Second-harmonic generation and birefringence of some ternary pnictide semiconductors

A first-principles study of the birefringence and the frequency-dependent second-harmonic generation (SHG) coefficients of the ternary pnictide semiconductors with formula ABC₂ (A=Zn, Cd; B=Si, Ge; C=As, P) with the chalcopyrite structures was carried out. The zero-frequency limits of χ₁₂₃⁽²⁾ 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 χ⁽²⁾(0). An analysis of the different contributions shows that the anomalously high value of the zero-frequency SHG in CdGeAs₂ 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 χ⁽²⁾ 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 χ⁽²⁾. 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 ZnGeP₂ and CdGeAs₂ 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.