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

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 tetragonal compounds on the basis of a newly formulated electron energy spectrum taking into account the combined influences of the anisotropies in the effective electron mass, the spin-orbit splitting and the presence of crystal field splitting. The corresponding results for QWs and QWWs of III-V compounds form a special case of our generalized analysis. The DMR has also been studied for QWs and QWWs of II-VI and IV-VI materials. It has been found, taking QWs and QWWs of CdGeAs2), InAs, US and PbSe as examples, that the DMR increases with increasing carrier degeneracy and decreasing film thickness in various oscillator), manners, emphasizing the influence of dimensional quantization and the energy band constants in different cases. An experimental method for determining the DMR in QWs and QWWs having arbitrary dispersion laws has also been suggested and the present simplified analysis is in agreement with the suggested relationship. The well-known results for QWs and QWWs of relatively wide gap materials having parabolic energy bands have also been obtained as special cases from this generalized analysis under certain limiting conditions.