Phonon-phonon interaction in spectral density function of semiconductor crystals

An electron Green's function has been taken to develop the theory. Fourier transformed electron Green's function has been evaluated with the help of equation of motion technique of quantum dynamics and Dyson equation approach. The response function has been provided the electron phonon linewidth and electron phonon shift from this technique. The perturbed mode energy has been dependent on electron band energy and electron phonon shift. The linewidth has been contributed by harmonic part, localized part, cubic, and quartic anharmonic parts. This study concludes that spectral density function has been contributed by harmonic part, electron part, defect part, cubic and quartic anharmonic parts. It has also been obtained that spectral density function shows a different delta function peaks which are affected by temperature and electron phonon coupling constant. It has been found that intensity of peaks have got sharper response when phonon frequency approaches to perturbed mode energy. The different excitations have been created in the form of exciton, polaron, combination, and difference bands. These have been responsible to broaden the delta function peaks. The different limiting cases of excitations have been undertaken, and their effect on intensity of spectral density function has been investigated in presence of impurity and anharmonicity. The effect of force constant change parameter and atomic force constants has been undertaken to investigate the present property.