  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.
