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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