New insights into the electronic properties of ordered semiconductor alloys: non-parabolic and non-analytic dependence on the order parameter

It is both fundamentally and practically important to understand the dependence of a physical property on order parameter $\eta $ for an ordered semiconductor alloy like Ga$_{x}$In$_{1-x}$P that is often found to be in a partially ordered phase. A conventional statistical theory based on a cluster expansion approach predicts that for any physical property P(x,$\eta )$ the leading term of the dependence is $\eta ^{2}$ with higher order corrections $\eta ^{4}$and etc., thus, always an analytic function of $\eta ^{2}$. From the practical application point of view, it is highly desirable to see that the $\eta ^{2}_{ }$term, corresponding to the pair correlation, alone can give adequate accuracy. However, we have found that for the electronic structure not only $\eta ^{2}_{ }$term is often inadequate but also non-analytic dependence on $\eta ^{2}_{ }$may sometimes arise, depending on the strength of the coupling among virtual crystal states caused by the alloying and ordering.[1] The predictions have been confirmed experimentally.[2] The results provide \textit{a priori} principle about the applicability of the conventional cluster expansion method to the description of the electronic structure of the semiconductor alloy, and a general understanding of the order parameter dependence of an electronic property in a semiconductor alloy. [1]Zhang et al, PRB80,045206(09). [2] Steiner et al, JAP106,063525(09). DOE/BES