Oscillator strength for intersubband transitions in strained n-type ${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathit{x}}$ quantum wells

The oscillator strength for conduction intersubband transitions in a ${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathit{x}}$ potential well is calculated using an inverse mass tensor for any arbitrary growth direction and various strain conditions. The occupancy of the specific conduction valleys and their associated effective masses are shown to depend on the strain condition, and these dependences are taken into consideration in the calculation of the oscillator strength. The result illustrates that the intersubband transition can occur for normal incident light (or for differently polarized electric field) if the ellipsoidals in the conduction valleys are tilted. A biaxial tensile strain does not affect the oscillator strength; however, the biaxial compressive strain causes an increase of the oscillator strength for the z-polarized electric field, but a decrease for the xy-polarized electric field, independent of the nature of conduction minima being Si- or Ge-like. This is due to the change of the occupied valleys under strain. The calculated result for a waveguide structure is also obtained to compare with a recent experimental result.