Dependence of the lattice parameters and the energy gap of zinc-blende-type semiconductors on isotopic masses

The dependence of the ${\mathit{E}}_0$ direct gap of Ge, GaAs, and ZnSe on isotopic masses at low temperatures has been investigated. Contributions of the variation of the lattice parameter to the gap shift of the binary compounds have been evaluated by using a volume-dependent lattice dynamics, while local empirical pseudopotential techniques have been employed to calculate gap shifts due to electron-phonon interaction. The dependence of these terms on the lattice-dynamical model and on the q→0 extrapolation of the pseudopotential form factors has been investigated. The contributions of the optical and acoustical modes to the isotopic shift are analyzed. The results are compared to previous experimental data, in the case of germanium, and to low-temperature reflectance measurements performed as part of this work on GaAs samples with different isotopic gallium composition. Particular attention has been paid to the differences in the effects of changing either the cation or the anion masses. The temperature dependence of the ${\mathit{E}}_0$ gap of ZnSe has also been calculated, and reasonable agreement with experiment has been found. © 1996 The American Physical Society.