Crystal lattice vibrations near charged center in dielectrics and semiconductors

Abstract

Charged impurity centers in semiconductors are promising objects for the design of quantum devices elements. A relevant problem in this scope is a calculation of rates of transitions due to various mechanisms between different states of such centers. In particular, it is important to thoroughly study nonradiative (phonon) transitions in charged impurities. Special case is associated with local and quasilocal phonon modes. In present work, we consider longitudinal radial oscillations of a crystal lattice with respect to the charged center. We treated the case for small deformation in an isotropic media, in approximation of the absence of any other free charges in the area where the equation is valid. We suppose that continuous media approximation for our equation is valid beyond the first coordination sphere of a lattice. The obtained equation is valid within the scope of approximations made for the consideration of longitudinal radial oscillations for any charged center in covalent semiconductor or dielectric at low free charge carriers concentration. The solution of the equation was numerically obtained. The discrepancies of the solution from free media oscillations are discussed. Our results are important for the calculation of nonradiative electronic transitions in charged impurity centers in dielectric and semiconductor crystals.