Semiconductor materials are being widely used in science and technology. The harmonic approximation gives the non-interacting nature of phonons. The concept of harmonicity is never found in nature. In presence of isotopic impurity, translational symmetry of real crystal is destroyed. This creates localized mode. The phonon Green`s function has been taken as containing the entire information of physical property. Fourier transformed phonon Green`s function has been obtained by applying equation of motion technique of quantum dynamics and Dyson equation approach. The response function has been obtained to give the phonon linewidth and phonon shift. Phonon linewidth and phonon shift are further separated into defect and non-defect parts. An expression of phonon density of states (DOS) has been found in terms of diagonal and non-diagonal parts. The effect of temperature, renormalized mode frequency, and perturbed mode frequency on phonon density of states of an isotopically disordered semiconductor crystals has been undertaken in this approach. It is found that excitations are responsible for measure the strength of DOS in both diagonal and non-diagonal parts. It is also found that renormalized mode frequency has been contributed by mass change parameter, force constant change parameter, and electron phonon coupling constant while perturbed mode frequency has been greatly affected by phonon shift.
Phonon, Phonon Green's function, Phonon linewidth, Perturbed mode frequency, Semiconductor, Phonon density of states
