Effective-mass reproducibility of the nearest-neighborsp3s*models: Analytic results

We derive the exact expressions for the effective masses of the conduction and all three hole bands at Γ in the nearest-neighbor ${\mathrm{sp}}^3{s}^{*}$ model, both with and without the spin-orbit interaction. From these expressions we find that the nearest-neighbor ${\mathrm{sp}}^3{s}^{*}$ model can usually fit the electron mass better than the light- and heavy-hole masses and will not be equally successful across a broad spectrum of materials.