One-dimensional modeling for optoelectrical simulation of a mesoporous perovskite solar cell

Gholamhosain Haidari

doi:10.1364/AO.58.007006

Applied Optics
Vol. 58,
Issue 26,
pp. 7006-7013
(2019)
•https://doi.org/10.1364/AO.58.007006

One-dimensional modeling for optoelectrical simulation of a mesoporous perovskite solar cell

Gholamhosain Haidari

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Gholamhosain Haidari, "One-dimensional modeling for optoelectrical simulation of a mesoporous perovskite solar cell," Appl. Opt. 58, 7006-7013 (2019)

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Abstract

The metal-halide perovskite solar cell (PSC) has risen to the forefront of photovoltaic research, and presents the potential for low-cost fabrication with high-power conversion efficiency. Better understanding of the PSC operation mechanism is necessary and required to further improve the performance of the device. Therefore, in addition to numerous experimental studies, some number of optoelectrical simulations are necessary. However, usually, simulations are either electrical or optical and more in relation to one-dimensional (1D) structures such as planar cells. In this study, an approach to optoelectrical simulation of a 3D solar cell, such as the mesoporous PSC, has been presented. First, the 3D layers, such as the mesoporous layer, are modeled to a 1D effective layer using Bergman’s effective medium theory. By using the spectral density function, this effective medium theory is able to introduce the 1D equivalent of the 3D layer. Then, the optical results by transfer matrix method are transferred to the SCAPS-1D code, in order to simulate the EQE spectrum and the JV curve of solar cells. The simulation results were compared with the experimental results for two mesoporous PSC, one without a capping perovskite layer and the other with the capping layer. The results of this study showed that the proposed procedure can simulate and therefore investigate the optoelectrical properties of 3D mesoporous solar cells, which can also be extended to similar 3D structures. This 1D simulation procedure, compared to 3D simulation, has a much lower execution time offering more simplicity and no need for commercial codes or specific hardware.

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Parameters	FTO	${TiO}_{2}$	${MAPbI}_{3}$	Spiro-MeOTAD
Band gap (eV)	3.5	3.2	1.5	2.91
Electron affinity (eV)	4	4	3.93	2.2
Dielectric permittivity ( $ε / ε_{0}$ )	9	9	6.5	3
CB effective density of states ( $1 / {cm}^{3}$ )	$2.2 \times 10^{18}$	$1 \times 10^{21}$	$2.5 \times 10^{20}$	$2.5 \times 10^{20}$
VB effective density of states ( $1 / {cm}^{3}$ )	$1.8 \times 10^{18}$	$2 \times 10^{20}$	$2.5 \times 10^{20}$	$2.5 \times 10^{20}$
Electron thermal velocity (cm/s)	$10^{7}$	$10^{7}$	$10^{7}$	$10^{7}$
Hole thermal velocity (cm/s)	$10^{7}$	$10^{7}$	$10^{7}$	$10^{7}$
Electron mobility ( ${cm}^{2} / Vs$ )	20	0.006	50	$2 \times 10^{- 4}$
Hole mobility ( ${cm}^{2} / Vs$ )	10	0.006	50	$2 \times 10^{- 4}$
Donor concentration ( $1 / {Cm}^{3}$ )	$2 \times 10^{19}$	$5 \times 10^{19}$	–	10% of NA
Acceptor concentration ( $1 / {Cm}^{3}$ )	—	10% of ND	$2.1 \times 10^{17}$	$3.0 \times 10^{18}$

Defect layer properties	${TiO}_{2}$	Mesoporous layer	${CH}_{3} {NH}_{3} {PbI}_{3}$	Spiro-MeOTAD
Energy for donor/acceptor tails (eV)	0.01	0.015	0.015	0.01
Energy for donor/acceptor tails (eV)	0.01	0.015	0.015	0.01
Band tail density of states ( ${cm}^{- 3} {ev}^{- 1}$ )	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$
Band tail density of states ( ${cm}^{- 3} {ev}^{- 1}$ )	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$
Capture cross section of electrons/holes in donor tail states ( ${cm}^{2}$ )	$1.0 \times 10^{- 17}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 17}$
	$1.0 \times 10^{- 17}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 17}$
Capture cross section of electrons/holes in acceptor tail states ( ${cm}^{2}$ )	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$
Gaussian defect
Donor/acceptor state density ( ${cm}^{- 3}$ )	$1.0 \times 10^{17}$	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$	$1.0 \times 10^{16}$
Donor/acceptor state density ( ${cm}^{- 3}$ )	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 19}$
Capture cross section of donor Gaussian state electron/holes ( ${cm}^{2}$ )	$1.0 \times 10^{- 18}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 18}$
	$1.0 \times 10^{- 18}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 18}$
Capture cross section of acceptor Gaussian state electron/holes ( ${cm}^{2}$ )	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 19}$
Energy level with respect to the reference (eV)	1.1/1.1	1.2/1.2	1.2/1.2	1.1/1.1
Characteristic energy (eV)	0.1/0.1	0.1/0.1	0.1/0.1	0.1/0.1

Defect layer properties	$mesoporous / {MAPbI}_{3}$	${MAPbI}_{3} / Spiro - MeOTAD$
Total density ( ${cm}^{2}$ )	$1.0 \times 10^{9}$	$1.0 \times 10^{9}$
Total density ( ${cm}^{2}$ )	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 18}$
Capture cross section for electrons/holes ( ${cm}^{2}$ )	$1.0 \times 10^{- 18}$	$1.0 \times 10^{- 19}$
Energy with respect to the reference (eV)	0.07	0.32

Parameters	FTO	${TiO}_{2}$	${MAPbI}_{3}$	Spiro-MeOTAD
Band gap (eV)	3.5	3.2	1.5	2.91
Electron affinity (eV)	4	4	3.93	2.2
Dielectric permittivity ( $ε / ε_{0}$ )	9	9	6.5	3
CB effective density of states ( $1 / {cm}^{3}$ )	$2.2 \times 10^{18}$	$1 \times 10^{21}$	$2.5 \times 10^{20}$	$2.5 \times 10^{20}$
VB effective density of states ( $1 / {cm}^{3}$ )	$1.8 \times 10^{18}$	$2 \times 10^{20}$	$2.5 \times 10^{20}$	$2.5 \times 10^{20}$
Electron thermal velocity (cm/s)	$10^{7}$	$10^{7}$	$10^{7}$	$10^{7}$
Hole thermal velocity (cm/s)	$10^{7}$	$10^{7}$	$10^{7}$	$10^{7}$
Electron mobility ( ${cm}^{2} / Vs$ )	20	0.006	50	$2 \times 10^{- 4}$
Hole mobility ( ${cm}^{2} / Vs$ )	10	0.006	50	$2 \times 10^{- 4}$
Donor concentration ( $1 / {Cm}^{3}$ )	$2 \times 10^{19}$	$5 \times 10^{19}$	–	10% of NA
Acceptor concentration ( $1 / {Cm}^{3}$ )	—	10% of ND	$2.1 \times 10^{17}$	$3.0 \times 10^{18}$

Defect layer properties	${TiO}_{2}$	Mesoporous layer	${CH}_{3} {NH}_{3} {PbI}_{3}$	Spiro-MeOTAD
Energy for donor/acceptor tails (eV)	0.01	0.015	0.015	0.01
Energy for donor/acceptor tails (eV)	0.01	0.015	0.015	0.01
Band tail density of states ( ${cm}^{- 3} {ev}^{- 1}$ )	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$
Band tail density of states ( ${cm}^{- 3} {ev}^{- 1}$ )	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$
Capture cross section of electrons/holes in donor tail states ( ${cm}^{2}$ )	$1.0 \times 10^{- 17}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 17}$
	$1.0 \times 10^{- 17}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 16}$	$1.0 \times 10^{- 17}$
Capture cross section of electrons/holes in acceptor tail states ( ${cm}^{2}$ )	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$	$1.0 \times 10^{- 15}$
Gaussian defect
Donor/acceptor state density ( ${cm}^{- 3}$ )	$1.0 \times 10^{17}$	$1.0 \times 10^{14}$	$1.0 \times 10^{14}$	$1.0 \times 10^{16}$
Donor/acceptor state density ( ${cm}^{- 3}$ )	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 19}$
Capture cross section of donor Gaussian state electron/holes ( ${cm}^{2}$ )	$1.0 \times 10^{- 18}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 18}$
	$1.0 \times 10^{- 18}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 18}$
Capture cross section of acceptor Gaussian state electron/holes ( ${cm}^{2}$ )	$1.0 \times 10^{- 19}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 20}$	$1.0 \times 10^{- 19}$
Energy level with respect to the reference (eV)	1.1/1.1	1.2/1.2	1.2/1.2	1.1/1.1
Characteristic energy (eV)	0.1/0.1	0.1/0.1	0.1/0.1	0.1/0.1

Abstract

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Applied Optics