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

机译：量子阱和量子阱线中的爱因斯坦关系：简化的理论和实验确定的建议

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摘要

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 CdGeAs_2, InAs, CdS and PbSe as examples, that the DMR increases with increasing carrier degeneracy and decreasing film thickness in various oscillatory 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.
机译：尝试在新公式化的电子能谱的基础上研究四方化合物的量子阱（QWs）和量子阱线（QWWs）中的扩散率-迁移率比（DMR）的爱因斯坦关系有效电子质量中的各向异性，自旋轨道分裂和晶体场分裂的存在。 III-V化合物的QW和QWW的相应结果是我们广义分析的一个特例。还对II-VI和IV-VI材料的QW和QWW进行了DMR研究。已经发现，以CdGeAs_2，InAs，CdS和PbSe的QW和QWW为例，DMR随载流子简并性的增加和膜厚度的减小而以各种振荡方式增加，从而强调了尺寸量化的影响以及不同范围的能带常数案件。还提出了一种实验方法，该方法用于确定具有任意色散律的QW和QWW中的DMR，本简化的分析与所建议的关系一致。作为特殊情况，在某些极限条件下，通过这种广义分析，还获得了具有抛物能带的较宽间隙材料的QW和QWW的众所周知的结果。

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