Thirty-band k · p model for Si-based optoelectronics

We use a 30-band k · p model to investigate intervalley splittings and optical transitions inside the fine structure of conduction subbands in [001] Si quantum wells. Ground and first excited doublets generated in the wells exhibit decaying oscillations as a function of well width with same periodicity and opposite phase. A uniform electric field superimposed along the well axis produces a damping of oscillation amplitudes while period and phase remain unchanged. These oscillations depend on the location of the bulk conduction band minima along the X-directions, and hence are indirect gap signatures. Within the k · p framework, we analyse the thirty Bloch components and parity of the doublet wave functions. Such a study allows us to develop an analytical approach, using a two-band k · p model, which reproduces intervalley splittings with goog agreement. It furthermore gives the keys to elucidate intersubband optical transitions between the two doublets. Indeed, optical matrix shows clear selection rules with a uniaxial polarization along the well axis. Moreover, matrix elements also oscillate with same period and phase, above the result given by the standard effective mass approximation.