Oscillator strengths for optical dipole interband transitions in semiconductor quantum dots

We calculate the oscillator strengths in a GaAs quantum dot, for which a comparison with the literature is made. We show that both the mixing of light- and heavy-hole states and the mixing of states with different envelope angular momenta in a quantum dot, requisite for single-particle, total-angular-momentum eigenstates, make a very significant contribution to the magnitude of the interband optical dipole. The implication of this for a more general, three-dimensionally confined semiconductor structure, such as a quantum box, is that valence-band mixing, as well as a correct superposition of Bloch and envelope states, in a quantum box are extremely important for calculating optical dipole transition strengths. We use a multiband envelope-function approximation in eight-band k⋅p theory, in which the energies are nonparabolic functions of the wave vector.