Electron–Phonon Interaction and Electron Transport

Semiconductor device operation depends on the drift velocity of carriers, electrons and holes, which is determined by the mobility. The mobility $$\mu $$ is expressed by $$e \langle \tau \rangle /m^*$$ , where e, $$\langle \tau \rangle $$ , and $$m^*$$ are the electronic charge, average of the relaxation time, and the effective mass. The relaxation time or scattering time is limited by various scatterings of carriers. Among them the phonon scattering plays the most important role. In this chapter we begin with the analysis of the lattice vibrations and the derivation of Boltzmann transport equation. Readers who are interested in the detailed treatments of the transport properties are recommended to refer the articles [1–14]. Then collision time, relaxation time and mobility are defined. The transition probabilities and transition matrix elements for the scattering due to various modes of phonons, impurity, electron–electron interaction and so on are evaluated using quantum mechanical approach. These results are used to evaluate scattering rates and relaxation times, and finally respective carrier mobility is obtained. In order to get an better insight into the electron transport, scattering rates and mobilities due to the various processes are evaluated numerically and plotted as functions of electron energy, temperature and carrier densities. In addition, electron mobility is evaluated by taking all the relevant scattering processes. Also a theoretical method to evaluate deformation potentials for phonon scattering is given, where the calculated lattice vibrations and the full band structures in the Brillouin zone are properly employed. Many figures obtained by numerical calculations are very informative for an understanding of semiconductor transport.