  A simple band model using higher order non-parabolic effect was adopted for
single layer molybdenum tungsten alloy disulfide (i.e.,
$\mathrm{Mo}_{1-x}\mathrm{W}_x\mathrm{S}_2$). The first-principles method
considering $2\times2$ supercell was used to study band structure of single
layer alloy $\mathrm{Mo}_{1-x}\mathrm{W}_x\mathrm{S}_2$ and a simple band
(i.e., effective mass approximation model, EMA) model with higher order
non-parabolic effect was used to fit the first-principle band structures in
order to calculate corresponding the hole mobility. In addition, we investigate
the alloy scattering effect on the hole mobility of
$\mathrm{Mo}_{1-x}\mathrm{W}_x\mathrm{S}_2$.
