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The direct energy gap Eg at Γ point is much larger than the split-off splitting Δ in Si (Eg =3.4 eV and Δ=0.044 eV) (Ref.) thus the contribution to the spin splitting of the lowest light-hole subband from the conduction bands can be neglected. Eg in Ge is relatively smaller (Eg =0.9eV and Δ=0.3eV) (Ref.) but the Γ6c conduction band is found to have no contribution to the spin splitting of the lowest heavy-hole subband. Thus the 6×6 Luttinger model rather than the larger (extended) Kane model (Ref.) is utilized in the study.
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As the electric field potential is included in solving the subband energy spectrum and envelope functions, in the basis composed of these subband envelope functions, only the second [instead of third (Ref.)] order perturbation calculation in Löwdin partitioning is required.
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