Lattice dynamics ofAgGaSe2. II. Theoretical aspects

We present a model calculation of the phonon spectrum of ${\mathrm{AgGaSe}}_2$ which is the ternary analog of the pseudobinary II-VI-compound ${\mathrm{Zn}}_{0.5}$ ${\mathrm{Cd}}_{0.5}$Se. We have used a simple Keating model and start from the series of force constants obtained by fitting independently the Raman modes of CdSe and ZnSe. Analyzing in great detail the dependence of the phonon frequencies and eigenvectors upon the different parameters which take part in the chalcopyrite distortion, we have successively taken into account the mass differences, the changes in force constants, the tetragonal distortion, and, finally, the anionic displacement. We have found a progressive constitution of the phonon spectrum in three bands with mainly ZnSe (GaSe) -like, CdSe (AgSe) -like, and mixed ${\mathrm{CdZnSe}}_2$ (${\mathrm{AgGaSe}}_2$) -like characters. This accounts satisfactorily for most experimental data. To get even better agreement, we have performed a least-mean-squares fit of the four parameters which enter the calculation. We find, in this way, that the bond-stretching constant for Ga-Se bonds is about 50% higher than the one for Zn-Se bonds while, in contrast, the strengths of Ag-Se and Cd-Se bonds appear very similar. This improved series of parameters results in zone-center modes in very good agreement with the experimental values.