8-band k·p modelling of mid-infrared intersubband absorption in Ge quantum wells

The 8-band k·p parameters which include the direct band coupling between the conduction and the valence bands are derived and used to model optical intersubband transitions in Ge quantum well heterostructure material grown on Si substrates. Whilst for Si rich quantum wells the coupling between the conduction bands and valence bands is not important for accurate modelling, the present work demonstrates that the inclusion of such coupling is essential to accurately determine intersubband transitions between hole states in Ge and Ge-rich Si1−xGex quantum wells. This is due to the direct bandgap being far smaller in energy in Ge compared to Si. Compositional bowing parameters for a range of the key modelling input parameters required for Ge/SiGe heterostructures, including the Kane matrix elements, the effective mass of the Γ2′ conduction band, and the Dresselhaus parameters for both 6- and 8-band k·p modelling, have been determined. These have been used to understand valence band intersubband transitions in a range of Ge quantum well intersubband photodetector devices in the mid-infrared wavelength range.