Complex Band Structures: From Parabolic to Elliptic Approximation

We show that the conventional nonparabolic approximation of real band structures can be modified and generalized to approximate the complex band structures of common semiconductors with a significant improvement of accuracy against the parabolic approximation. The improvement is due to the inherent elliptic nature of the complex band structures in the vicinity of the bandgap, which has a critical impact on the band-to-band tunneling probability. Important parameters are extracted and tabulated for Si, Ge, GaAs, and GaSb, with a maximum error of <; 1.4% compared to the numerical target.