LO-phonon-induced screening of electron-electron interaction in D- centres and quantum dots

A problem of screening of electron-electron interaction by LO phonons is investigated for bound two-electron systems in bulk semiconductors and semiconductor quantum dots. We consider a D- centre and a two-electron quantum dot and obtain the effective LO-phonon-induced interaction between the electrons, i.e., Veff(r12)∼e2/[εeff(r12)r12], where r12 is the interelectron distance and εeff(r12) is the effective phonon dielectric function. The calculated phonon dielectric function rapidly increases for small r12 starting from the high-frequency dielectric constant, ε∞, and reaches some constant value, ε-bar, at relatively small interelectron distances. We have found that-in most casesεbar is less than the static dielectric constant, εs. Only in the weakly ionic compounds, like GaAs, ε-bar ∼ εs. We argue that-in the bound few-electron systems-ε-bar better approximates the average LO-phonon-induced screening than the commonly used εs. We have also shown that the coupling with LO phonons leads to the increase of the binding energy of the two-electron system confined in the quantum dot