The pinning effect in a polar semiconductor quantum dot with Gaussian confinement: A study using the improved Wigner–Brillouin perturbation theory

The effect of electron–phonon interaction on a few low-lying energy levels in a polar semiconductor quantum dot with Gaussian confinement is studied by using an improved Wigner–Brillouin perturbation theory (IWBPT). In the absence of the electron–phonon interaction, the electronic ground state plus one phonon state is degenerate with the first excited electronic state plus the zero-phonon state at some value of the confinement length. Similarly, the electronic ground state plus one phonon state is also degenerate with the second excited electronic state plus the zero-phonon state at a larger value of the confinement length. It is shown that the electron–phonon interaction lifts these degeneracies and as a result, the excited state energy levels bend downward and get pinned to the ground state plus one phonon state as the confinement frequency is increased. Our calculations are finally applied to GaAs and InSb quantum dots.