wafer-based tandem junction solar cells

Solar Energy 150 (2017) 287–297

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Analytical model for simulating thin-film/wafer-based tandem junction solar cells Lauren Davidson a,b,c, K.A.S.M. Ehteshamul Haque a,b,c, Fatima Toor a,b,c,d,⇑ a

Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, USA Optical Science and Technology Center, University of Iowa, Iowa City, IA 52242, USA c University of Iowa Informatics Initiative, University of Iowa, Iowa City, IA 52242, USA d Physics and Astronomy Department, University of Iowa, Iowa City, IA 52242, USA b

a r t i c l e

i n f o

Article history: Received 5 August 2016 Received in revised form 6 February 2017 Accepted 20 April 2017

Keywords: Solar cell simulation Tandem solar cells Perovskite absorbers Silicon absorbers Thin-film solar cells Wafer-based solar cells

a b s t r a c t Replacing the present-day commercial single junction silicon (Si) solar cells with low cost, high efficiency solar cells is imperative, in order to compete with other existing energy technologies. Many research groups have looked into using III–V materials, tandem junction solar cells and thin-film technologies to reach higher efficiencies. However, many of these techniques involve expensive materials or costly manufacturing processes. In this research, we focus on a tandem junction solar cell design that is based on a thin-film perovskite top cell and wafer-based Si bottom cell. In order to analyze the performance of the tandem cell, an analytical model is needed to compute the quantum efficiency and characteristic solar cell data. The highly versatile Matlab-based analytical model presented in this work is capable of modeling different kinds of tandem cells based on a variety of solar absorber combinations. The model allows user to adjust input parameters, such as reflectivity, material thickness, donor and acceptor densities, and carrier lifetimes in order to optimize the quantum efficiency, maximum power output, open circuit voltage, and short circuit current quantities of the cell. Using this analytical model, we were able to design a perovskite and black Silicon (bSi) tandem cell, which reached an efficiency of greater than 30%. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Wafer-based monocrystalline silicon (c-Si) solar cells reached a maximum efficiency of 25% (Green et al., 2016) in the 1999 and have improved little in recent years, prompting the research of different cell materials and designs to create cost competitive and higher efficiency cells. Several research groups are exploring different techniques to reach high efficiency in single junction solar cells, such as using III–V materials (Kayes et al., 2011) or by creating tandem junction cells with different absorbers (Yamaguchi, 2003). While III–V solar cells have reached efficiencies greater than 40% (Green et al., 2016), the materials and fabrication processes required to manufacture III–V at an industrial scale, are expensive. Commercial scale Si solar cells exhibit average efficiencies of 17–19% because the 25% cell requires several costly processes to manufacture; for solar energy generation to be cost competi⇑ Corresponding author at: Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, USA. E-mail address: [email protected] (F. Toor). http://dx.doi.org/10.1016/j.solener.2017.04.053 0038-092X/Ó 2017 Elsevier Ltd. All rights reserved.

tive, expensive manufacturing processes are not an option. Given the presence of extensive infrastructure to manufacture Si solar cells, it is only judicious that any low cost and high efficiency solar cell architecture utilizes Si. Nanostructured ‘black silicon’ (bSi) solar cells (Toor et al., 2016a, 2016b), which use an inexpensive chemical etching technique to form an antireflection (AR) coating on the Si surface have recently been developed and have reached a record efficiency of 22.1% in p-type c-Si in 2015 (Savin et al., 2015). Even with better optical absorption due to bSi, the champion bSi solar cell efficiency remains at 22.1% relative to 25% for cells that do not utilize bSi AR. The reason for the lower efficiency of bSi solar cells is that they suffer from poor electrical performance when illuminated by blue light (350–475 nm light wavelength) due to a high surface area with dangling bond-like defects and high doping density that results in a high probability for electrons excited by light to relax back to their lowest-energy state, leaving no energy to collect. These effects result in low energy conversion efficiency for the blue wavelengths of bSi solar cells. Therefore, the use of lead-based hybrid perovskite layer to collect the blue light instead of bSi eliminates this as

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Fig. 2. Structure of a single junction Si solar cell with surface texturing, aluminum back surface field, and silver contact.

2. Methodology Fig. 1. The molecular structure of perovskite. Reprinted by permission from Nature Publishing Group: Nature Materials 13, 838–842 (2014), copyright (2014) License number: 3852560435429.

a problem for bSi. Thin-film perovskite solar cells, which are relatively cheap to manufacture, have demonstrated extremely rapid progress with the first 10.9% efficient cell demonstrated in mid-2012 and in early 2014 cells reached 17.9% (Green et al., 2014). Si has an intrinsic bandgap of 1.1 eV while the perovskite bandgap can be tuned over a wide range from 1.5 eV to 2.3 eV. Based on these bandgaps, Si and the perovskite make an excellent pair for tandem solar cell architecture that can revolutionize solar energy generation due to the high efficiency and low cost potential. Perovskites are materials described by the formula ABX3, where X is an anion, A and B are cations of different sizes (A being larger than B) (Chilvery et al., 2015). In this work, A will be an organic cation, specifically, methylammonium (MA) (CH3NH+3); B will be an inorganic cation, lead (Pb), and X will be a halide anion based on iodide (I
), or a mixed iodide and bromide, I3
x Brx, or iodide and chloride (I3
x Clx). A schematic molecular structure of the perovskite is shown in Fig. 1. Perovskite semiconductors have attracted attention since the beginning of their incorporation into photovoltaic devices by Miyasaka et al. in 2009, with cells exhibiting 4% efficiency (Kojima et al., 2009). Since 2009, there has been extremely rapid progress with the first 10.9% efficient cell demonstrated in mid-2012 to 17.9% cells in early 2014. The perovskite absorber properties that are desired for this work include a larger bandgap than Si that enables the necessary optical properties and longer diffusion lengths. Due to the tunable bandgap of perovskites (1.5–2.2 eV), they are ideal candidates to be paired with Si, in order to obtain a highly efficient cell. However, perovskite solar cells have been known to degrade due to exposure to UV light and humidity. Recent research has addressed this issue of degradation by adding a protective coating to the perovskite based solar cells. For example, Koushik et al. (2017) proposed atomic layer deposition (ALD) based aluminum oxide (Al2O3) coating and Rajamanickam et al. (2016) demonstrated solution processed graphene-polyaniline (PANI) composite as effective coatings to reduce the degradation of perovskite solar cells. Hence, our research focused around a tandem junction solar cell design comprised of the thin-film, lead-based perovskite top cell and wafer-based Si bottom cell. This research demanded a new analytical model since PC1D (Lien and Wuu, 2009) and SCAPS (Minemoto and Murata, 2014), the two leading solar cell modeling programs, were incapable of modeling our specific solar cell as the programs result in convergence errors.

2.1. Matlab-based analytical model The Matlab model was designed in conjunction with the structure of a typical solar cell as shown in Fig. 2. Photocurrents are generated in three regions of the p-n junction device: the base, emitter, and the space charge region or the depletion region. The base is a p-type Si substrate and is the thickest absorber of the cell. The emitter is highly doped n-type Si with surface texturing in order to reduce surface reflection and increase light absorption. The depletion region is where the p-type substrate and n-type substrate meet, and while the photocurrent is small in this region, the calculation cannot be ignored (Sze and Ng, 2006). The back surface field (BSF) is the bottom layer of the cell and consists of a highly doped material (Fig. 2 shows an aluminum BSF). The BSF reduces rear surface recombination, which adversely affects the short circuit current and open circuit voltage. In our model, the BSF of the cell is simulated by decreasing the rear surface recombination velocity for electrons according to Sze and Ng (2006) (see Table 1).

Table 1 Constants used in Matlab analytical model. Symbol

Parameter

Value

q h k c n

Charge of electron Planck constant Boltzmann constant Speed of light Refractive index of air

1.602  10
19 C 6.626  10
34 J-s 1.3807  10
23 J/K 299,792,458 m/s 1

Table 2 Input parameters of the model. Symbol

Parameter

Units

Nd Dp

Donor density Hole diffusion coefficient in emitter Hole lifetime in emitter Hole diffusion length in emitter Acceptor density Electron diffusion coefficient in base Electron lifetime in base Electron diffusion length in base Depletion width Thickness of substrate Junction depth of n+ region Surface recombination velocity for electrons Surface recombination velocity for holes Band gap energy Conduction band effective density of states Valence band effective density of states Temperature Total cell thickness Wavelength

cm
3 cm2/s s cm cm
3 cm2/s s cm cm cm cm cm/s cm/s eV cm
3 cm
3 K cm nm

sp

Lp Na Dn

sn

Ln W H’ xj Sn Sp Eg Nc Nv T H k

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Fig. 3. Schematic of the proposed tandem junction solar cell with perovskite top cell and bSi bottom cell.

The Matlab program allows a user to input parameters for the emitter, base, and depletion region. The parameters of the model that are defined by the user are given in Table 2. While the Matlab program was designed based upon the structure of the single junction solar cell shown above, it is also capable of modeling a tandem cell, as discussed in the text later. The input values can be altered for both the top and bottom cell, depending on the absorber materials being used; however, this research focuses on using a perovskite top cell and a Si bottom cell (see Fig. 3) The Matlab model characterizes the tandem cell by computing the internal quantum efficiency (IQE), external quantum efficiency (EQE), open circuit voltage (Voc), short circuit current density (Jsc), fill factor (FF), and the overall efficiency of the cell (g). Each of these parameters is essential for optimizing the cell design for high performance. The model calculates the quantities based off of the input values given in Table 2. The model first calculates the photocurrent produced in the emitter, base, and space charge region using the one-dimensional, steady-state continuity equations under low-injection conditions (Sze and Ng, 2006). The photocurrent density for holes in the emitter (Je), the photocurrent density for electrons in the base (Jb), and the photocurrent density in the space charge region (Jscr) are given by Eqs. (1)– (3) respectively.

Fig. 5. An n-terminal tandem cell configuration. The different regions of the cell are modeled in the Matlab program.

Fig. 4. Parametric study of the efficiency of the tandem cell (n-terminal) with respect to the perovskite cell thickness. The nanostructured black Si bottom cell results in the highest overall efficiency profile.

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Fig. 6. Energy band diagram of the tandem cell (n-terminal configuration).

Fig. 7. The (a) IQE, (b) EQE, and (c) IV curves of a single junction bSi solar cell. The theoretical values were compared with experimental data taken from a bSi cell provided by Toor et al. (2011) (cell area = 1 cm2).

L. Davidson et al. / Solar Energy 150 (2017) 287–297

Je ¼

" # q/ð1
RÞaLp

a

2S 4

Jb ¼

2 L2 p

p Lp Dp


1

Z     3 x x cosh Lpj þ sinh Lpj
axj 5     ð1Þ
aLp e x x sin Lpj þ cosh Lpj

þ aLp
e
axj Sp Lp Dp



Sp Lp Dp

" # q/ð1
RÞaLn e
aðxj þWÞ Þ 2 4

a2 L2n
1 

J ph ðkÞ dk qFðkÞ½1
RðkÞ

IQEðkÞ ¼

aLn
SDn Lnn cosh

 

Sn Ln Dn

 0

 0

J scr ¼ q/ð1
RÞe
axj ½1
e
aW 

ð4Þ ð5Þ

Once the IQE and EQE values are calculated, the model computes the Jsc, Voc, FF, and g values of the cell, and these quantities are given by Equations (6)–(9).

J sc ¼

3 0


e
aH þ sinh HLn þ aLn e
aH 5  0  0 sinh HLn þ cosh HLn xj Lp

EQEðkÞ ¼ IQEðkÞ½1
RðkÞ

291

q 10

ð2Þ V oc ¼

Z

½1
RðkÞFðkÞIQEðkÞdk

  J ph kT ln þ1 q Js

ð6Þ

ð7Þ

ð3Þ

Since the photon flux (/), absorption coefficient (a) as a function of wavelength, and the reflectivity of the absorber (R) are dependent upon the wavelength of light along the solar spectrum, the IQE and EQE of the cell are function of k; these quantities are given by Eqs. (4) and (5) respectively.

Jm V m J sc V oc

ð8Þ

Pm ð%Þ P in

ð9Þ

FF ¼

g¼

Fig. 8. The (a) IQE, (b) EQE, and (c) I-V curves of perovskite/bare Si tandem cell (series connection) as simulated by the Matlab model (cell area = 1 cm2).

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Once the input parameters have been set for both the top and bottom cells, the analytical model allows the user to determine the type of bottom cell to be simulated and choose the series versus n-terminal configuration of the tandem cell design. The model is capable of modeling three different types of bottom cells: bare c-Si without any AR coating, a silicon nitride (SiNx) coated cell, and a nanotextured black Si (bSi) cell. The SiNx based AR coating is one of the options in the models since it is the most commonly used AR coating in commercial c-Si solar cells. The optimization of the bottom cell is discussed further in Section 2.2. Once the bottom cell has been determined, the user has the choice between an n-terminal configuration and a series connected tandem cell. The differences between these two configurations are discussed further in Section 2.3. When all the parameters of the tandem cell have been set, the model produces the IQE, EQE, reflectivity curves of the cell as well as the photon flux curve based on the AM1.5G solar spectrum. The model also produces the I-V curves of the top and bottom cells individually and combined; it also shows the power curve with the maximum power point. The model then outputs the following data values for the top, bottom, and tandem cells: Jsc, Voc, FF, and g.

2.2. Silicon bottom cell The efficiency of the perovskite/Si tandem cell changes depending on the type of bottom cell modeled: a bare c-Si cell, a SiNx coated cell, or a bSi cell. The bare c-Si cell produces the lowest efficiency of the three types of cells. c-Si has a high solar-spectrumweighted average reflectivity (Rave) of around 40%, which adversely affects the performance of the cell. Due to the high reflectivity of bare c-Si, less light is absorbed, producing a smaller photocurrent, resulting in a lower cell efficiency. The application of a SiNx AR coating significantly decreases the surface reflectivity of the cell (Rave ranging from 3% to 8%), resulting in better light absorption. While the SiNx coating improves the efficiency of the tandem cell compared with bare Si, the best performing solar cell, in terms of efficiency, is comprised of nanostructured bSi. The decrease in surface reflectivity of the bSi cell (Rave as low as 1.4%) (Toor et al., 2011) improves light absorption across the spectrum and results in the most efficient tandem cell of the three configurations. Fig. 4 shows the efficiency profiles of the three types of cells (n-terminal configuration) against varying perovskite absorber thickness. The image shows that the tandem cell design can be optimized by using a bSi bottom cell.

Fig. 9. The (a) IQE, (b) EQE, and (c) I-V curves of a perovskite/Si (with SiNx passivation) tandem cell (series connection) as simulated by the Matlab model (cell area = 1 cm2).

L. Davidson et al. / Solar Energy 150 (2017) 287–297

2.3. Tandem cell configurations The model allows the user to decide whether to simulate a series connected tandem cell or a cell in the n-terminal configuration. A series connected cell is also known as a current matched tandem cell. The photocurrents in both the top and bottom cell should ideally be the same. Otherwise, the smaller of the two currents sets the photocurrent throughout the tandem cell (Parikh and Toledo, 2007). The current matching limits the efficiency of the series connected tandem cell. Even though the series connected cell operates with a lower efficiency, it is less expensive to manufacture than the n-terminal cell due to fewer number of process steps and cell layers. The n-terminal configuration, as shown in Fig. 5, externally wires the top and bottom cells. Because of this, the currents in the cellsare independent of each other and do not need to match. The top cell absorbs shorter wavelengths, and the bottom cell sees only the photons that are transmitted through the top cell. The photocurrent in the top cell is added to the photocurrent in the bottom cell to obtain the total photocurrent from the tandem cell. Since the currents can be added rather than matched, the n-terminal configuration gives a cell with higher efficiency. When modeling the perovskite and Si tandem cell, an n-terminal

293

configuration was used, and consisted of the layers given in Fig. 5. Fig. 6 depicts the energy band diagram of the n-terminal tandem cell where TiO2 (Eg = 3.2 eV14) forms the electron transport layer, spiro-OMeTAD (Eg = 2.98 eV15) forms the hole transport layer, and silica glass (Eg = 8.4 eV16) forms the transparent insulating layer and the perovskite and Si layers have band gap energies of 1.6 eV and 1.12 eV, respectively. In our model, for both the series and n-terminal solar cell configurations, the IQE and EQE values are calculated separately for each cell. The open circuit voltages, Voc, of the cells are computed individually. They are added to give the total Voc for the series connected cell. For the n-terminal case, it is assumed that both cells will operate at their individual maximum power points (MPP). Provided this, the power and efficiency of the individual cells are added to give the total output power and efficiency (Parikh and Toledo, 2007). 3. Simulation results and discussion 3.1. Single junction solar cell simulation To test the accuracy of the Matlab model, we first parameterized a single junction bSi solar cell. The values were set using a

Fig. 10. The (a) IQE, (b) EQE, and (c) I-V curves of a perovskite/bSi tandem cell (series connection) as simulated by the Matlab model (cell area = 1 cm2).

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Fig. 11. The (a) IQE, (b) EQE, and (c) I-V curves of perovskite/bare Si tandem cell (n-terminal configuration) as simulated by the Matlab model (cell area = 1 cm2).

solar cell fabricated and tested by Toor et al. (2011), and then the experimental data was compared with the theoretical model data. The IQE, EQE, and I-V curves of the experimental and theoretical model are shown in Fig. 7. The photon flux is normalized with respect to the standard AM1.5G irradiance (1000 W/m2). The output characteristics of the modeled solar cell were as follows: g = 17.28%, Voc = 594.2 mV, Jsc = 35.23 mA/cm2, and FF = 82.61%. The Matlab model data was within 3% of the experimental values given by Toor et al. (2011), where the efficiency obtained was 17.2%. This built confidence in the accuracy of the Matlab model, since the tandem cell is modeled using the same principles and equations of the single junction cell. 3.2. Tandem junction solar cell simulation We modeled a tandem junction solar cell using the thin-film, lead-based perovskite top cell (chemical formula CH3NH3PbI3) and a wafer-based Si bottom cell. By keeping the bottom cell parameters constant except for varying reflectivity, we simulated a tandem cell with a bare Si bottom cell, a cell with a SiNx coating, and a bSi bottom cell. Common parameters, such as hole and electron lifetimes (Leijtens et al., 2014), diffusion lengths (Bai et al.,

2014), and absorber thickness (Gonzalez-Pedro et al., 2014; Liu et al., 2014) of the perovskite top cell were entered into the program, and the parameters for the Si bottom cell are the same parameters as the single junction solar cell from Section 3.1. The simulated IQE, EQE, and I-V curves of the three different series connected tandem cells (based on the bare Si, SiNx coated, and bSi bottom cells) are given in Figs. 8–10. The simulated IQE, EQE, and I-V curves of the three different n-terminal tandem cells are given in Figs. 11–13. The solar cell output parameters for the individual and tandem cells are given in Tables 3–6. For the perovskite/SiNx tandem cell, the parameters for the top cell and bottom cell were kept constant except for the reflectivity data, which was set accordingly for a SiNx AR coating. Similar technique was followed for the bSi bottom cell case, with appropriate reflectivity data from Toor et al. (2011) The reflectivity data for all three types of bottom cells are shown in Figs. 8 (a)–13(a). 3.3. Optimizing perovskite parameters Perovskites have tunable bandgaps from 1.5 eV to 2.2 eV, which makes them ideal materials to be paired with Si in a tandem solar

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Fig. 12. The (a) IQE, (b) EQE, and (c) I-V curves of a perovskite/Si (with SiNx passivation) tandem cell (n-terminal configuration) as simulated by the Matlab model (cell area = 1 cm2).

cell. We conducted a parametric study in which the bandgap and the thickness of the perovskite absorber were varied. Keeping the rest of the parameters of the cells constant, the thickness of the perovskite layer was varied from 50 nm to 700 nm, starting with a bandgap of 1.5 eV, and the efficiency of the tandem cell was obtained. This process was repeated for bandgap values up to 2.2 eV, in steps of 0.1 eV. Fig. 14 shows the efficiency contours that can be reached for a certain bandgap and thickness of a tandem cell based on a bare Si bottom cell, SiNx coated bottom cell and a bSi bottom cell. The contour plots show that the highest range of efficiencies for a particular absorber thickness is reached at a bandgap of approximately 1.65 eV. The lead-based perovskite (CH3NH3PbI3) has a bandgap of 1.57 eV, but if the chemical formula is altered to include chlorine (CH3NH3PbI3
xClx), a bandgap of 1.6 eV can be achieved. The mixed-halide CH3NH3PbI3
xClx perovskite exhibits better environmental stability and carrier transport with diffusion lengths of up to 1.9 lm for electrons and 1.2 lm for holes than its pure iodide version (CH3NH3PbI3), which has a carrier diffusion length of approximately 100 nm. Adjusting the chemical composition of the perovskite can thus optimize the top cell.

3.4. The analytical model’s potential While this research focused on modeling a tandem junction solar cell comprised of a perovskite top cell and Si bottom cell, the Matlab analytical model is a versatile model and can be used to model different types of tandem cells. The model can be used to model GaAs/Si tandem cells, as well as for any other material, provided that the reflectivity and absorption data is available. Because of the model’s versatility, it can be a useful tool in optimizing solar cell design. By adjusting different property values, such as carrier lifetimes and doping densities, we can parameterize the solar cell efficiency and current and voltage data. From this data, we can pinpoint the exact inputs and manufacturing processes that need to be changed in order to create solar cells with higher efficiencies.

4. Conclusion In this research, we present a Matlab-based analytical model for a tandem junction solar cell based on a thin-film, lead-based perovskite top cell and a wafer-based Si bottom cell. The model first

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Fig. 13. The (a) IQE, (b) EQE, and (c) I-V curves of a perovskite/bSi tandem cell (n-terminal configuration) as simulated by the Matlab model (cell area = 1 cm2).

Table 3 Output parameters of perovskite/bare Si cell (series connection).

Table 5 Output parameters of perovskite/bSi cell (series connection).

Data

Perovskite top cell

Bare Si bottom cell

Tandem cell

Data

Perovskite top cell

bSi bottom cell

Tandem cell

Jsc (mA/cm2) Voc (mV) FF (%) g (%)

13.16 840.3 86.56 9.570

12.69 625.7 83.27 6.61

12.69 1466 91.25 16.98

Jsc (mA/cm2) Voc (mV) FF (%) g (%)

13.16 840.3 86.56 9.57

18.59 635.6 83.46 9.86

13.16 1476 91.29 17.73

Table 4 Output parameters of perovskite/SiNx cell (series connection).

Table 6 Efficiency of the tandem cell (n-terminal configuration).

Data

Perovskite top cell

SiNx bottom cell

Tandem cell

Jsc (mA/cm2) Voc (mV) FF (%) g (%)

13.16 840.3 86.56 9.57

18.23 635.1 83.45 9.66

13.16 1475 91.29 17.73

Tandem cell type

Perovskite top cell efficiency (%)

Si bottom cell efficiency (%)

Tandem cell efficiency (%)

Bare Si bottom cell SiNx bottom cell bSi bottom cell

14.46 14.46 14.46

11.32 17.09 17.32

25.78 31.55 31.78

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the tandem cell. The versatile model was used to simulate perovskite/Si tandem cell using different kinds of Si bottom cells (bare Si, SiNx coated, bSi), but it can be easily modified to analyze other absorbers. This model allows us to optimize specific absorber properties in order to reach higher efficiencies, aiding in the progress of solar cell research. Acknowledgements We gratefully acknowledge the Iowa Energy Center Grant Number: OG-16-019, the Internal Funding Initiative (IFI) grant sponsored by the University of Iowa Vice President of Research Office, and the 2015 Old Gold Summer Fellowship awarded by the University of Iowa to Fatima Toor. References

Fig. 14. Tandem cell (n-terminal configuration) efficiency contour plots with respect to perovskite bandgap and thickness for bottom cell of (a) bare Si, (b) Si with SiNx AR coating, and (c) bSi.

calculates the photocurrent of the tandem cell from the parameters entered by the one-dimensional, steady state continuity equations. From there, it calculates the quantum efficiency curves as well as the current-voltage and power curves for the individual cells and

Bai, S., Wu, Z.W., Wu, X.J., Jin, Y.Z., Zhao, N., Chen, Z.H., Mei, Q.Q., Wang, X.Z., Ye, Z., Song, T.Y., Liu, R.Y., Lee, S.T., Sun, B.Q., 2014. High-performance planar heterojunction perovskite solar cells: preserving long charge carrier diffusion lengths and interfacial engineering. Nano Res. 7, 1749–1758. Chilvery, A.K., Batra, A.K., Yang, B., Xiao, K., Guggilla, P., Aggarwal, M.D., Surabhi, R., Lal, R.B., Currie, J.R., Penn, B.G., 2015. Perovskites: transforming photovoltaics, a mini-review. J. Photon. Energy 5. Gonzalez-Pedro, V., Juarez-Perez, E.J., Arsyad, W.S., Barea, E.M., Fabregat-Santiago, F., Mora-Sero, I., Bisquert, J., 2014. General working principles of CH3NH3PbX3 perovskite solar cells. Nano Lett. 14, 888–893. Green, M.A., Ho-Baillie, A., Snaith, H.J., 2014. The emergence of perovskite solar cells. Nat. Photon. 8, 506–514. Green, M.A., Emery, K., Hishikawa, Y., Warta, W., Dunlop, E.D., 2016. Solar cell efficiency tables (version 48). Prog. Photovoltaics Res. Appl. 24, 905–913. Kayes, B.M., Nie, H., Twist, R., Spruytte, S.G., Reinhardt, F., Kizilyalli, I.C., Higashi, G. S., 2011. 27.6% conversion efficiency, a new record for single-junction solar cells under 1 sun illumination. In: 37th IEEE Photovoltaic Specialists Conference, pp. 000004–000008. Kojima, A., Teshima, K., Shirai, Y., Miyasaka, T., 2009. Organometal halide perovskites as visible-light sensitizers for photovoltaic cells. J. Am. Chem. Soc. 131, 6050. Koushik, D., Verhees, W.J.H., Kuang, Y., Veenstra, S., Zhang, D., Verheijen, M.A., Creatore, M., Schropp, R.E.I., 2017. High-efficiency humidity-stable planar perovskite solar cells based on atomic layer architecture. Energy Environ. Sci. 10, 91–100. Leijtens, T., Stranks, S.D., Eperon, G.E., Lindblad, R., Johansson, E.M.J., McPherson, I.J., Rensmo, H., Ball, J.M., Lee, M.M., Snaith, H.J., 2014. Electronic properties of meso-superstructured and planar organometal halide perovskite films: charge trapping, photodoping, and carrier mobility. ACS Nano 8, 7147–7155. Lien, S.Y., Wuu, D.S., 2009. Simulation and fabrication of heterojunction silicon solar cells from numerical computer and hot-wire CVD. Progr. Photovolt. 17, 489– 501. Liu, D.Y., Gangishetty, M.K., Kelly, T.L., 2014. Effect of CH3NH3PbI3 thickness on device efficiency in planar heterojunction perovskite solar cells. J. Mater. Chem. A 2, 19873–19881. Minemoto, T., Murata, M., 2014. Device modeling of perovskite solar cells based on structural similarity with thin film inorganic semiconductor solar cells. J. Appl. Phys. 116. Parikh, V.Y., Toledo, T.U.o., 2007. Studies of Two-Terminal and Four-Terminal Polycrystalline Thin Film Tandem Solar Cells Based on II–VI Materials. University of Toledo. Rajamanickam, N., Kumari, S., Vendra, V.K., Lavery, B.W., Spurgeon, J., Druffel, T., Sunkara, M.K., 2016. Stable and durable CH3NH3PbI3 perovskite solar cells at ambient conditions. Nanotechnology 27, 235404. Savin, H., Repo, P., von Gastrow, G., Ortega, P., Calle, E., Garín, M., Alcubilla, R., 2015. Black silicon solar cells with interdigitated back-contacts achieve 22.1% efficiency. Nat. Nano 10, 624–628. Sze, S.M., Ng, K.K., 2006. Physics of Semiconductor Devices. Wiley-Interscience. Toor, F., Branz, H.M., Page, M.R., Jones, K.M., Yuan, H.-C., 2011. Multi-scale surface texture to improve blue response of nanoporous black silicon solar cells. Appl. Phys. Lett. 99, 103501. Toor, F., Miller, J.B., Davidson, L.M., Duan, W., Jura, M.P., Yim, J., Forziati, J., Black, M. R., 2016a. Metal assisted catalyzed etched (MACE) black Si: optics and device physics. Nanoscale 8, 15448–15466. Toor, F., Miller, J.B., Davidson, L.M., Nichols, L., Duan, W., Jura, M.P., Yim, J., Forziati, J., Black, M.R., 2016b. Nanostructured silicon via metal assisted catalyzed etch (MACE): chemistry fundamentals and pattern engineering. Nanotechnology 27, 412003. Yamaguchi, M., 2003. III–V compound multi-junction solar cells: present and future. Sol. Energy Mater. Sol. Cells 75, 261–269.