*3.2. Thickness Optimization of Hole Transport Layer*

By incorporating the optimized thickness of PCBM (400 nm), the thickness of NPB was optimized using the same material parameters, as shown in Table 1. Similar to other conducting polymers, the variable-range hopping charge-transport process in NPB is also complicated in nature and depends on the film thickness of the polymer [37]. Similarly, the nature and density of traps states that perovskite-polymer interfaces are very crucial to define the transport through the polymer. Therefore, the interface trap states between the polymer and perovskite absorber layer are introduced in the simulation, where detailed information about the interface trap states are listed in Table 2.



In order to optimize the thickness of NPB as the hole-transport layer a series of simulations were performed and the photovoltaic responses were determined by varying the thickness of NPB from 10 to 1000 nm and the obtained photovoltaic parameters such as open-circuit voltage, short-circuit current, fill-factor, and power-conversion efficiency are shown in Figure 3. The figures clearly demonstrate that the open-circuit voltage behavior

is different from the other parameter's response. The open circuit voltage monotonously decreases as the thickness of NPB increases. Nevertheless, the short-circuit current, fillfactor, and power-conversion efficiency demonstrate a very similar response, where all these photovoltaic parameters and most importantly the power-conversion efficiency are slightly improved from 10 to 100 nm approximately and continuously degraded when the thickness of NPB increases from 100 to 1000 nm. Therefore, from the above results, it can be justified that the 100 nm is the most optimum thickness of NPB (gives maximum power-conversion efficiency ~16.5%) as the hole-transport layer for the current proposed Ag/BCP/PCBM/Cs2TiBr6/NPB/ITO perovskite solar cell.

**Figure 3.** (**a**) Open-circuit voltage, (**b**) short-circuit current, (**c**) fill-factor, and (**d**) power-conversion efficiency of proposed solar cell Ag/BCP/PCBM/Cs2TiBr6/NPB/ITO as a function of NPB layer thickness varied from 10 to 1000 nm.
