A theory of the effects of carrier-carrier scattering on mobility in semiconductors

Abstract

A theory is developed which allows account to be taken of the effects of carrier-carrier scattering on the mobilities of the carriers in a semiconductor. It is valid in general at low temperatures where carrier-carrier scattering effects are most important and assumes that the carriers are non-degenerate and move in bands which can be characterized by simple isotropic effective masses. Electron-electron and hole-hole scattering usually produce only small reductions in the mobility although, if ionized impurity scattering were the completely predominant scattering mechanism, they could reduce it by as much as ~ 40 per cent. Electron-hole scattering, mainly due to the opposite drift velocities of the electrons and holes and a consequent drag effect, can produce large effects on the mobility altering both its magnitude and temperature dependence. These effects are most clearly seen in the minority carrier mobility and their inclusion yields mobilities in substantial agreement with those measured in Ge. In some cases, e.g. holes in n-type InSb, the drag effect is strong enough to give the minority carriers a negative mobility.