*3.5. External Quantum Efficiency of Proposed Solar Cell*

The external quantum efficiency response of the proposed Ag/BCP/PCBM/Cs2TiBr6/ PTAA/ITO solar cell was simulated as a function of photons wavelength and the result is shown in Figure 6. The quantum efficiency for a photovoltaic device can be defined as the fraction of the free carriers collected from the respective electrodes to the total number of incident photons of a given wavelength (or energy) onto the top surface of the solar cell. Mathematically, the quantum efficiency and short-circuit current (*Jsc*) are directly related to each other as a function of photon wavelength (*ϕ* (*λ*)) and can be expressed as [43,44]

$$J\_{\rm SC} = q \int \varphi(\lambda) \, Q E(\lambda) d\lambda \tag{8}$$

Here, we theoretically analyzed the external quantum efficiency of the proposed solar cell as a function of wavelength from 300 to 1000 nm, as shown in Figure 6. For simplicity, the observed external quantum efficiency response can be classified into two well-define regions. (i) Region I: Between 300 to 700 nm, (ii) Region II: Above 700 nm. In region I, the reduction of quantum efficiency is generally observed due to the reflection of photons as well as the low carrier diffusion length. As Cs2TiBr6 has a very high career diffusion length, therefore the excellent quantum efficiency response (>95%) is observed compared to the ideal quantum efficiency (100%) for region I [4]. It can be clearly demonstrated that the

front-end (ITO) of proposed solar cell offers low optical reflections of photons. Hence, the proposed device shows the maximum external quantum efficiency for region I, which is a reasonably well-accepted value, as shown in Figure 6. In addition, as the energy band gap of Cs2TiBr6 is 1.55 eV, consequently, no photons are absorbed inside the proposed device for the higher photon's wavelength for region II, as shown in Figure 6.

**Figure 6.** External quantum efficiency response as a function of incident photon wavelength for the proposed solar cell.

#### *3.6. Thermal Stability of the Proposed Solar Cell*

The perovskite based solar cell has many types of defects, which in turn leads to some issues such as high carrier recombinational losses, degradation of interfacial contacts, and hence poor photovoltaic stability. The photovoltaic degradation becomes further aggravated when the perovskite solar cell is exposed to the higher ambient temperature. Therefore, the proposed solar cell is further characterized for the stability analysis by calculating the variation of photovoltaic parameters as a function of ambient temperature varied from 300 to 450 ◦K, as shown in Figure 7. From the figure, it is clearly observed that all the photovoltaic parameters are gradually degraded at higher temperature, but the rate of thermal degradation is different for each photovoltaic parameter. For a given temperature range if a linear model is applied for the relation between the normalized photovoltaic parameter and ambient temperature then their slope can be used as the rate of degradation (per ◦K) for a given photovoltaic parameter. From the figure, it is realized that both the short-circuit current and fill-factor shows very slow thermal degradation (rates of degradation are 2 × 10−<sup>4</sup> and 3 × 10−<sup>4</sup> per ◦K, respectively), while the open-circuit voltage and power-conversion efficiency also show very slow thermal degradation but higher than those in the short-circuit current and fill-factor for the proposed solar cell (rates of degradation are 1 × 10−<sup>3</sup> and 1.5 × 10−<sup>3</sup> per ◦K, respectively). Therefore, it can be stated from the above discussion that the proposed solar cell shows a relatively stable behavior within the given temperature range.

**Figure 7.** Degradation response of (**a**) normalized open-circuit voltage, (**b**) normalized short-circuit current, (**c**) normalized fill-factor, and (**d**) normalized power-conversion efficiency of the proposed solar cell Ag/BCP/PCBM/Cs2TiBr6/NPB/ITO as a function of ambient temperature varied from 300 to 450 ◦K.
