Charged Impurity Limited Scattering and Mobility in p-type GaS, GaSe, InS and InSe*

The valence bands of many monolayer and few-layer two-dimensional (2D) materials such as GaS, GaSe, InS, and InSe, have a “Mexican hat” dispersion in which the valence band edge is approximately a ring in the 2D Brillouin zone. This results in a singular density of states (DOS) at the band edge that diverges as 1/√E. The ionized impurity scattering rate depends on the DOS through both the integral over final states and the polarization function in the screened Coulomb potential. We calculated the static charge polarizability within the random phase approximation and evaluated the ionized impurity scattering rate and the mobility as a function of temperature and carrier concentration. The results are compared to those obtained from Thomas-Fermi screening and a parabolic dispersion. The underestimation of the ionized impurity scattering rate using Thomas Fermi screening is strongly temperature dependent ranging from 2 orders of magnitude at 5K to a factor of 4 at 300K. At 77K, for an ionized impurity density of 10¹¹ cm^-2, the hole mobility of GaS ranges from 20 cm²/Vs at a hole concentration of 10¹² cm^-2 to 200 cm²/Vs at 10¹³ cm^-2.