Debye-Waller Factor in an Isotopically Disordered Semiconductor Crystal

The diagonal and non-diagonal parts for the Debye-Waller factor have been established using equation of motion technique of quantum dynamics and the Dyson equation approach. The double time temperature dependent phonon Green function has been taken to find the phonon linewidth and phonon shift. Renormalized mode frequency has been investigated in terms of electron-phonon coupling constant and temperature. The effect of electron-phonon interaction on the Debye-Waller factor has been studied in low temperature limit in low impurity concentration in semiconductor crystals.