Rashba spin-orbit coupling and spin relaxation in silicon quantum wells

Silicon is a leading candidate material for spin-based devices, and two-dimensional electron gases (2DEGs) formed in silicon heterostructures have been proposed for both spin transport and quantum dot quantum computing applications. The key parameter for these applications is the spin relaxation time. Here we apply the theory of D’yakonov and Perel’ (DP) to calculate the electron spin resonance linewidth of a silicon 2DEG due to structural inversion asymmetry for arbitrary static magnetic field direction at low temperatures. We estimate the Rashba spin-orbit coupling coefficient in silicon quantum wells and find the $T_1$ and $T_2$ times of the spins from this mechanism as a function of momentum scattering time, magnetic field, and device-specific parameters. We obtain agreement with existing data for the angular dependence of the relaxation times and show that the magnitudes are consistent with the DP mechanism. We suggest how to increase the relaxation times by appropriate device design.

Figure 1

(Color online) Strong, internal electric fields are common in silicon quantum well devices. $\mathrm{D}1$: A typical, high-mobility $\mathrm{SiGe}$ heterostructure uses a donor layer to populate a high-density 2DEG. The charge separation results in an $E_z\sim {10}^6\mathrm{V}∕\mathrm{m}$. $\mathrm{D}2$: A proposed quantum dot quantum computer (Ref. 13) which utilizes a tunnel-coupled back gate to populate the quantum well without the need for a nearby donor layer. Here, $E_z>{10}^5\mathrm{V}∕\mathrm{m}$ due to the image potential formed on the back gate.

Figure 2

(Color online) Spin relaxation times as a function of static magnetic field direction (where $\theta =0$ is perpendicular to the 2DEG plane) for specific values of 2DEG density and Rashba asymmetry. The quantum well is assumed to be completely donor-layer populated and as such, $\alpha$ is calculated directly with Eq. (5) as a function of the 2DEG density.

Figure 3

ESR linewidth lifetime $T_2$ from Eq. (17) for constant asymmetry coefficient $\alpha =1\mathrm{m}∕\mathrm{s}$, as a function of 2DEG mobility $\mu$ and density $n_s$. For donor-layer populated quantum wells, divide the times listed by ${\alpha }^2$: $T_2\left(\alpha \right)=T_2\left(\alpha =1\right)∕{\alpha }^2$. The magnetic field is assumed to be $B=0.33\mathrm{T}$, perpendicular to the plane of the 2DEG.