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. It uses a recently developed computational approach based on the self-consistent linear muffin-tin orbital (LMTO) band-structure method, which is applied using the local density approximation to density functional theory with a simple a-posteriori gap correction. The susceptibilies are obtained in the independent particle approximation, i.e., without local field and excitonic effects. The zero frequency limits of χ (2) 123 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(0). However, the anomalously high value of the zero frequency SHG in CdGeAs2 (the material with the most favorable combination of A, B, and C) is rather exceptional than typical for this group of compounds. An analysis of the different contributions in the frequency dependent SHG spectra shows that this value appears as a result of a very small interband term in the zero frequency limit which cannot compensate the large intraband contribution as it happens in most of the other materials of this class. The smallness of the interband term in CdGeAs2 is a result of a very delicate balance between different interband transitions, any of which can give positive or negative contribution in SHG. While we find the empirical observation that a smaller value of the gap is strongly correlated with a larger value of the SHG to be generally true when comparing various element substitutions within this family in a qualitative sense, simple inverse power scaling laws between gaps and χ values are not supported by our results. The case of CdGeAs2 clearly shows that this is an oversimplification and that for reliable predictions of trends of SHG coefficients one has to study the interplay between different terms which contribute in SHG. We have also studied the relation between χ and the chalcopyrite crystal structure by considering some of these materials in an alternative layered zincblende type latttice. We find that the (001) oriented 1 + 1 superlattice structure has significantly lower gaps than the chalcopyrite and correspondingly higher χ. However, this smaller gap structure is characterized by a large alternatingly compressive and tensile lateral strain in the layers, which makes it unfavorable. We also find that the distortions from the ideal chalcopyrite tend to increase the gap and decrease both the interand intraband contributions to χ, but the net value of χ is only slightly changed in most cases. These effects are larger for the Cd compounds than for the Zn-compounds. As far as the birefringence is concerned, we find our calculations for ZnGeP2 and CdGeAs2 to be in fair agreement with experiment (discrepancies being rather constant and of order 10 %) in the frequency range corresponding to the middle of the gap but to deviate from the data when the absorption edges of the band gap at high energy and the phonon absorption bands at low energy are approached. It is presently not clear whether this reflects a deficiency in the theory or imperfections in the samples.