Strong-confinement approach for impurities in quantum dots

The problem of a donor impurity in a confined geometry with dielectric mismatch at the boundaries has been studied. It is shown that in the limit of dot size smaller than the effective Bohr radius, the problem admits an extremely simple perturbative solution for arbitrary impurity locations. The first-order energy corrections (‘‘binding’’ energy) are obtained analytically for the s- and p-like states, and with a minimal numerical effort for the d,f,g,... states. Important charge-induced polarization effects are found for the particular case of a silicon dot embedded in an amorphous silicon dioxide (a-${\mathrm{SiO}}_2$) matrix.