The Einstein relation in quantum wells and quantum well wires: simplified theory and asuggestion for experimental determination

Abstract

An attempt is made to study the Einstein relation for the diffusivity–mobility ratio(DMR) in quantum wells (QWs) and quantum well wires (QWWs) of tetragonalcompounds on the basis of a newly formulated electron energy spectrum takinginto account the combined influences of the anisotropies in the effective electronmass, the spin–orbit splitting and the presence of crystal field splitting. Thecorresponding results for QWs and QWWs of III–V compounds form a special case ofour generalized analysis. The DMR has also been studied for QWs and QWWsof II–VI and IV–VI materials. It has been found, taking QWs and QWWs ofCdGeAs2, InAs, CdS and PbSe as examples, that the DMR increases with increasing carrierdegeneracy and decreasing film thickness in various oscillatory manners, emphasizing theinfluence of dimensional quantization and the energy band constants in different cases. Anexperimental method for determining the DMR in QWs and QWWs having arbitrarydispersion laws has also been suggested and the present simplified analysis is in agreementwith the suggested relationship. The well-known results for QWs and QWWsof relatively wide gap materials having parabolic energy bands have also beenobtained as special cases from this generalized analysis under certain limitingconditions.