Issue 
EPJ Photovolt.
Volume 12, 2021



Article Number  1  
Number of page(s)  7  
Section  High Efficiency Materials and Devices  New concepts  
DOI  https://doi.org/10.1051/epjpv/2021001  
Published online  17 February 2021 
https://doi.org/10.1051/epjpv/2021001
Regular Article
Improved design of InGaP/GaAs//Si tandem solar cells
^{1}
Grupo de Investigación en Ciencias de la Orinoquia, Universidad Nacional de Colombia Sede Orinoquia, Arauca, Colombia
^{2}
Centro de Investigación y de Estudios Avanzados del IPN, Electrical Engineering DepartmentSEES, Ciudad de México, México
^{*} email: amorales@solar.cinvestav.mx
Received:
19
June
2020
Received in final form:
16
January
2021
Accepted:
19
January
2021
Published online: 17 February 2021
Optimizing any tandem solar cells design before making them experimentally is an important way of reducing development costs. Hence, in this work, we have used a complete analytical model that includes the important effects in the depletion regions of the IIIV compound cells in order to simulate the behavior of two and fourterminal InGaP/GaAs//Si tandem solar cells for optimizing them. The design optimization procedure is described first, and then it is shown that the expected practical efficiencies at 1 sun (AM1.5 spectrum) for both two and fourterminal tandem cells can be around 40% when the appropriate thickness for each layer is used. The optimized design for both structures includes a double MgF_{2}/ZnS antireflection layer (ARC). The results show that the optimum thicknesses are 130 (MgF_{2}) and 60 nm (ZnS), respectively, while the optimum InGaP thickness is 220 nm and GaAs optimum thickness is 1800 nm for the fourterminal tandem on a HIT silicon solar cell (with total tandem efficiency around 39.8%). These results can be compared with the recent record experimental efficiency around 35.9% for this kind of solar cells. Therefore, triple junction InGaP/GaAs//Silicon tandem solar cells continue being very attractive for further development, using high efficiency HIT silicon cell as the bottom subcell.
Key words: IIIV/Si tandem solar cells / hybrid tandem/multijunction solar cells / antireflecting coating
© S. TorresJaramillo et al., published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
Over the last decades, photovoltaic energy has become one important contributor to the current energy production, around 1.7% of the world power supply [1]. Thin film solar cells based on CdTe, copper indium gallium selenide (CIGS) or amorphous silicon have been developed as a cheaper alternative to crystalline silicon cells [2–7]. On the other hand, tandem cells, or multijunction cells, as they are also called, were originally used for spacecrafts, where materials such as galliumarsenide (GaAs) and germanium (Ge) substrates were combined for the first time to achieve high efficiencies [8–10]. In order to create costeffective tandem cells, the most obvious way is to add new materials on top of conventional singlejunction cells based on silicon or thin film materials such as CIGS. Adding an additional junction layer to industrial PV cells can be the cheapest way to further improve photovoltaic efficiency [11]. Specifically, a very attractive alternative for having very high efficiency solar cells is the coupling of different generation solar cells (e.g. Perovskite/CIGS, IIIV/Si) [12,13]. Experimentally, the new technologies that couple two or more solar cell junctions based on IIIV materials and Si, have exceeded the efficiency limit for a single junction, reaching efficiencies around 36%. This achievement is due to the optimization of parameters such as reflectance and thickness of each junction material [14]. In this regard, the use of HIT (HJ) silicon solar cells, as bottom cells, is important because they have been reported to be the record efficiency silicon cells [1]. Besides, IIIV semiconductor multijunction solar cells are attractive because they have achieved more than 40% under solar concentration [15].
Essig et al. [14] have demonstrated experimental conversion efficiencies of 32.5% and 32.8% (AM1.5) for IIIV//Si twojunction solar cells based on mechanical stacking of GaInPGaAs//Si cells. In addition, they showed a threejunction GaInP/GaAs//Si cells with a record 35.9% efficiency All of the above was achieved with the use of ZnS/MgF_{2}based antireflective coatings to prevent optical losses in the device [14]. In this work, it is shown that improved designs of twoterminal and fourterminal threejunction InGaP/GaAs//Si tandem solar cells with a double antireflection coating (Fig. 1) can achieve even higher efficiencies, around 39.8%, at one sun (AM1.5). The model used for the IIIV solar subcells includes the effects related to the carrier recombination within the spacecharge regions which cause the reduction of both the illumination current and the opencircuit voltage of very thin solar cells. Therefore, the calculations and design results are more realistic than those typically reported without considering these spacecharge effects.
Fig. 1 (a) Schematics of a fourterminal InGaP/GaAs//SiHJ solar cell. The top subcell is formed by the twoterminal IIIV tandem. (b) Schematics of a twoterminal InGaP/GaAs/SiHJ solar cell. In this case, the tunnel junctions are not depicted, nor they are considered for the calculations. 
2 Fourterminal tandem solar cells
In order to determine the expected efficiencies for the tandem cell structures shown in Figure 1, the calculations for each of the IIIV subcells (np homojunctions) were made using reported values for transport parameters such as mobilities and carrier lifetimes, as will be explained below. The parameters assumed for the IIIV compounds are given in Table 1 [16,17]. The (front and back) surface recombination velocities for each IIIV subcell were assumed to be S = 10^{3} cm/s. This is an intermediate value between passivated and nonpassivated surfaces.
In addition, previously reported optical parameters such as refraction and extinction coefficients were also taken in account to evaluate the total cell reflectance R(λ) at each wavelength of the AM1.5 solar spectrum [18–20]. For this purpose, an optical matrix method [21] was used for the calculation of the spectral reflectance R(λ), assuming a MgF_{2}/ZnS antireflecting double layer (ARC). Figure 2 shows the results for the spectral reflectance taking in account different thicknesses for the double ARC used for these tandem cells. The thicknesses used for the calculations shown in Figure 2 are the optimized values, as will be explained below, and the thicknesses used for the experimental record efficiency InGaP/GaAs//Si tandem solar cells reported recently [14].
Fig. 2 Reflectance for tandem solar cells with a double layer ARC system. 
2.1 IIIV Top subcell optimization
The InGaP and GaAs tandem homojunctions constitute the top (twoterminal) subcell, and they were assumed to be connected in series (through a tunnel junction), so that the photocurrent (shortcircuit) density for each junction should be the same. The thickness for each material is designed to satisfy this condition.
The optimization proceeded using a twostep process. In the first step, a first order approximation for the photocurrent of each subcell was calculated using the following equation:(1)
with direct bandgap absorption coefficients calculated by(2)
where q is the electron charge, α_{k} is the absorption coefficient, d_{k} is the thickness of each junction (k = 1, 2) above the i ^{th} junction, λ _{gapi} is the wavelength corresponding to the band gap of the i ^{th} material (λ _{gapi} = hc/E _{gapi} where h is the Planck's constant and c is the speed of light in the air). N _{0} is the photon flux density due to the AM1.5 solar spectrum. This first order approximation allowed the estimation of the required thickness for each subcell. (3) (4) (5)
Then, in the second step (See Eqs. (3)–(5)) [22], a more realistic calculation for the photocurrent density was made considering the calculated spectral reflectance R(λ) in the solar spectrum, where R(λ) takes in account the effect associated to the antireflection coating.
L_{n} and L_{p} are the minority carrier diffusion lengths, D_{n} and D_{p} the diffusion coefficients, τ_{n} and τ_{p} are the minority carrier lifetimes, W_{p} and W_{n} are the layer thickness, x_{p} and x_{n} the space charge region lengths, S_{p} and S_{n} are the respective surface recombination velocities, and α(λ) the absorption coefficient as a function of wavelength [22]. N ′ _{0} is the available photon flux for each subcell.
In addition, both the volumetric and the surface recombination are considered for the dark currents at each junction, accordingly to a previously reported analytical model [22]. This provides an improved design to our previous approach [23] because now we are also including the effects due to the depletion region in each of the IIIV compound cells. This is important because a parameter that determines the photoelectric properties of a thin film solar cell is the thickness of the space charge region (depletion region) in both the ptype and ntype sides of each of the homojunctions. For this purpose, let us remember that the spacecharge width in a solar cell can be calculated by means of the following expressions:(6) (7)
where ε is the dielectric permittivity of the semiconductor, V is the bias voltage and V_{bi} is the builtin potential. In other words, there is a variation of depletion layer thickness as a function of the applied voltage which causes a variation of both the generated photocurrent and the generationrecombination dark current densities as a function of the bias voltage. All this affects the optimized thickness for each of the subcells, as well as the total efficiency.
Then, for each of the junctions, the total J as a function of voltage can be calculated using an equivalent model with two diodes:(8)
where J_{0i} and J_{00i} are the dark saturation currents due to diffusion and generation–recombination in the spacecharge region, respectively. They are given by(9)
and(10)where, n_{i} is the intrinsic carrier density for each semiconductor.
In addition, the photogenerated current density J _{Li} should include the photogenerated carriers in this spacecharge region (see Eq. (5)) [22]. All these effects become important for thin film solar cells.
2.2 Bottom subcell characteristics
The bottom subcell will be assumed to be a typical heterojunction silicon HIT solar cell. The experimental JV parameters used for the HIT bottom subcells under the AM1.5 spectrum [24], are given in Table 2. The corresponding dark saturation current density J _{0} was estimated from the J_{sc} and V_{oc} values given in Table 2, assuming an ideal exponential JV curve for this kind of solar cells, since they are limited by carrier diffusion.
Notice that such silicon solar cells will generate a reduced photocurrent density when they are stacked below the above IIIV subcells. However, ideally their dark current characteristics will not be modified. Then, when such a silicon solar cell is used for the threejunctions tandem cell, the expected photocurrent density J_{L} can be estimated using the following procedure. J_{L} for the silicon cell (under the IIIV subcell) was approximated by the following expression:(11)where α is the absorption coefficient for crystalline silicon and d is the reported thickness for the assumed high efficiency HIT solar cell (98 µm) [25]. The full JV curve for the silicon HIT solar cell, under the IIIV compound subcell, can be calculated from this photocurrent density J _{ L } and the dark saturation current density J _{0} determined as explained above.
3 Twoterminal tandem solar cells
The use of the model described in the previous section, and the mentioned considerations corresponding to each of the materials involved, enabled the calculation of the output parameters and characteristic contributions of each of the subcells of a twoterminal tandem cell. In this case, the thickness of each absorber layer was chosen so that the illumination current densities are the same for each subcell (InGaP/GaAs) and the silicon HIT cell. Thus, the procedure is similar to what was done for the IIIV compound junctions in tandem. In this case, the appropriate ARC thicknesses were chosen to cause the largest photocurrent density for the whole cell. Then, the thickness for each of the IIIV compound subcells are selected to generate a constant photocurrent density for the whole tandem cell structure.
4 Results
4.1 Optimized fourterminal tandem solar cells
The external quantum efficiencies for each subcell as a function of wavelength are shown in Figure 3 for the different ARC thicknesses considered. The thickness of each absorber layer was chosen so that the illumination current densities reach the maximum value for each subcell. In this case, the top and bottom junctions were assumed to have absorber layers with bandgaps of 1.9 eV (InGaP), 1.43 eV (GaAs), and 1.08 eV (Si), respectively. Figures 4 and 5 show the calculated PV/JV characteristics for each of the subcells. From these, the efficiencies for the subcells can be determined. Ideally, the total efficiency will be the sum of the subcell efficiencies. Unlike the twoterminal solar cells where the current density of the junctions must be the same, in the fourterminal cell (where the tandem is mechanically made) the maximum possible photocurrent density can be achieved for each subcell.
In Table 3, the optimized efficiency for the ARC used for the reported experimental record efficiency cells [14] is also given. Notice that in this case, the calculated efficiency (39.5%) is slightly less as compared to cells with our optimized ARC which gives a total efficiency of 39.8%. The experimental record efficiency for this kind of cells, under the AM1.5 solar spectrum, is around 35.9% [14]. Therefore, in accordance with the above results, we still can expect some improvement for this kind of solar cells in the near future.
Fig. 3 External quantum efficiency for the fourterminal cell with a double layer ARC system. 
Fig. 4 Power versus voltage for each subcell in the fourterminal tandem cell. 
Fig. 5 Current versus voltage for each subcell in the fourterminal tandem cell. 
Calculated illumination current density, open circuit voltage, fill factor and power conversion efficiency for each of the subcells and the fourterminal tandem cells.
4.2 Optimized twoterminal tandem solar cells
The EQE results for the twoterminal tandem cell are shown in Figure 6 for an ARC with respective optimum layers of 130 and 60 nm. The contribution of each subcell is also shown in this figure. As explained before, the ARC coating thickness was chosen so that the cell achieves the largest photocurrent density. The JV curve can be calculated from the two diodes in series model for each of the InGaP/GaAs and Si subcells, as shown in Figure 7. The thickness of each absorber layer was chosen so that the illumination current densities are the same for each subcell. In this case, the maximum efficiency was obtained when the top and bottom junctions had absorber layers with thicknesses of 166 nm (InGaP), 360 nm (GaAs), and 98 µm (Si), respectively. The total tandem cell conversion efficiency would be 39.6% as given in Table 4. This value is comparable with the expected efficiency for the optimized fourterminal tandem cell.
Fig. 6 External quantum efficiency for the twoterminal cell with an optimum a double ARC system. 
Fig. 7 Current and power versus voltage curves for the twoterminal tandem cell. 
Calculated illumination current density, open circuit voltage, fill factor and power conversion efficiency for the twoterminal tandem cells.
4.3 Comparison with our previous results
The maximum efficiency expected for the fourterminal tandem cell in our previous work [23] was 41.7%, while the efficiency achieved in this work is 39.8%, as explained above. This difference is explained by the effects due to the spacecharge regions in each of the IIIV compound subcells. In addition, a double antireflection coating was used here which allows for a larger sunlight absorption, compensating some of the loss due to the recombination in the depletion regions. However, our calculations suggest that by optimizing the subcell layer thicknesses it is still possible to achieve a higher efficiency than the recent record reported [14].
5 Conclusion
By including a double ARC and the effects due to the spacecharge regions in the IIIV compound subcells, InGaP/GaAs//Silicon tandem solar cells were optimized for each of the two or fourterminal configurations. The fourterminal tandem cell efficiency at 1 sun should reach around 39.8% when the appropriate thicknesses for each layer, including the antireflection coating, are used. In the specific case of MgF_{2}/ZnS as ARC, the optimum thickness is 130 and 60 nm respectively, while the calculated optimum InGaP thickness is 220 nm and GaAs optimum thickness is 1800 nm. The results shown here can be compared with the experimental record efficiency already achieved (35.9%) for this type of solar cells [14]. Then, it is still possible to improve this record efficiency.
Author contribution statement
S. TorresJaramillo made the calculations and wrote the paper draft; R. BernalCorrea developed the original code and supervised the calculations; A. MoralesAcevedo proposed the research and the methodology, validated the results and wrote the final version of the paper.
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Cite this article as: Santiago TorresJaramillo, Roberto BernalCorrea, Arturo MoralesAcevedo, Improved design of InGaP/GaAs//Si tandem solar cells, EPJ Photovoltaics 12, 1 (2021)
All Tables
Calculated illumination current density, open circuit voltage, fill factor and power conversion efficiency for each of the subcells and the fourterminal tandem cells.
Calculated illumination current density, open circuit voltage, fill factor and power conversion efficiency for the twoterminal tandem cells.
All Figures
Fig. 1 (a) Schematics of a fourterminal InGaP/GaAs//SiHJ solar cell. The top subcell is formed by the twoterminal IIIV tandem. (b) Schematics of a twoterminal InGaP/GaAs/SiHJ solar cell. In this case, the tunnel junctions are not depicted, nor they are considered for the calculations. 

In the text 
Fig. 2 Reflectance for tandem solar cells with a double layer ARC system. 

In the text 
Fig. 3 External quantum efficiency for the fourterminal cell with a double layer ARC system. 

In the text 
Fig. 4 Power versus voltage for each subcell in the fourterminal tandem cell. 

In the text 
Fig. 5 Current versus voltage for each subcell in the fourterminal tandem cell. 

In the text 
Fig. 6 External quantum efficiency for the twoterminal cell with an optimum a double ARC system. 

In the text 
Fig. 7 Current and power versus voltage curves for the twoterminal tandem cell. 

In the text 
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