Identifying recombination pathways in perovskite solar cells by simulating temperature-dependent light ideality factor

Abstract

This decade witnessed rapid progress in the development of organic–inorganic hybrid lead-halide perovskite-based solar cells. In particular, this class of solar cells showed high-power conversion efficiency and significant potentiality to realize a low-cost terawatt-scale power generation. This is mainly due to its high optical absorption coefficient with sharp absorption onset, long charge-carrier lifetime, tunable bandgap, and low-cost fabrication. However, despite advancement in the device performance, the underlying physics of charge-carrier dynamics needs important attention to develop insight into the performance bottlenecks and thereby better control and optimization over the device performances. Among the performance bottlenecks, the charge-carrier recombination is considered to be one of the dominant mechanisms that limit solar cell behavior. Therefore, in this work, the underlying interest is to identify recombination mechanisms by simulating the temperature-dependent light ideality factor. We consider a standard sandwich device structure with CH₃NH₃PbI₃ as an active layer. The Spiro and TiO₂ are taken as a hole- and electron-transporting layers, respectively. We utilized a one-dimensional drift–diffusion equation to simulate temporal open-circuit voltage V_OC (t) with varying light intensity, Φ, between 0.2 and 2.0 Sun equivalent and device temperature, T between 100 and 300 K. The temporal light ideality factor, n_id,l (t) is determined by evaluating the slope of the plots between V_OC (t) vs ln(Φ). The plot of temperature-dependent light ideality factor shows a fast rise in its value between the temperatures 100 to 150 K and tends slowly toward 2.0 as temperature increases. The observations clearly indicate that the recombination of charge-carriers is predominantly due to trap states, interfacial, or bulk, activated at higher temperatures. Further, the activation energy E_A ~ 1 eV is obtained from the V_OC vs T plot by extrapolating to T = 0. The value of E_A matches with the interfacial energy gap between the perovskite and the electron- and hole-transporting layers corroborating the dominance of interfacial recombination. Thus, the work carried out shed light on the recombination mechanisms in such a class of solar cells and their alternative variants.

Appendix: Description of parameters utilized for simulation

Description	Symbol	Value	Unit
Boltzmann constant	k B	8.62 × 10–5	eV K−1
Permittivity of free space	ε0	552434	e2 eV−1 cm−1
Charge of the species in units of e	q	1
Elementary charge	e	1.62 × 10–19	C
Temperature	T	100—300	K
Layer and subsection thickness array	d cell	{{200 × 10–7}; {2 × 10–7, 340 × 10–7, 2 × 10–7}; {100 × 10–7}}	cm
Number of points in layers and subsections array	p cell	{{100}; {40, 200, 40}; {100}}
Interfacial region thickness	d int	2 × 10–7	cm
Interfacial points	p int	40
Toggle Open Circuit	OC	Closed Circuit = 0, Open Circuit = 1
Layer description	Stack	{‘Spiro’, ‘MAPbI3’, ‘TiO2’}
Electron affinity	EA	[− 2.8, − 3.8, − 4.1]	eV
Ionization potential	IP	[− 4.9, − 5.4, − 6.4]	eV
Bandgap energies (EA–IP)	E g	[2.1, 1.6, 2.3]	eV
Equilibrium Fermi energies	E 0	[− 4.75, − 4.6, − 4.25]	eV
SRH trap energies	E t_bulk	[− 3.4, − 4.6, − 5.75]	eV
Electrode Fermi energies (anode and cathode)	[φA, φC]	[− 4.75, − 4.25]	eV
Built-in voltage (φC–φA)	V bi	0.5	eV
Effective density of states	N 0	[1 × 1019, 1 × 1019, 1 × 1019]	cm−3
Mobile ion defect density	N ion	[0, 1 × 1018, 0]	cm−3
density of iodide vacancies	DOS ion	[1 × 10–6, 1.21 × 1022, 1 × 10–6]	cm−3
Mobilities	μ e	[0.02, 20, 0.09]	cm2 V−1 s−1
	μ h	[0.02, 20, 0.09]	cm2 V−1 s−1
	μ ion	[0, 1 × 10–10, 0]	cm2 V−1 s−1
Relative dielectric constants	ε	[4, 23, 12]
Uniform generation rate	G 0	[0, 2.6 × 1021, 0]	cm−3 s−1
Recombination coefficient	krad (k)	[3.2 × 10–11, 3.6 × 10–12, 1.5 × 10–10]	cm3 s−1
SRH time constant for electrons	τ n_bulk	[1 × 10–6, 1 × 10–7, 1 × 10–6]	s
SRH time constant for holes	τ p_bulk	[1 × 10–6, 1 × 10–7, 1 × 10–6]	s
Interfacial SRH time constants for electrons	τ n_inter	[1 × 10–9, 1 × 10–12]	s
Interfacial SRH time constants for holes	τ p_inter	[1 × 10–9, 1 × 10–12]	s
Initial scan point	V start	0	V
Final scan point	V end	1.2	V
Layer thicknesses	D	[200, 400, 100]	nm
Layer points	p arr	[110, 230, 60]
Cumulative layer thicknesses	d cum	[200, 600, 700]	nm
Intrinsic fermi energies	E if	[− 3.85, − 4.60, − 5.25]	eV
Donor densities	N D	[0, 0, 1.5853 × 1016]	cm−3
Acceptor densities	N A	[1.5853 × 1016, 0, 0]	cm−3
Intrinsic carrier densities	n i	[0.2517, 1.1677 × 104, 0.0034]	cm−3
Equilibrium electron densities	n 0	[3.9957 × 10–18, 1.1677 × 104, 1.5853 × 1016]	cm–3
Equilibrium hole densities	p 0	[1.5853 × 1016, 1.1677 × 104, 7.3862 × 10–22]	cm−3