Electron-phonon scattering and anisotropy of conductivity in quasi-two-dimensional systems

Abstract

The inverse relaxation time tensor in quasi-two-dimensional systems is calculated for elastic electron scattering by both acoustic and optical phonons. It is shown that in the general case the relaxation time is anisotropic. Also, on the basis of the Boltzmann equation in the anisotropic relaxation time approximation the electrical conductivity in these systems is calculated. It is found that anisotropy of the conductivity is defined not only by the anisotropy of effective mass and the relaxation time but also by the ratio of the Fermi level to the one-dimensional conduction band half-width. A comparison with available experimental data has been carried out. Qualitative agreement of theory with experiment was obtained.

Anisotropy of the thermoelectric power in superlattices

“…The transverse thermopower, α ⊥ , as ε F > 2ε 0 (twodimensional case), obeys the next concentration dependence: where [9]. Formula (6) fits the experimental data in [10] where it was observed that the thermopower of the GaAs/Ga 1−x Al x As SLs is reduced by the elevated concentration.…”

“…From formulae (4) and ( 5) it transpires that on the impurity scattering the thermopower anisotropy (relation of the transverse component of the thermopower to the longitudinal one), in contradistinction to the anisotropy of the electrical conductivity [9], is merely dictated by the Fermi level to the mini-band width ratio and is irrespective of the effective mass anisotropy and superlattice constant.…”

“…where n = m⊥ε0 π 2 h2 a (sin Z 0 − Z 0 cos Z 0 ) and n is the quasi-twodimensional electron gas concentration [9].…”

Поперечный Эффект Нернста-Эттингсгаузена В Сверхрешетках При Электрон-Фононном Рассеянии

“…Однако если рассеяние упругое, то межзонные процессы несущественны и можно ограничиться случаем, когда заполнена лишь одна мини-зона. Продольная и поперечная компоненты обратного времени релаксации при рассеянии на акустических (r = 0) и полярных оптических (r = 1) фононах пропорциональны плотности состояний g(ε) и имеют вид [20] 1…”

Hall effect in a two-dimensional electron gas

“…When calculating these components, it is presupposed that the scattering of conduction electrons is by acoustic phonons. The relaxation time at such types of scattering can be written as [7]:…”