Analytical descriptions of the band structure of direct-band-gap zinc-blende-structure semiconductors in the kp Kane model

In the framework of the well-known kp Kane band theory, accurate analytical approximations of conduction- and valence-band dispersion of direct-band-gap zinc-blende-structure semiconductors are derived when the spin-orbit-splitting energy does not exceed the band-gap energy. These approximations include the interactions with the remote bands. The expressions of the eigenfunctions are also obtained. The present analysis elucidates and unifies previous analytical band descriptions.