Maximum theoretical electron mobility in n-type Ge1−xSnx due to minimum doping requirement set by intrinsic carrier density

The amount of doping to make a semiconductor extrinsic depends on the intrinsic carrier density at a particular temperature. The impurity scattering in the presence of doping determines the maximum mobility exhibited by the semiconductor. In the present work, we estimate the values of intrinsic carrier density of the alloy Ge1−xSnx for 0 < x < 0.2 at and around 300 K. Since the alloy exhibits a direct-gap nature at x ≥ 0.08, the electron mobility is enhanced due to low effective mass in the lower Γ valley and reduced non-equivalent intervalley scattering. The electron mobility, calculated by considering all scattering processes, increases with increasing x, attains a peak and then decreases. The peak mobility is as high as 105 cm2/V s for donor density equaling intrinsic density. With a 50-fold increase in donor density, the mobility is 3 × 103 cm2/V s, which is still higher than the value in similarly doped bulk Ge.