Intersubband transitions in a p-type δ-doped SiGe/Si quantum well

The absorption spectrum in a p-type Si/${\mathrm{Si}}_{0.6}$${\mathrm{Ge}}_{0.4}$/Si structure with a δ-doped quantum well grown on the Si(001) substrate is calculated. For the bound-to-bound intersubband transitions, the depolarization effect due to the complicated couplings among valence bands is included and the inclusion of this effect is found to be essential in understanding the absorption spectrum. The effects of subband multiplicity, nonparabolicity, and valence-band anisotropy are also incorporated into an implicit formula for an effective plasma frequency in order to facilitate the calculation. For the bound-to-continuum intersubband transition, the large-box model is adopted to circumvent the difficulty in normalizing the traveling wave function of the continuum state. The depolarization effect is not significant for the latter bound-to-contiuum transition because of the small overlap of the initial- and final-state wave functions. In this case, the absorption for the normal-incidence light becomes larger than that for the parallel-incidence light. The total absorption including the bound-to-bound and bound-to-continuum intersubband transitions shows a good agreement with the experimental data. The results provide a better understanding of intersubband transition in the valence band and further show that normal-incidence transitions can be significant.