Second-harmonic generation and birefringence of some ternary pnictide semiconductors

Abstract

A first-principles study of the birefringence and the frequency-dependent second-harmonic generation (SHG) coefficients of the ternary pnictide semiconductors with formula ${\mathrm{ABC}}_2$ $(A=\mathrm{Zn},$ Cd; $B=\mathrm{Si},$ Ge; $C=\mathrm{As},$ P) with the chalcopyrite structures was carried out. The zero-frequency limits of ${\chi }_{123}^{\mathrm{}\left(2\right)\mathrm{}}$ were found to be in reasonable agreement with available experimental data for all the considered materials. We found that substitution of P by As, Si by Ge, and Zn by Cd is favorable to get a higher value of ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}\mathrm{}\left(0\right).$ An analysis of the different contributions shows that the anomalously high value of the zero-frequency SHG in ${\mathrm{CdGeAs}}_2$ appears as a result of a very small interband term in the zero-frequency limit which, contrary to most of the other materials of this class, does not compensate the large intraband contribution. Simple inverse power scaling laws between gaps and ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ values are not supported by our results. We find that the (001) oriented $1+1$ superlattice structure has significantly lower gaps than the chalcopyrite and correspondingly higher ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}.$ However, this smaller gap structure is characterized by a large alternatingly compressive and tensile lateral strain in the layers, which makes it unfavorable. The calculated values of the birefringence for ${\mathrm{ZnGeP}}_2$ and ${\mathrm{CdGeAs}}_2$ are in fair agreement (discrepancies being rather constant and of the order of 10%) with experiment in the frequency range corresponding to the middle of the gap.