Near equilibrium mobility tensor in a semiconductor superlattice : scattering by acoustical phonons

Abstract

Re~u le 12 juin 1980, revise le 22 aofit, accepte le 26 septembre 1980) Résumé. 2014 On étudie la mobilité à faible champ dans un super-réseau à base de semiconducteurs. Dans le cas de la diffusion par les phonons acoustiques, on obtient des formules analytiques. La discussion des résultats montre que la règle de conservation des k doit être entourée de précautions dans un tel système (processus Umklapp). Abstract. 2014 The near equilibrium mobility tensor in a one-dimensional superlattice is studied. Analytical formulae are given for acoustical phonon scattering. Discussion of the results shows that the k conservation rule must be carefully handled (U-processes).

Phonon-limited near equilibrium transport in a semiconductor superlattice

“…We have performed a numerical computation of (k). The main feature is a very weak variation of w ith k. However, the mean value ç > decreases with d as expected, and may be used as a correcting factor, see figure 6. Now, we can derive the mobility tensor ii through (14), (15), (22), (23).…”

“…Note that (24) is more general than equation (8) of [6] since it includes the Ilmklapp integral. The restriction (r) on the integration domain over k'li is easy to interpret from figure 5 and the comment made in reference [6]. The integral over (r) in (24) can be reduced to 2 k1 for normal processes, k1 being in general a solution of the following equation : k, can generally be given as a computer solution in association with P.W.…”

“…The usual (3D) relaxation time is found with m* M 1/2 instead of (m*)3/2. Now, the near-equilibrium relaxation-time for Nprocesses only can be derived from (24), (25) : expressions have already been given in [6].…”

“…A second novelty lies in the selection rules. In [6], we gave rough estimates of such effects with the deformation-potential scattering. In the present paper, a general derivation of the mobility tensor will be given.…”

“…Combining (6) and 3with the orthogonality relations (7), we obtain the secular system of equations in which 60(k) is given by the effective mass approximation. Then the total energy versus wavevector relation is given by :…”