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

Abstract

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.

High performance planar germanium-on-silicon single-photon avalanche diode detectors

“…Figure 6c shows the band structure of the Ge-Si heterointerface calculated at T = 125 K using the deformation potentials from ref. 47 without any applied electric field for clarity and includes the three main trapped states for dislocations in Ge plotted as dashed lines inside the bandgap 48 . Whilst the 80−90 meV activation energy extracted from Fig.…”

Vanishing Zeeman energy in a two-dimensional hole gas

“…The Ge Luttinger parameters γ 1,2,3 and deformation potentials were taken from Ref. 49 , while the parameter κ was taken from Ref. 50 .…”

Design optimization of tensile-strained SiGeSn/GeSn quantum wells at room temperature

“…Their values are given in Table III. The six-band Luttinger parameters for SiGe are not described by bowing parameters, 49 so Eq. ( 22) cannot be directly used.…”