3.2.4. ETL Variation

Using TiO2 as ETL is very popular in normal PSCs. However, other candidates are required to be inspected to see more suitable alternatives to TiO2. In this subsection, we investigate the influence of changing the conduction band offset (CBO) by varying ETL affinity. The CBO is calculated as,

$$\text{CBO} = \Delta E\_{\text{c}} = \chi\_{\text{abscorber}} - \chi\_{\text{ETL}} \tag{10}$$

The simulated ETL affinity is changed in the range of 3.9 eV to 4.26 eV, which gives a CBO in the range of −0.09 to 0.27 eV. Figure 17 shows the variation of the performance parameters vs CBO. As shown in the figure, *Voc* increases gradually with the increasing of CBO and reaches 0.758 V when CBO is 0.17 eV (which is corresponding to ZnO as ETL). *Jsc* changes slightly and reaches 20.09 mA/cm2 for the same CBO (0.17 eV). The fill factor (*FF*) increases up to 61.50% and then slightly decreases. The efficiency behavior is the same as the *Voc* trend. It has an optimum value of 9.35% which occurs when utilizing ZnO as ETL.

**Figure 17.** Effect of electron affinity of ETL on PCE.

Figure 18 displays the energy band diagrams of the HTL-free PSC for three cases; namely, when the ETL material is TiO2 (Figure 18a), ZnO (Figure 18b) and PCBM (Figure 18c). In the first case, the CBO is negative (−0.09 eV), while it is positive for the second case (having 0.17 eV) and the third case (having 0.27 eV). Regarding the first case, a cliff is formed at the ETL/absorber interface which does not hinder the flow of photogenerated electrons toward the front electrode. However, the activation energy for carrier recombination (*Ea*) becomes lower than the energy gap of the absorber (*Eg*), where *Ea* is given by *Ea* = *Eg* − |CBO|. For this case, the main recombination mechanism of the solar cell is the interface recombination of *Ea* < *Eg* [60,61], and the recombination probability of the electrons at the ETL/absorber interface rises significantly. Therefore, *Ea* directly links with the open circuit voltage and *Voc* is, consequently, reduced for negative values of CBO.

On the other hand, when the CBO is positive, a spike is formed at the ETL/absorber interface, as shown in Figure 18b,c. This spike behaves like a barrier against the flow of photogenerated electrons. When CBO is positive, *Ea* is equal to *Eg*. When the spike is low enough (Figure 18b), the barrier is not strong and the flow of electrons towards the contact is substantial. However, when the barrier spike is too high (>0.2 eV), as in the third case, the normal flow of photogenerated electrons to PCBM is affected drastically. As a result, the equivalent series resistance of the cell is increased, resulting in *FF* deterioration. As a result, the best choice for the ETL material is ZnO, which gives *Voc* = 0.757 V, *Jsc* = 20.09 mA/cm2, *FF* = 61.50%, and PCE = 9.35%. The main parameters of the ETL materials mentioned here are listed in Table S3 (see Supplementary Material).

**Figure 18.** The energy band diagrams of the hybrid hetero-homojunction HTL-free PSC for three cases: (**a**) CBO = −0.09 eV, (**b**) CBO = 0.17 eV and (**c**) CBO = 0.27 eV.

#### *3.3. Comparison of Various Designed Structures*

The illuminated *J*–*V* characteristics and quantum efficiency of optimized HTL-free and other cases of homojunction-based lead-free PSCs are compared in detail in Figure 19. The studied cases are related to the initial hetero-homojunction, while the other four cases are associated with the HTL-free configuration. The first case is the initial homo design, having optimized p-layer thickness and doping. The second case is the HTL-free structure with an optimized doping. The third case is taken for ZnO as an ETL, and the bulk defect density is 5 × <sup>10</sup><sup>17</sup> cm−3, while the fourth case is dedicated for TiO2 as an ETL, and the defect density is 1 × 1015 cm−3. The last case is the final optimized HTL-free structure whose ETL material is ZnO and its defect density is 1 × 1015 cm<sup>−</sup>3.

**Figure 19.** A comparison between (**a**) the illuminated *J*–*V* characteristics and (**b**) quantum efficiency of optimized HTL-free and other cases of homo-junction-based lead-free PSCs.

Referring to Figure 19, it is clear that our proposed HTL-free cell after optimization has superior photovoltaic properties than the other four candidates. The homojunctionbased carbon PSC shows an apparent improvement in *Voc* owing to the improved *Vbi* inside the perovskite layer caused by homojunction, thus boosting the quantum efficiency (Figure 19b). Table 5 gives the main parameters to compare between the different cases. These results demonstrate that the HTL-free hybrid cell is a better choice compared to the conventional homojunction PSCs.


**Table 5.** Comparison between five different cases of hybrid hetero-homojunction-based PSCs.

Finally, we investigate the effect of interface traps, which arise due to the structural mismatch between two dissimilar materials, on the performance of the initial heterohomojunction (case 1) and the final optimized HTL-free cell (case 5). Figure 20 demonstrates the influence of the interfacial defects of ETL/absorber layer on the device efficiency. Both interface defect density (in the range 108–1018 cm−2) and defect energy level position (in the range 0.1–1.2 eV relative to *Ev* of the perovskite) are investigated simultaneously. As displayed, the interface quality of the ETL/absorber layer has a substantial role on the cell performance, especially for the optimized HTL-free cell. The dependency of the efficiency on the interface defect density is more noticeable than the energy level. For both studied cases, the efficiency almost does not change for a given value of interface defect density. Reducing the interface trap density from 1 × 1018 to 1 × 108 cm−<sup>2</sup> results in a rise in the efficiency of about 1% and 2.5% for case 1 and case 5, respectively. This shows that the optimized HTL-free cell is more sensitive to the variations of the trap density than the conventional hetero-homojunction case. Working on methods to reduce the interface trap density, by passivation for instance, draws another promising route to improve the efficiency.

**Figure 20.** Effect of interfacial trap parameters on the efficiency of (**a**) initial hetero/homojunction solar cell and (**b**) final optimized HTL-free structure.

It should be mentioned here that the realization of the homojunction pn design is feasible and has been demonstrated experimentally. Many techniques have been investigated to attain doped perovskite films [35]. For instance, by control the stoichiometry of the PbI2/MAI precursor ratio, a p-type MAPbI3 with rich MAI can be obtained while an n-type MAPbI3 with rich PbI2 can be generated [36]. Besides, the defect-assisted self-doping could offer an opportunity for the deposition of p- or n-type compounds [33]. More intensive research is needed to explore the likelihood of obtaining p- and n-type lead-free perovskite materials in order to fabricate efficient p-n junctions to benefit from enhanced charge separation and limited recombination rates.
