Improved fits of the effective masses at Γ in the spin-orbit, second-nearest-neighborsp3s*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 Γ in the spin-orbit, second-nearest-neighbor ${\mathrm{sp}}^3{s}^{*}$ 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 ${\mathrm{sp}}^3{s}^{*}$ 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.