Dipole matrix elements and the nature of charge oscillation under coherent interband excitation in quantum wells

Abstract

An empirical pseudopotential method is used to model two type-I quantum-well systems, allowing the investigation of interband dipole-matrix elements and charge oscillation under coherent optical excitation. Each relevant (microscopically varying) wave function is expressed as an exact envelope-function expansion to which various approximations are made, in analogy with envelope-function methods such as the k⋅p model. The approximation to the quantum-well energy eigenfunctions of a single envelope function multiplying a band-edge zone-center state, the “atomic picture,” is shown to underestimate by orders of magnitude the interband dipole-matrix element. Including terms due to the second band edge, which play only a minor role in the exact envelope-function expansion, provides a good approximation to the true dipole-matrix element, which is significantly greater than the atomic picture predicts. In addition, the effect on the interband charge oscillation of omitting the second band-edge terms is shown to be a reduction of the oscillation from the width of the well to the atomic scale. These results confirm that the earlier results of Burt hold for realistic three-dimensional systems.