ImpactU Versión 3.11.2 Última actualización: Interfaz de Usuario: 16/10/2025 Base de Datos: 29/08/2025 Hecho en Colombia
Resonant relaxation time for impurity electrons and localized phonons (wave packets) interaction: Application to the thermal conductivity of MgO:Fe 2+, ZnS:
For a relaxation time which is a rapidly varying function of $\ensuremath{\omega}$, phonons are more properly described by wave packets than by plane waves. Approximating the line shape of a wave packet by a Lorentzian function, the effect of localized phonons can be taken into account implicitly in the derivation of the resonant relaxation time $\ensuremath{\tau}(\ensuremath{\omega},T)$ for impurity electron-phonon interaction. In this phenomenological model the energy spread $\ensuremath{\hbar}\ensuremath{\delta}\ensuremath{\omega}$ of the wave packet simply adds to the width $\ensuremath{\hbar}\ensuremath{\Gamma}(T)$ of the expression of $\ensuremath{\tau}(\ensuremath{\omega},T)$ obtained for plane waves. The results for the calculated thermal conductivity agree with the experimental data, and at low temperature, where localized-phonon effects are not negligible, a quantitative agreement with Casimir's theory is also obtained.