On the Einstein Relation in Non-linear Optical, Optoelectronic and the Related Materials: Simplified Theory and a Suggestion for Experimental Determination: Part-I
K.P. Ghatak, D.K. Basu, S. Bhattacharya, S. Ghosal, S.K. Biswas, A. Malik and G. Majumdar
An attempt is made to study the Einstein relation for the diffusivitymobility ratio (DMR) in nonlinear optical 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 and the spin orbit splitting constant together with the inclusion of crystal field splitting in the Hamiltonian within the framework of k.p formalism. The corresponding results for III-V, ternary and quaternary types of optoelectronic materials form a special case of our generalized analysis. We have also studied the DMR in II-VI, Bi, IV-VI and stressed materials on the basis of various band models as applicable for such specialized materials. It has been found taking n-Cd3As2, n-CdGeAs2, n-InAs, n-InSb, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, CdS, Bi, PbS, PbTe, PbSe and stressed InSb as examples of the aforementioned compounds that the DMR increases with increasing electron concentration in various manners for different band constants of the said materials and the rates of variation are totally band structure dependent. An experimental method of determining the DMR in degenerate samples having arbitrary dispersion laws has also been suggested and the present simplified analysis is in agreement with the suggested relationship. In addition, the well-known results for non-degenerate wide gap materials have been obtained as special cases of our generalized theory under certain limiting conditions.