Second-harmonic generation of I-III-VI2 chalcopyrite semiconductors: Effects of chemical substitutions - art. no. 165212

We report first-principles calculations of the second-order optical respons e coefficients in the I-III-VI2 (I=Ag,Cu; III=Ga,In; VI=S,Se,Te) chalcopyri te semiconductors. The computational approach uses the length-gauge formula tion of perturbation theory which explicitly separates pure interband from mixed intraband-interband contributions. The expressions for static and fre quency dependent second-harmonic generation coefficients are evaluated from band structures based on the local density approximation but including sem iempirical gap corrections. The linear muffin-tin orbital method is used to calculate the required band structures and matrix elements. The results ar e in good agreement with experiment for the compounds for which data are av ailable and provide predictions in the other cases. The trends show that th e dominating factor determining chi ((2)) is the anion rather than the grou p I or group In cation. The chi ((2)) values clearly fall into separated gr oups with increasing value going from S to Se to Te. While this correlates approximately inversely with the band Sap, several exceptions are notable: (1) Cu compounds have smaller gaps than corresponding Ag compounds and neve rtheless have slightly lower chi ((2)); (2) AgGaTe2 has a higher gap than A gInSe2 but nevertheless has a much higher chi ((2)). An analysis of the var ious contributions to the frequency dependent imaginary part of the respons e functions, Im{chi ((2))(- 2 omega,omega,omega)}, is presented in an attem pt to correlate the chi ((2)) values with band structure features. The main findings of this analysis are that (1) there is a large compensation betwe en intra/inter- and interband contributions frequency by frequency as well as in the static values; (2) the static chi ((2)) value is strongly affecte d by the sign of the low frequency parts of these separate contributions; ( 3) these low frequency parts correspond to only a few valence and conductio n bands and only to so-called 2 omega resonances; (4) the general shape of the Im{chi ((2))(-2 omega,omega,omega)} response functions is determined by the band structures alone while the intensity, which ultimately explains t he difference between tellurides and selenides, arises from the magnitude o f the matrix elements. Starting from AgGaSe2, the smaller effect on the chi ((2)) due to In subsitution for Ga than to Te substitution for Se can be e xplained by the fact that the Ga to In substitution changes the gap only in a small region near the center of the Brillouin zone, while the Se to Te s ubstitution changes the gap throughout the Brillouin zone. This shows that contributions from other parts of the Brillouin zone than the center domina te the behavior. The difference between Cu and Ag based compounds can be ex plained on the basis of a different degree of compensation of inter- and in tra/interband contributions.