Comparison between 6-band and 14-band k⋅p formalisms in SiGe/Si heterostructures

We report on a comparison between a 14-band and a 6-band k·p model to describe the valence band of pseudomorphic SiGe/Si heterostructures. A strong variation between both models is observed for the description of the valence band dispersion and for the calculation of the intersubband dipolar matrix elements for in-plane wave vectors as small as 10% of the Brillouin zone size. We show that the 6-band formalism overestimates the amplitude of the intersubband absorption by a factor of 2 for light polarized in the layer plane. The origin of the polarization of the intersubband transitions is discussed and the limits of both models for the calculation of the energy band diagram and dipole matrix elements are outlined. We finally show that the usual axial approximation procedure, which is often used to build a cylindrical 4-band or 8-band Hamiltonian, cannot give a cylindrical 14-band Hamiltonian.