A simple mobility model for electrons and holes

This article reports a trial to find a simple quantitative relation which explains drift mobilities for electrons and holes in various semiconductors on the same point of view as the saturation velocity analysis which was presented at ISPSD´97 by the author (Takata, Proc. ISPSD´97, pp. 133-136, 1997). A newly proposed model was based on the primitive mobility equation (μ_d=q·τ_m /m_dr*) and the factors which determine a momentum relaxation time (τ_m=L_m/v_eff) were chosen such that a mean free path (L_m) was equal to the lattice constant (a) times 40 (L_m≈40·a) and the effective velocity (v_eff) equalled the thermal velocity (v _th). Then the author tried to find the simplest rule for effective masses (m_dr^*) to explain the experimental values for electrons and holes in the major indirect-transition-type semiconductors, such as diamond, 4H-SiC, 6H-SiC, 3C-SiC, Si, GaP, AlSb, Ge and GaAs. On many materials, the conductive effective mass (m_c^*) is fitting for the electron´s effective mass (m_dr^*) and the longitudinal effective mass (m₁^*) for the hole´s. This model may be useful for evaluation of approximate mobilities for newly developing materials such as SiC or diamond. The author proposes that conventional transport theory has serious problems for such materials, especially in terms of holes. Even if the theory of this paper is not solid, there is room to discuss some new fundamental mechanisms on these subjects