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Volumn 80, Issue 15, 2009, Pages

Hole spin relaxation in [001] strained asymmetric Si/SiGe and Ge/SiGe quantum wells

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EID: 72449188233     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.155311     Document Type: Article
Times cited : (9)

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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.
    • The direct energy gap Eg at Γ point is much larger than the split-off splitting Δ in Si (Eg =3.4eV and Δ=0.044eV) (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.
    • 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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    • In fact, even when the expressions of the spin-orbit coupling coefficients in Ref. are adopted and the nondegenerate perturbation method with only the lowest unperturbed subband of each hole state considered is utilized to obtain envelope functions Ψλαn, the results in Ref. still can not be repeated.
    • In fact, even when the expressions of the spin-orbit coupling coefficients in Ref. are adopted and the nondegenerate perturbation method with only the lowest unperturbed subband of each hole state considered is utilized to obtain envelope functions Ψλαn, the results in Ref. still can not be repeated.


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