Supplemental Material

Numerical simulation: Toward the design of high-efficiency perovskiteplanar 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

1Key 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:

(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-basedperovskite solar cells.

3. TABLES1. AMPS-1D parameters set for the baseline solar cells.

Parameters and units / Compact TiO2 / CH3NH3PbI3 / Spiro-MeOTAD
Dielectric Constant / 1001 / 302 / 33
Band Gap (eV) / 3.2 / 1.54 / 2.915
Electron Affinity (eV) / 4 / 3.934 / 2.25
Thickness (nm) / 90 / 400 / 400
Electron and Hole Mobility (cm2/V/S) / 0.006, 0.0061 / 50, 506 / 0.0001, 0.00017
Acceptor Concentration (cm-3) / 0 / (2.14×1017)4 / (3×1018)8
Donor Concentration (cm-3) / (5×1019)1 / 0 / 0
Effective Conduction Band Density (cm-3) / (1×1021)9 / (2.5×1020)4 / 2.5×1020
Effective Valence Band Density (cm-3) / (2×1020)5 / (2.5×1020)4 / 2.5×1020
Characteristic Energy for Donor and Acceptor-Like Tails (eV) / 0.01,0.01 / (0.015, 0.015)10 / 0.01, 0.01
Band Tail Density of States(1/cm3/eV) / 1×1014 / 1×1014 / 1×1014
Capture Aross Section for Electrons and Holes in Donor Tail States (cm2) / 1×10-15, 1×10-17 / 1×10-15, 1×10-17 / 1×10-15, 1×10-17
Capture Cross Section for Electrons and Holes in Acceptor Tail States (cm2) / 1×10-17, 1×10-15 / 1×10-17, 1×10-15 / 1×10-17, 1×10-15
Gaussian Defects Donor and Acceptor State Density (cm-3) / 1×1017, 1×1017 / 1×1014, 1×1014 / 1×1016, 1×1016
Gaussian Defects Donor and Acceptor Peak Energy (eV) / 1.1, 1.1 / 1.2, 1.2 / 1.1, 1.1
Standard Deviation (eV) / 0.1, 0.1 / 0.1, 0.1 / 0.1, 0.1
Capture Cross Section of Donor-Like Gaussian State for Electron and Holes (cm2) / 1×10-19, 1×10-18 / 1×10-20, 1×10-19 / 1×10-19, 1×10-18
Capture Cross Section of Acceptor-Like Gaussian State for Electron and Holes (cm2) / 1×10-18, 1×10-19 / 1×10-19, 1×10-20 / 1×10-18, 1×10-19

Left and right contact workfunction: -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.TABLES2. Parameters set for the thin inserted layer.

Parameters and units / Layer at the TiO2/CH3NH3PbI3 interface
Dielectric Constant / 302
Band Gap (eV) / 1.54
Electron Affinity (eV) / 3.934
Thickness (nm) / 4
Electron and Hole Mobility (cm2/V/S) / 50, 506
Acceptor Concentration (cm-3) / (2.14×1017)4
Donor Concentration (cm-3) / 0
Effective Conduction Band Density(cm-3) / (2.5×1020)4
Effective Valence Band Density (cm-3) / (2.5×1020)4
Characteristic Energy for Donor and Acceptor-Like Tails (eV) / (0.015, 0.015)10
Band Tail Density of States(1/cm3/eV) / 1×1014
Capture Aross Section for Electrons and Holes in Donor Tail States (cm2) / 1×10-15, 1×10-17
Capture Cross Section for Electrons and Holes in Acceptor Tail States (cm2) / 1×10-17, 1×10-15
Switch-Over Energy (eV) / 0.7
Density of Midgap Acceptor and Donor-Like States (cm-3eV-1) / 1×1016 to 1×1021
Capture Cross Section of Electrons and Holes in Donor Midgap States (cm2) / 1×10-17, 1×10-18
Capture Cross Section of Electrons and Holes in Acceptor Midgap States (cm2) / 1×10-18, 1×10-17

Reference

1K. Wojciechowski, M. Saliba, T. Leijtens, A. Abate, and H. J. Snaith, Energ. Environ. Sci. 7, 1142 (2014).

2A. Poglitsch and D. Weber, J. Chem. Phys. 87, 6373 (1987).

3D. Poplavskyy and J. Nelson, J. Appl. Phys. 93, 341 (2003).

4W. Abu Laban and L. Etgar, Energ. Environ. Sci. 6, 3249 (2013).

5M. K. Wang, C. Gratzel, S. J. Moon, R. Humphry-Baker, N. Rossier-Iten, S. M. Zakeeruddin, and M. Gratzel, Adv. Funct. Mater. 19, 2163 (2009).

6C. C. Stoumpos, C. D. Malliakas, and M. G. Kanatzidis, Inorg. Chem. 52, 9019 (2013).

7H. J. Snaith and M. Gratzel, Appl. Phys. Lett. 89, 262114 (2006).

8J. Garcia-Canadas, F. Fabregat-Santiago, H. J. Bolink, E. Palomares, G. Garcia-Belmonte, and J. Bisquert, Synth. Met. 156, 944 (2006).

9B. C. O'Regan, J. R. Durrant, P. M. Sommeling, and N. J. Bakker, J. Phys. Chem. C 111, 14001 (2007).

10S. De Wolf, J. Holovsky, S. J. Moon, P. Loper, B. Niesen, M. Ledinsky, F. J. Haug, J. H. Yum, and C. Ballif, J. Phys. Chem. Lett. 5, 1035 (2014).