Improved fits of the effective masses at Gamma in the spin-orbit, second-nearest-neighbor sp(3)s* model: Results from analytic expressions

We derive and study exact analytic expressions for the effective masses of the conduction-and all three hole-bands at Gamma in the spin-orbit, second-nearest-neighbor sp(3)s* model. Using these expressions we determine parameters for six common III-V materials (GaAs, AlAs, GaSb, AlSb, InAs, and InP), tailored for [001]-oriented heterostructure calculations. Beyond their use in fitting band structures, the effective-mass formulas show that the second-nearest-neighbor sp(3)s* model is not without Limitations. We show that there is an upper bound on the reproducible electron-light-hole effective-mass mismatch, so that even this model may not be sufficient for certain materials.