On the generalized einstein relation in ultrathin films of ternary chalcopyrite semiconductors in the presence of crossed electric and magnetic fields

Abstract

The Einstein relation for the diffusivity-mobility ratio of the c a r r i e r s in semiconductors (hereafter referred to as DMR) is a very useful relation since by being a thermodynamic relation, this is independent of any scattering mechanism and is, therefore, m o r e accurate than any of the individual relations for diffusivity or mobility which are considered to be the two most widely used para m e t e r s of c a r r i e r transport in semiconductor physics. Furthermore, the connection of DMR with the velocity auto-correlation function /I/, i t s relation with the screening length /2/, and the different modifications of the same ratio under various physical conditions have been widely investigated i n the literature /3 to 6/. Nevertheless, the DMR in ultrathin films of degenerate ternary chalcopyrite semiconductors bas yet to be theoretically worked out for the m o r e difficult case which occurs from the consideration of all types of anisotropies in the energy spectrum since the above class of semiconductors a f e being studied in /7, 8/ for their peculiar physical characteristics. It may be noted in this context that, in such ultrathin films where the' film dimension is comparable to the de-Broglie wavelength of the c a r r i e r s along the direction normal to the film (say, the z-direction) may be viewed as c a r r i e r confinement in a one-dimensional potential well leading to the quantization (known as quantum size effect) of the wave vector of the c a r r i e r s along the direation of z-axis which produces a discrete energy spectrum. Besides, with the advent of liquid phase epitaxy and other techniques, such ultrathin films have been experimentally realized /9/. Inthe present communication, we shall derive a generalized expression of the DMR in ultrathin films of degenerate terqmry chalcopyrite -_ 1) 92,