Analysis of inelastic scattering processes of electrons by localized electrons in quantum dots

The inelastic Coulomb scattering rate 1/τin of conduction electrons has been theoretically evaluated in the presence of localized states such as quantum dots. By a diagrammatical method, we have formulated 1/τin and its relation to the conductivity σloc(ω) through localized states. The dependence of τin on temperature T is examined in the case that σloc(ω) follows the Mottʹs model. It is found that 1/τin varies as View the MathML source where d is the dimensionality and Δ is tunneling energy between the localized states in the asymptonic T=0 limit, in agreement with Imryʹs calculation. It is also found that calculated 1/τin deviates from View the MathML source as T increases, suggesting the importance of correction term at high temperature.