Use of local density approximation within range separated hybrid exchange-correlation functional to investigate Pb doped SnO$_2$ as an electron transport layer

In this study, the structural, electronic and optical properties of Pb doped rutile SnO$_2$ were investigated using the range separated hybrid exchange-correlation functional method. In the calculations, LDA functional was used instead of PBE functional. The electronic structure of SnO$_2$ obtained by this method is quite compatible with the experimental data. The SnO$_2$ has an important usage area in optoelectronic devices due to its transparent and conductive nature. One of these important areas is the use of SnO$_2$ as an electron transport layer (ETL) in perovskite solar cells. Therefore, the energy level of the conduction band of the SnO$_2$ is important. In the Pb doped SnO$_2$ cases, the band gap narrows as the Pb doping rate increases. The bandgap of SnO$_2$ can be narrowed from 3.60 eV to 3.02 eV with a %12.5 Pb doping ratio, and this narrowing is proportional to the amount of Pb. The calculation results obtained in this study show that the decrease in the energy level of the bottom of the conduction band plays an important role in the narrowing of the band gap and there is no significant change in the energy level of the top of the valence band. Due to this effect of the Pb atom, the energy level of the conduction band can be adjusted by using the doping ratio of the Pb atom and the band gap can be narrowed in a controlled manner. With the Pb doping, the energy levels of the SnO$_2$ ETL can be adjusted in a range according to the type of perovskite used in solar cell. In addition, the doping with Pb does not create electron traps in the band gap, which is important in the transport process of electrons.