Electronic band structure of semiconductor alloys: From ab initio to k·p via computational alchemy, on example of Ge1-x

Invariant expansion of the 30-band k.p model and its parameters for III-V compounds

“…The number of points is higher than in Ref. [19] because of the lower crystal symmetry (zinc blende vs diamond). The E k•p,i are the corresponding energies of the fitted k•p band structure.…”

“…The procedure of finding the 30 band k • p parameters, by adjusting the k•p band structure to the DFT reference one, has been described in details in Ref. [19]. A central point of this procedure is a minimization of the objective function S, defined as:…”

“…The function, after minimization, is also a measure of the accuracy of the fit, with zero representing a perfect match. The method of steepest descent has been used to find a minimum, which was previously shown to work very well for diamond structure materials [19]. The diagonal E mα and ∆ αα parameters are taken from the Γ-point energies [19], while the off-diagonal ∆ − is fitted together with the other parameters.…”

“…The method of steepest descent has been used to find a minimum, which was previously shown to work very well for diamond structure materials [19]. The diagonal E mα and ∆ αα parameters are taken from the Γ-point energies [19], while the off-diagonal ∆ − is fitted together with the other parameters. This procedure is a kind of approximation, because the energies at the Γ point are already affected by the off-diagonal ∆ − term [60].…”

“…An accurate description of the first conduction bands across the entire Brillouin Zone (BZ) is of fundamental importance for quantitatively correct description of carrier transport phenomena [17], direct and indirect absorption calculations [18], optical gain calculations [19], etc. Therefore k •p models able to finely describe bands relevant for devices operation, with a complete set of material parameters, are desired.…”