A simple mobility model for electrons and holes

Abstract

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 (/spl mu//sub d/=q/spl middot//spl tau//sub m//m/sub dr/*) and the factors which determine a momentum relaxation time (/spl tau//sub m/=L/sub m//v/sub eff/) were chosen such that a mean free path (L/sub m/) was equal to the lattice constant (a) times 40 (L/sub m//spl ap/40/spl middot/a) and the effective velocity (v/sub eff/) equalled the thermal velocity (v/sub th/). Then the author tried to find the simplest rule for effective masses (m/sub dr//sup */) 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/sub c//sup */) is fitting for the electron's effective mass (m/sub dr//sup */) and the longitudinal effective mass (m/sub 1//sup */) 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.