Electron Phonon Collisions, Fermi Dirac Distribution and Bloch's T5T^5 law

In this paper, we model exchange of energy between electrons in solids and the phonon bath as electron-phonon collisions. Phonons are modelled as packets which create a lattice deformation potential of which electrons scatter. We show how these collisions exchange energy between electrons and phonons, leading to Fermi-Dirac distribution for electrons. Using these collisions, we derive the temperature dependence of resistivity of metals and the Bloch's $T$ and $T^5$ law for high and low temperature regime respectively. Unlike standard derivations of $T$ dependence of high temperature resistivity, our derivation rests fundamentally on the temperature dependence of the scattering angle.Comment: 14 pages, 10 Figures. arXiv admin note: text overlap with arXiv:1710.0348