Temperature dependence of Dyakonov-Perel spin relaxation in zinc-blende semiconductor quantum structures

The Dyakonov-Perel mechanism, intimately related to the spin splitting of the electronic states, usually dominates the spin relaxation in zinc-blende semiconductor quantum structures. Previously it has been formulated for the two limiting cases of low and high temperatures. Here we extend the theory to give an accurate description of the intermediate regime which is often relevant for room temperature experiments. Employing the self-consistent multiband envelope function approach, we determine the spin splitting of electron subbands in $n\text{−}\left(001\right)$ zinc-blende semiconductor quantum structures. Using these results we calculate spin relaxation rates as a function of temperature and obtain excellent agreement with experimental data.

Figure 1

(Color online) Spin-relaxation rates ${\tau }_z^{-1}$ and ${\tau }_{\pm }^{-1}$ as a function of carrier density $n$ and for different temperatures $T$ in asymmetric (001) grown ${\mathrm{Al}}_{0.35}{\mathrm{Ga}}_{0.65}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$-QWs (upper row) and ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{Sb}∕\mathrm{In}\mathrm{As}$-QWs (lower row). The momentum scattering was assumed to be isotropic (type I, see Table ) and independent of $T$.

Figure 2

(Color online) Calculated BIA spin splitting parameters $\gamma$ (left axis) and $⟨k_z^2⟩$ (right axis) as a function of carrier density $n$ for symmetrically doped ${\mathrm{Al}}_{0.4}{\mathrm{Ga}}_{0.6}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$-QWs with $L=75\mathrm{\AA }$.

Figure 3

(Color online) Calculated spin-relaxation time ${\tau }_z$ of different samples (a)–(h) as a function of temperature $T$ in comparison with room temperature measurements (squares) from Terauchi et al. (Ref. 20). The theoretical results refer to the degenerate limit (dotted lines), to the nondegenerate limit (dashed lines), and to the generalized theory (full lines). For each set of curves, the upper curve corresponds to scattering at weakly screened ionized impurities (type III), while the middle and lower curves represent momentum scattering of types II and I, respectively (see Table ).

Figure 4

(Color online) (a) Spin-relaxation time ${\tau }_z$ and (b) measured (Refs. 21, 31) Hall mobility ${\mu }_{\text{Hall}}$ as a function of temperature $T$. In (a) the labeling of the calculated curves is analogous to Fig. 3 and the measured values (Ref. 21) are represented by squares. The sample parameters are those of sample (d) in Table . In the very low temperature range $T<13\mathrm{K}$, no theoretical evaluation of ${\tau }_z$ is possible due to lack of experimental data for the Hall mobility.