First-principle Calculations of Electron-Phonon Interactions in $A^{II}B^{IV}C^{V}_2$ Crystals

$Ab-initio$ probabilities of phonon-assisted intervalley scattering of electrons in the conduction bands of ternary chalcopyrite compounds $ZnSiP_2$ and $ZnGeP_2$ between the central $\Gamma$ minima and the lowest lateral minima (valleys) at $T$ and $N$ points have been calculated using the density functional theory. The equilibrium parameters of crystal structures, spectra of electrons and phonons are calculated self-consistently and are in fairly good agreement with the experiment and available theoretical calculations. The electron-phonon coupling constants with short-wave (inter-valley) phonons in the chalcopyrite phosphides are close to their values in $Si$, $Ge$ and in binary analog $GaP$.