TRANSPORT PROPERTIES OF A lWO-DIMENSIONAL ELECTRON GAS IN SUPERLATTICES

Abstract

A theoretical study is given of the transport properties of a two­ dimensional (20) electron gas in superlattices. The motion of the electrons is confined to planes parallel to the interfaces of the superlattice layers by the potential wells fonned due to the superlattice structure. A part of the study has been petfmmed in the absence of a magnetic field while the other part is concemed with the case when an in-plane quantizing magnetic field is applied. In the absence of a magnetic field the potential wells are taken to be infinitely deep square wells while in the presence of an in-plane quantizing magnetic field, parabolic potential wells are considered. The 20-electrons undergo both elastic interactions with impurities and inelastic interactions with 30-phonons. The latter type of interactions cause the transfer of some of the phonon momentum to electrons. This, in tum, produces a phonon-drag contribution to the thermopower that outweighs substantially the diffusive contribution at low temperatures.

In earlier theoretical treatments, the phonon-drag thetmopower was expressed in terms of integrals over the components of the phonon wavevector. The divergences of these integrals were dealt with by considering a lifetime broadening. In the present work, it has been shown that these divergences can be entirely obliterated by keeping some terms, which were neglected, in previous treatments. Also, as an alternative approach, the divergences have been tackled successfully by determining the limits of the integrals in a more accurate manner than was done hithetto.

Also, in earlier treatments the phonons were assumed to be in the boundary scattering regime at low temperatures. The phonon relaxation time was accordingly taken to be a constant independent of phonon wavevector.