**2. Device Structure and Simulation Parameters**

### *2.1. SCAPS Highlight*

Numerical simulation was performed in the work by utilizing the SCAPS-1D program [46]. SCAPS (solar cell capacitance simulator) is a one-dimensional simulation program dedicated for various types of solar cells. The program is widely utilized to simulate the device parameters of PSCs and other solar cell structures. Most of the simulation results are consistent with measurements and offer vital indications and predictions for experimental work. Based on SCAPS simulations, one can get cell parameters like dark and illuminated current density vs voltage (*J*–*V*) characteristics, quantum efficiency (QE) and energy bands. This can be done by solving the electron (Equation (1)) and hole (Equation (2)) continuity equation coupled with Poisson's equation (Equation (3)), together with the constitutive equations (Equations (4) and (5)),

$$\frac{dI\_n}{d\boldsymbol{x}} = G(\boldsymbol{x}) - \boldsymbol{\mathcal{U}}\_n \tag{1}$$

$$\frac{d\mathbb{J}\_p}{d\boldsymbol{x}} = \mathbb{G}(\boldsymbol{x}) - \mathbb{U}\_p \tag{2}$$

$$\frac{d}{dx}\left(\varepsilon\_r \varepsilon\_o \frac{d\psi}{dx}\right) = -\frac{q}{\varepsilon} \left(p - n + N\_D^+ - N\_A^- + p\_t - n\_t\right) \tag{3}$$

$$J\_n = -\frac{n\mu\_n}{q} \frac{dE\_{Fn}}{dx} \tag{4}$$

$$J\_p = \, + \frac{p\mu\_p}{q} \frac{dE\_{FP}}{dx} \tag{5}$$

where *<sup>G</sup>* denotes the generation rate (cm−3·s<sup>−</sup>1) and *<sup>x</sup>* is the distance along the device. The electron and hole recombination rates (cm−3·s−1) are denoted by *Un* and *Up*, respectively. *ε<sup>r</sup>* is the dielectric constant, *q* is electron charge and *ψ* is the electrostatic potential. *N*<sup>+</sup> *<sup>D</sup>* and *N*− *<sup>A</sup>* are donor and acceptor doping concentration. *p*(*x*), *n*, *pt* and *nt* represent the free hole, free electrons, trapped electron, and trapped hole concentrations, respectively. The electron and hole mobilities are denoted by *μ<sup>n</sup>* and *μ<sup>p</sup>* while the Fermi level of the electrons and holes are denoted by *EFn* and *EFp*, respectively.

After applying the appropriate boundary conditions at the contacts and the interfaces, Equations (1)–(5) are transported to a system of coupled differential equations in (*ψ*, *n*, *p*) or (*ψ*, *EFn*, *EFp*). SCAPS numerically computes a steady state and a small signal solution of this resulting system. The first step in every calculation is to discretize the structure by a coarse meshing in the middle of a layer. Meanwhile, a finer meshing near the interfaces and contacts are utilized. Further, the mesh can be optimized during the calculations. The system of equations is solved numerically, using a Gummel iteration scheme with Newton-Raphson sub-steps [46].
