Supporting Information for

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(a) Energy band diagram and (b) electric field distribution of the bottom cell (at .... with 7.2% Efficiency by Incorporation of Silver, ACS Energy Letters, 1 (2016) ...

Supporting Information for “Proposition of an Environment Friendly Triple Junction Solar Cell Based on Earth Abundant CBTSSe/CZTS/ACZTSe Materials” [DOI 10.1002/pssr.201700335] Uday Saha and Md. Kawsar Alam1 Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka 1205, Bangladesh.

S1. Simulation Methodology Simulation of the triple junction solar cell was done is two steps: (a) optical simulation for calculating absorption and optical generation rate and (b) electrical simulation for finding the PCE and other characteristics features of the tandem cell. In optical simulation, we first solved Maxwell’s curl equation using finite difference time domain (FDTD) analysis for optical electric field (

) distribution inside different layers [Eqns. (S1) to (S3)].



S1

, where , while

, and ,

S2

1

S3

are the magnetic, electric, and displacement fields, respectively,

is the complex relative dielectric constant and

is the angular frequency.

       Corresponding Author. Email Addresses: [email protected] ; kawsar.alam @alumni.ubc.ca.

1

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Each material was modeled by their respective refractive index (n) and extinction coefficient ( ) as a function of wavelength. The absorbed power (

) inside different layers was

then calculated from the optical electric field [Eq. (S4)]. 1 2 Thus, the generation rate,

,

,

S4

according to the Eqs. (S5) and (S6).

was obtained from , ,

where

,

, ,

S5 ,

,

S6

is the Planck’s constant. For optical simulation, we used periodic boundary conditions in

horizontal ( ) direction and perfectly matched layer (PML) boundary condition on top and bottom surfaces (in

direction). We have used AM 1.5G standard solar spectrum as the input radiation

source for optical simulation.

Electrical characteristics of the tandem cell were calculated in two parts. In first part, we simulated top, middle and bottom cells separately and derived their characteristics features. In this respect, Poisson’s equation, drift-diffusion equations and continuity equations were solved selfconsistently (Eqs. (S7) to (S11)) for electrons and holes and performance metrics such as open circuit voltage (

, short circuit current (

, fill factor (

) and efficiency ( ) were found from

the J-V characteristics of top, middle and bottom cells independently.

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. ε

V

1

1

where ),

q ,

.

S7 ,

S8

,

S9

,

.

S10

,

S11

is the dc dielectric permittivity, is the electrostatic potential (electric field,

is the net charge density (

impurity density),



, which includes the contribution

from the ionized

is the electron (hole) current density, q is the positive electron charge,

is the mobility of electron (hole),

is the diffusivity of electron (hole) (

and p are electron and hole densities, respectively,



), n

is the net recombination rate (the

difference between the recombination rate and generation rate),

is the Boltzmann constant and

T is the temperature (the subscripts n and p indicate quantities that are specific to the carrier type). Generation rate calculated from the optical simulation was given as an input in the continuity equations and the equation set [Eqs. (S7) to (S11)] was solved self-consistently using Dirichlet boundary conditions and Neumann conditions at the boundaries and interfaces, respectively. We have used Lumerical FDTD and Device solution module packages for optical and electrical simulations, respectively. Next, each cell was modeled by the single-diode equivalent circuit as shown in Fig. S1 where,

is the photon generated current density,

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and

represent series

and shunt resistances, respectively. The current density through the diode,

can be calculated

from:

1 ,

where

is the dark diode reverse-saturation current,

12

is the bias voltage across the diode and

is the ideality factor.

  ) 

 

Fig. S1. Equivalent circuit model for individual cells.

Then, we matched the J-V characteristics derived from the circuit model with the device simulation results for each cell through least square regression method and obtained the circuit parameters

,

, ,

and

for each cell. The values of these parameters are dynamically

changed with absorber thickness to match the J-V characteristics of device simulation. Typical matching of J-V and P-V characteristics for 250 nm CBTSSe, 300nm CZTS and 1000 nm ACZTSe absorbers is shown for top, middle and bottom cells in Fig. S2, respectively.

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(b)

(a) J (mA/cm 2 )

15 10 5

Device Simulation Circuit Model

0

(c)

0

0.5

1

(d)

Voltage (V)

J (mA/cm 2 )

15 10 Device Simulation Circuit Model

5 0 0

(e)

0.2

0.4

0.6

0.8

Voltage (V)

J (mA/cm 2 )

20

(f)

15 10 Device Simulation Circuit model

5 0 0

0.2

0.4

Voltage (V)

Fig. S2.  Comparison between device simulation and circuit model for top cell (a) (J-V)top and (b) (PV)top characteristics; middle cell (c) (J-V)middle and (d) (P-V)middle characteristics and bottom cell (e) (JV)bottom and (f) (P-V)bottom characteristics. 

After obtaining the model parameters of each cell, we have applied the series circuit rules for top, middle and bottom cells and generated the J-V characteristics of our triple junction tandem cell via Matlab Simulink (Fig. S3). The tunneling junction was modeled as ohmic contact. This method of analysis enables us to compare the performances of individual cells conveniently and we can clearly comprehend their contributions in a tandem architecture. Moreover, this method is also computationally efficient.

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(a)

(b)

Top Cell

+

+

-

Middle Cell

+ -

Bottom Cell

 

+ -

-

Fig. S3.  (a) Topology of CBTSSe/CZTS/ACZTSe tandem stacks and (b) Matlab Simulink model of triple junction solar cell. 

S2. Design of the Bottom Cell  

In the bottom cell (ITO/ZnO(n)/ZnS(n)/ACZTSe(p)/CZTSe(p+)/Mo), built-in potential originates from ZnS and ACZTSe, and CZTSe(p+) serves a back-surface field (BSF) layer. Due to the low carrier concentration in ACZTSe(p) (~1014 cm-3 at 45% of Ag/(Cu+Ag) ratio [1]) compared to ZnS(n) (~1016 cm-3 ), the depletion region extends throughout the entire active pregion. As a result, the minority carriers generated in this region are drifted by the built-in electric field which ensures effective collection of generated charges. The depletion region in the p-side was calculated to be more than 2.5 micron for 1×1014 cm-3 and 5×1016 cm-3 doping in ACZTSe (pregion) and ZnS (n-region), respectively (from Eq. (S13))

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/

2

where

( ) is the permittivity,

built-in potential

(

,

13

) is the doping concentration of the n (p) region and the

can be calculated from Eq. (S14).



ln



.

14

(a) e‐

e‐ e‐

Mo h+ CZTSe (p+)

ZnO (n)

h+ ACZTSe (p)

ZnS (n)

h+

ITO

(b) ZnS (n) ZnO (n) ACZTSe (p) CZTSe(p+) ITO

Mo

Fig. S4.  (a) Energy band diagram and (b) electric field distribution of the bottom cell (at 1000 nm and 200 nm thickness of ACZTSe and CZTSe, respectively). Arrows in (a) represent drift motion of carriers. 

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Here,

is the bandgap of the p-region, ∆

is the difference between the electron

affinities of n and p regions,

is the density of state (DOS) of electron in n region and

the DOS of hole in p region.

and

is

are the equilibrium concentration of electrons and holes

in n and p regions, respectively. Additionally, as the carrier concentration in CZTSe (~1016 cm-3) is few orders higher than that of ACZTSe (~1014cm-3) [1], CZTSe acts as a BSF layer in the bottom cell and reduces the back surface recombination. The band diagram and the electric field distribution of the bottom cell are shown in Fig. S4(a) and S4(b), respectively. It can be readily noticed from the electric field variation that the built-in field is extended throughout the active layer and correspondingly, a linear slope exists in the energy band diagram of Fig S4(a). Further, it can be seen that the ZnS (n) (buffer layer), CZTSe(p+) (BSF layer) are also depleted.

S3. Model Verification  

We modeled three experimental structures to benchmark our used parameters and Table S1 shows the comparison between our simulation results and experimentally reported values. The optical and basic electrical parameters of CdS, ZnS, ZnO and AZO as well as recombination parameters, taken from literature (optical [2-14]; electrical [1, 2, 11, 13, 15-27], are listed in Table S2. In this regard, it should be noted that n-type behavior of ZnS with carrier density in the range of 1.6×1016cm-3-3.8×1017cm-3 has been reported in literature [28]. In this work, we have considered 5×1016 cm-3 carrier concentration for ZnS which falls in the range of the experimentally reported values.

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Table S1 Comparison of simulation results with the experimental data of individual cells  

Top cell (mV)

(mA/cm2) FF

Efficiency (%)

Experimental [26]

611

17.4

0.489

5.20

Simulation

648

17.8

0.47

5.42

Middle cell Experimental [29] Simulation

661

19.5

0.658

8.4

648.33

21.25

0.621

8.54

Bottom Cell Experimental [30]

513.4

35.2

0.698

12.6

Simulation

533.1

33.91

0.704

12.73

   

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Table S2 Basic electrical parameters of CdS, ZnS, ZnO and AZO. Features

CdS

ZnS

ZnO

AZO

(n)

(n)

(n)

(n++)

DC permittivity

10 [15, 16]

9 [15, 16]

9 [15, 16]

9 [15, 16]

Bandgap (eV)

2.42 [16, 17]

3.58 [17]

3.37

3.37 [21, 23]

[21, 23] Electron affinity (eV)

3.75 [15, 16]

3.8 [20]

4 [15]

4 [15]

Electron effective

0.25 [17, 18]

0.22 [17]

0.275

0.275

[16, 17]

[16, 17]

0.59

0.59 [16, 17]

mass (me/mo) Hole effective mass

5 [17, 18]

1.76 [17]

[16, 17]

(mp/mo) Electron mobility

160 [16, 17]

230 [17]

150 [17]

(cm2/V-s)

50 [16, 17, 31]

15 [16, 17]

40 [17]

50 [22, 23]

5 [16, 17]

0

0

0

0

Donor

5×1016

5×1016 [28]

1.5×1017

8×1018

concentration(cm-3)

[16, 17]

[15, 16]

[16, 17]

SRH life time (s)

7.5×10-10

5×10-10 [16]

-

-

1.5×10-10[16]

-

-

-

-

1 ×107

Hole mobility (cm2/V-s) Acceptor concentration (cm-3)

[16, 17] Radiative

1.02×10-10

recombination

[16]

(ehp capture rate cm3/s) Surface

-

Recombination

(AZO/Al and

Velocity

AZO/MgF2)

(cm/s)

[32]

 

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S4. Optical Modeling of Tandem Cell  

Figures S5 (a) and (b) represent the generation and absorption profiles of the tandem cell obtained from FDTD simulation at 250nm CBTSSe, 300nm CZTS and 1000 nm ACZTSe thicknesses. Due to lower penetration depth, higher energy photons get absorbed within relatively lower thicknesses of the top cell. As the top cell absorbs high energy photons, it requires higher power to match the generation rate with middle and bottom cells (Fig. S5(b)). Middle cell absorbs relatively less energy photons and the penetration depth of these photons are is higher than that of the top cell. As a result, the middle cell requires higher thickness of the main absorber (CZTS) than that of the top cell. However, it entails less power to generate the same amount of electronhole pair. On the contrary, bottom cell absorbs long wavelength photons and requires much higher thickness than top and middle cells to use the solar spectrum efficiently. As low energy photons get absorbed in the bottom cell, it requires much less power to generate the same amount of carrier generated in top and middle cells. Due to different bandgap materials, solar spectrum is used efficiently in our CBTSSe/CZTS/ACZTSe solar cells. The refractive index and extinction coefficient of our main absorber layers in top (CBTSSe), middle (CZTS) and bottom cell (ACZTSe) are shown in Fig. 5(c) and Fig. 5(d) respectively [2, 14, 33].

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(b)

(a)

CBTSSe

CBTSSe

CZTS

CZTS

ACZTSe

ACZTSe

(d)

(c)

Fig. S5.  (a) Generation rate (cm-3s-1) profile, (b) absorbed power per unit volume (Wm-3) of the tandem cell (at 250 nm, 300 nm and 1000 nm thickness of CBTSSe, CZTS, ACZTSe respectively). Solar illumination is in the negative Y direction. The layers dimension with respect to Y axis positions are 0.5-0.7 : CZTSe, 0.7-1.7 : ACZTSe, 1.7-1.8 : ZnS, 1.8-1.9 : ZnO, 1.9-2.0 : ITO, 2.0-2.3 : CZTS, 2.3-2.37 : ZnS, 2.37-2.42 : ZnO, 2.42-2.52 : FTO, 2.52-2.77 : CBTSSe, 2.77-2.85 : ZnS, 2.852.9 : ZnO, 2.9-3.3 : AZO and 3.3-3.4 : MgF2 in Y axis. We apply periodic boundary condition in X- direction. (c) refractive index ( ) and (d) extinction coefficient ( ) of CBTSSe, CZTS and ACZTS used in simulation.    

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References [1] T. Gershon, Y.S. Lee, P. Antunez, R. Mankad, S. Singh, D. Bishop, O. Gunawan, M. Hopstaken, R. Haight, Photovoltaic Materials and Devices Based on the Alloyed Kesterite Absorber (AgxCu1–x)2ZnSnSe4, Advanced Energy Materials, 6 (2016) 1502468. [2] S. Adachi, Physical Properties, in: Copper Zinc Tin Sulfide-Based Thin-Film Solar Cells, John Wiley & Sons Ltd, NJ, USA, 2014, pp. 149-179. [3] M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry, McGraw-Hill, Inc., NY, USA, 2009. [4] W.L. Bond, Measurement of the Refractive Indices of Several Crystals, Journal of Applied Physics, 36 (1965) 1674-1677. [5] M. Debenham, Refractive Indices of Zinc Sulfide in the 0.405–13-μm Wavelength Range, Appl. Opt., 23 (1984) 2238-2239. [6] M. Fang, A. Aristov, K.V. Rao, A.V. Kabashin, L. Belova, Particle-free Inkjet Printing of Nanostructured Porous Indium Tin Oxide Thin Films, RSC Advances, 3 (2013) 19501-19507. [7] C.A. Klein, Room-temperature Dispersion Equations for Cubic Zinc Sulfide, Appl. Opt., 25 (1986) 1873-1875. [8] J.-H. Lee, K.-H. Ko, B.-O. Park, Electrical and Optical Properties of ZnO Transparent Conducting Films by the Sol–Gel Method, Journal of Crystal Growth, 247 (2003) 119-125. [9] H.H. Li, Refractive Index of Alkaline Earth Halides and its Wavelength and Temperature Derivatives, Journal of Physical and Chemical Reference Data, 9 (1980) 161-290. [10] E.D. Palik, Handbook of optical constants of solids, Academic press, CA, USA, 1998. [11] C. Persson, R. Chen, H. Zhao, M. Kumar, D. Huang, Electronic Structure and Optical Properties from First-Principles Modeling, in: Copper Zinc Tin Sulfide-Based Thin-Film Solar Cells, John Wiley & Sons Ltd, NJ, USA, 2014, pp. 75-105. [12] A. Guchhait, Z. Su, Y.F. Tay, S. Shukla, W. Li, S.W. Leow, J.M.R. Tan, S. Lie, O. Gunawan, L.H. Wong, Enhancement of Open-Circuit Voltage of Solution-Processed Cu2ZnSnS4 Solar Cells with 7.2% Efficiency by Incorporation of Silver, ACS Energy Letters, 1 (2016) 1256-1261. [13] J. Ge, C.R. Grice, Y. Yan, Cu-based Quaternary Chalcogenide Cu2BaSnS4 Thin Films Acting as Hole Transport Layers in Inverted Perovskite CH3NH3PbI3 Solar Cells, Journal of Materials Chemistry A, 5 (2017) 2920-2928.

13 of 15   

[14] W. Gong, T. Tabata, K. Takei, M. Morihama, T. Maeda, T. Wada, Crystallographic and Optical Properties of (Cu, Ag)2ZnSnS4 and (Cu, Ag)2ZnSnSe4 Solid Solutions, Physica Status Solidi (c), 12 (2015) 700-703. [15] S.-Y. Kuo, M.-Y. Hsieh, Efficiency Enhancement in Cu2ZnSnS4 Solar Cells with Subwavelength Grating Nanostructures, Nanoscale, 6 (2014) 7553-7559. [16] U. Saha, M.K. Alam, Proposition and Computational Analysis of a Kesterite/Kesterite Tandem Solar Cell with Enhanced Efficiency, RSC Advances, 7 (2017) 4806-4814. [17] O. Madelung, II-VI compounds, in: Semiconductors: Data Handbook, Springer Berlin Heidelberg, Berlin, Heidelberg, 2004, pp. 173-244. [18] W. Martienssen, Semiconductors, in: W. Martienssen, H. Warlimont (Eds.) Springer Handbook of Condensed Matter and Materials Data, Springer Berlin Heidelberg, Berlin, Heidelberg, 2005, pp. 575-694. [19] V.P. Devarajan, D. Nataraj, T. Pazhanivel, K. Senthil, M. Seol, K. Yong, J. Hermannsdorfer, R. Kempe, Molecular Conformation Dependent Emission Behaviour (Blue, Red and White Light Emissions) of All-trans-[small beta]-carotene-ZnS Quantum Dot Hybrid Nanostructures, Journal of Materials Chemistry, 22 (2012) 18454-18462. [20] A. Jha, S.K. Sarkar, D. Sen, K.K. Chattopadhyay, A Carbon Fiber-ZnS Nanocomposite for Dual Application as an Efficient Cold Cathode as well as a Luminescent Anode for Display Technology, Nanoscale, 7 (2015) 2536-2544. [21] J. Anderson, G.V.d.W. Chris, Fundamentals of Zinc Oxide as a Semiconductor, Reports on Progress in Physics, 72 (2009) 126501. [22] Z. Fan, J.G. Lu, Zinc Oxide Nanostructures: Synthesis and Properties, Journal of nanoscience and nanotechnology, 5 (2005) 1561-1573. [23] D.P. Norton, Y.W. Heo, M.P. Ivill, K. Ip, S.J. Pearton, M.F. Chisholm, T. Steiner, ZnO: Growth, Doping &Amp; Processing, Materials Today, 7 (2004) 34-40. [24] Z.-K. Yuan, S. Chen, H. Xiang, X.-G. Gong, A. Walsh, J.-S. Park, I. Repins, S.-H. Wei, Engineering Solar Cell Absorbers by Exploring the Band Alignment and Defect Disparity: The Case of Cu- and Ag-Based Kesterite Compounds, Advanced Functional Materials, 25 (2015) 6733-6743. [25] D. Shin, B. Saparov, D.B. Mitzi, Defect Engineering in Multinary Earth-Abundant Chalcogenide Photovoltaic Materials, Advanced Energy Materials, (2017) 1602366. [26] D. Shin, T. Zhu, X. Huang, O. Gunawan, V. Blum, D.B. Mitzi, Earth-Abundant Chalcogenide Photovoltaic Devices with over 5% Efficiency Based on a Cu2BaSn(S,Se)4 Absorber, Advanced Materials, 29 (2017) 1606945. 14 of 15   

[27] J. Ge, P.J. Roland, P. Koirala, W. Meng, J.L. Young, R. Petersen, T.G. Deutsch, G. Teeter, R.J. Ellingson, R.W. Collins, Y. Yan, Employing Overlayers To Improve the Performance of Cu2BaSnS4 Thin Film based Photoelectrochemical Water Reduction Devices, Chemistry of Materials, 29 (2017) 916-920. [28] Y. Yu, J. Jie, P. Jiang, L. Wang, C. Wu, Q. Peng, X. Zhang, Z. Wang, C. Xie, D. Wu, Y. Jiang, High-gain Visible-Blind UV Photodetectors Based on Chlorine-Doped n-type ZnS Nanoribbons with Tunable Optoelectronic Properties, Journal of Materials Chemistry, 21 (2011) 12632-12638. [29] B. Shin, O. Gunawan, Y. Zhu, N.A. Bojarczuk, S.J. Chey, S. Guha, Thin film Solar Cell with 8.4% Power Conversion Efficiency Using an Earth‐abundant Cu2ZnSnS4 Absorber, Progress in Photovoltaics: Research and Applications, 21 (2013) 72-76. [30] W. Wang, M.T. Winkler, O. Gunawan, T. Gokmen, T.K. Todorov, Y. Zhu, D.B. Mitzi, Device Characteristics of CZTSSe thin‐film solar cells with 12.6% efficiency, Advanced Energy Materials, 4 (2014). [31] G.K. Paul, S. Bandyopadhyay, S.K. Sen, Transport Properties of As-Prepared Al-Doped Zinc Oxide Films Using Sol–Gel Method, Physica Status Solidi (a), 191 (2002) 509-518. [32] G. Altamura, Development of CZTSSe thin films based solar cells", in, Department of Material Chemistry, Université Joseph-Fourier - Grenoble I, 2014. [33] J. Ge, P. Koirala, C.R. Grice, P.J. Roland, Y. Yu, X. Tan, R.J. Ellingson, R.W. Collins, Y. Yan, Oxygenated CdS Buffer Layers Enabling High Open-Circuit Voltages in Earth-Abundant Cu2BaSnS4 Thin-Film Solar Cells, Advanced Energy Materials, 7 (2017) 1601803.

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