k.p theory beyond standard 8-band theory parametrization

The k·p method is known to be very efficient to accurately describe either the conduction band or the valence band or even both of them in the vicinity of a given point of the Brillouin zone. Recently multiband k·p Hamiltonians including up to 30 bands (and above), which allow us to calculate the band diagram of bulk materials for Td or Oh group semiconductors, have been proposed [1]. The strain effect on the electronic structure has been included through the strain Bir-Pikus Hamiltonian. An envelope function formalism based on this 30band k.p method which allows to calculate the subband structure of both electron and hole quantum wells, even for indirect band gap semiconductors, has been introduced some time after [2,3]. Many physical phenomena such as optical generation or recombination, optical gain realization, Auger effect, impact ionization and more generally hot carriers and hot phonons mechanisms require an accurate Bloch state description for the conduction bands (resp. valence bands) well above (resp. well below) the conduction (resp. the valence) band extremum. Such multiband k.p electronic structures are consequently used in the modelling of optoelectronic and electronic devices. An example is the description of optical gain in an indirect band gap material like germanium under tensile strain [4] corresponding usefully to actual experimental configuration investigated presently [5]. Under a magnetic field perturbation, the k.p method is without rival while for all other cases, in particular nanostructure electronic structure descriptions, the question of the best approach between the k.p method, the empirical pseudo-potential method or the LCAO method can be discussed.