photocurrent, even though its bottom subcell has the highest individual FF of 80%.The overall FF of CuInSe 2 3J is