Supplemental Material
Numerical simulation: Toward the design of high-efficiency perovskite planar
solar cells
Feng Liu,1 Jun Zhu,1 Junfeng Wei,1 Yi Li,1 Mei Lv,1 Shangfeng Yang,2
Bing Zhang,3 Jianxi Yao,3 and Songyuan Dai1,3
1
Key Laboratory of Novel Thin Film Solar Cells, Institute of Plasma Physics, Chinese
Academy of Sciences, P.O. Box 1126, Hefei, 230031, P. R. China
2
Hefei National Laboratory for Physical Sciences at Microscale, Department of
Materials Science and Engineering, University of Science and Technology of China,
Hefei, 230026, P. R. China
3
State Key Laboratory of Alternate Electrical Power System with Renewable Energy
Sources, North China Electric Power University, Beijing, 102206, P. R. China
1. The Poisson equation (1), hole continuity equation (2) and electron continuity
equation (3) are shown as follows:
d 
dψ 


  x 
  q  p( x)  n(x)  N d ( x)  N a ( x)  pt ( x)  nt ( x) 
dx 
dx 
dpn
p  pn 0
dp
d 2 pn
dξ
 Gp  n
 pnμ p
 μ p ξ n  Dp
dt
τp
dx
dx
dx 2
dn p
dt
 Gn 
np  np0
τn
dn p
d 2np
dξ
 n pμ n
+ μ nξ
 Dn
dx
dx
dx 2
(1)
(2)
(3)
where ε is the permittivity and q the electron charge, G the generation rate and D the
diffusion coefficient. ψ is the electrostatic potential and n, p, nt, pt are the free electron,
free hole, trapped electron and trapped hole, respectively. N+d is the ionized donor-like
doping concentration and N-a the ionized acceptor-like doping concentration. ξ is the
electric field.
2.
FIG. S1. Schematic diagram of the planar heterojunction-based perovskite solar cells.
3. TABLE S1. AMPS-1D parameters set for the baseline solar cells.
Compact
Parameters and units
CH3NH3PbI3
TiO2
Dielectric Constant
1001
302
Band Gap (eV)
3.2
1.54
Electron Affinity (eV)
4
3.934
Thickness (nm)
90
400
0.006,
Electron and Hole Mobility (cm2/V/S)
50, 506
0.0061
Acceptor Concentration (cm-3)
0
(2.14×1017)4
Donor Concentration (cm-3)
(5×1019)1
0
Effective Conduction Band Density
(1×1021)9 (2.5×1020)4
(cm-3)
Effective Valence Band Density (cm-3)
(2×1020)5 (2.5×1020)4
Characteristic Energy for Donor and
(0.015,
0.01,0.01
Acceptor-Like Tails (eV)
0.015)10
3
14
Band Tail Density of States(1/cm /eV)
1×10
1×1014
Capture Aross Section for Electrons and
1×10-15,
1×10-15,
Holes in Donor Tail States (cm2)
1×10-17
1×10-17
Capture Cross Section for Electrons and
1×10-17,
1×10-17,
Holes in Acceptor Tail States (cm2)
1×10-15
1×10-15
Gaussian Defects Donor and Acceptor
1×1017,
1×1014,
State Density (cm-3)
1×1017
1×1014
Gaussian Defects Donor and Acceptor
1.1, 1.1
1.2, 1.2
Peak Energy (eV)
Standard Deviation (eV)
0.1, 0.1
0.1, 0.1
Capture Cross Section of Donor-Like
1×10-19,
1×10-20,
Gaussian State for Electron and Holes
1×10-18
1×10-19
(cm2)
Capture Cross Section of Acceptor-Like
1×10-18,
1×10-19,
Gaussian State for Electron and Holes
1×10-19
1×10-20
(cm2)
Spiro-MeOTAD
33
2.915
2.25
400
0.0001, 0.00017
(3×1018)8
0
2.5×1020
2.5×1020
0.01, 0.01
1×1014
1×10-15, 1×10-17
1×10-17, 1×10-15
1×1016, 1×1016
1.1, 1.1
0.1, 0.1
1×10-19, 1×10-18
1×10-18, 1×10-19
Left and right contact work function: -4.4 eV (FTO) and -5.1 eV (Au), respectively. Ohmic contact
with surface recombination speed of electrons and holes: 1×107 cm/s.
4.
FIG. S2. J-V curves of the solar cells that result from the numerical simulation with parameters set
in Table S1.
5.
FIG. S3. Effective absorption coefficient of the CH3NH3PbI3 films (derived from Ref. 10).
6. TABLE S2. Parameters set for the thin inserted layer.
Layer at the TiO2/CH3NH3PbI3
Parameters and units
interface
Dielectric Constant
302
Band Gap (eV)
1.54
Electron Affinity (eV)
3.934
Thickness (nm)
4
2
Electron and Hole Mobility (cm /V/S)
50, 506
Acceptor Concentration (cm-3)
(2.14×1017)4
Donor Concentration (cm-3)
0
-3
Effective Conduction Band Density (cm )
(2.5×1020)4
Effective Valence Band Density (cm-3)
(2.5×1020)4
Characteristic Energy for Donor and
(0.015, 0.015)10
Acceptor-Like Tails (eV)
Band Tail Density of States(1/cm3/eV)
Capture Aross Section for Electrons and
Holes in Donor Tail States (cm2)
Capture Cross Section for Electrons and
Holes in Acceptor Tail States (cm2)
Switch-Over Energy (eV)
Density of Midgap Acceptor and
Donor-Like States (cm-3eV-1)
Capture Cross Section of Electrons and
Holes in Donor Midgap States (cm2)
Capture Cross Section of Electrons and
Holes in Acceptor Midgap States (cm2)
1×1014
1×10-15, 1×10-17
1×10-17, 1×10-15
0.7
1×1016 to 1×1021
1×10-17, 1×10-18
1×10-18, 1×10-17
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