Band mixing effects on quantum well gain

Abstract

Gain in a quantum well is studied by using the optical matrix elements and the band structure computed by the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> method within the envelope function approximation. Due to band mixing, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> method gives nonparabolic bands which affect both the minimum confinement energies and the density of states functions. The density of states functions are found to differ considerably from the simple step-like shape computed from the band edge effective masses. The band mixing also results in large differences in the momentum vector dependence of the matrix elements, and moreover, some of the transitions which were previously assumed to be forbidden become partially allowed. The quantum well gain spectra calculated by the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> method and the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> -selection rules clearly show the effects of band mixing both in shape and in peak magnitude. These results are considerably different than those obtained from the conventional methods which consider an effective mass electron (or hole) in a finite one-dimensional potential well with parabolic bands and with matrix elements which have constant total magnitude. A practical conclusion which is reached from these comparisons is that the threshold excitation in a quantum well laser is found to be strongly underestimated if band mixing effects are ignored.