Electron-Electron Interactions: Screening

In this chapter we will investigate how the presence of other charges and dipoles influences the charge-charge interaction.

Consider for example a net charge introduced into a semiconductor, and consider how the electrons in the conduction band react to it. The net charge could be for example the charge of the ionized Si impurity in GaAs or P impurity in Si. One can ask, what is the electric field that the carriers see? Do they see the full Coulomb field of the ionized impurity or a reduced field? We know from elementary Electromagnetic theory that the presence of an insulating medium around a charge partially screens the charge, and introduces the bound electron permittivity term eb in the Coulomb potential for example. We also saw in Chapter 10 how one can derive the permittivity of bound charges ɛ_b in a medium. But what about the presence of free electrons? What happens to the net field in a metal where we have both bound and free charges? We saw how the free carriers change the total permittivity of a system, and how this can be incorporated in the optical properties of solids, but we did not look at the consequences for carriercarrier and carrier-charge interactions. The free carriers were given a classical Drude treatment which is adequate for optics, but we did not investigate how the medium affects the net interaction between the charges themselves. To answer this question we have to start from a first principle point of view and give the problem a quantum mechanical treatment. Let us examine these questions from a fundamental point of view following closely the book by J. Ziman (see references).