Optical Spin Injection and Spin Lifetime in Ge Heterostructures

We demonstrate optical orientation in $\mathrm{Ge}/\mathrm{SiGe}$ quantum wells and study their spin properties. The ultrafast electron transfer from the center of the Brillouin zone to its edge allows us to achieve high spin polarizations and to resolve the spin dynamics of holes and electrons. The circular polarization degree of the direct gap photoluminescence exceeds the theoretical bulk limit, yielding $\sim 37\%$ and $\sim 85\%$ for transitions with heavy and light holes states, respectively. The spin lifetime of holes at the top of the valence band is estimated to be $\sim 0.5\mathrm{ps}$ and it is governed by transitions between light and heavy hole states. Electrons at the bottom of the conduction band, on the other hand, have a spin lifetime that exceeds 5 ns below 150 K. Theoretical analysis of the spin relaxation indicates that phonon-induced intervalley scattering dictates the spin lifetime of electrons.

Figure 1

(a) 8-band $\mathbf{k}·\mathbf{p}$ calculation of energy levels and wave function square amplitudes for a ${\mathrm{Si}}_{0.15}{\mathrm{Ge}}_{0.85}/\mathrm{Ge}/{\mathrm{Si}}_{0.15}{\mathrm{Ge}}_{0.85}$ quantum well. (b) Sketch of the luminescence process. Immediately after direct gap excitation, electrons can thermalize towards the edge of the $\Gamma$ valley and recombine radiatively. For $\Gamma$ valley electrons, however, the most effective process is scattering to the low-energy $L$ valleys, where they can recombine after ${\tau }_L$. The ultrafast time scale ${\tau }_{\Gamma \mathrm{\text{−}}L}<1\mathrm{ps}$ sets the lifetime for electrons at $\Gamma$.

Figure 2

(a) Color-coded contour plot of the photoluminescence intensity recorded for analyzer angles ranging from 0° to 360° for the $\mathrm{Ge}/{\mathrm{Si}}_{0.15}{\mathrm{Ge}}_{0.85}$ MQW sample at 4 K and under left-handed (${\sigma }^{-}$) circularly polarized excitation at 1.165 eV. The black and blue lines at the lower left panel refer to spectra resolved for analyzer angles of 135° and 45°, respectively. Their intensity difference at the lower energy spectral region ($<0.8\mathrm{eV}$) stems from spin polarization of electrons, and at higher energies ($>1\mathrm{eV}$) from spin polarization of both electrons and holes. (b) Peak amplitude modulations of the $c\Gamma 1\mathrm{\text{−}}HH1$, $cL1\mathrm{\text{−}}HH1$ and phonon replica emissions. (c) Optical selection rules of the ${\sigma }^{-}$ excitation. Dipole allowed transitions of heavy holes ($m_j=3/2$) are 3 times larger than of light holes ($m_j=1/2$). Their energy levels are split by confinement and strain.

Figure 3

Dots: Measured temperature dependence of the circular polarization degree at the peak region of the no-phonon ($cL1\mathrm{\text{−}}HH1$) emission (orange dots). Results of the LA phonon-assisted emission (red dots) are shown at $T<20\mathrm{K}$ where it is well resolved from the $cL1\mathrm{\text{−}}HH1$ peak. Black line: Modeled temperature dependence of the electron spin lifetime due to electron-phonon interaction. Blue line: Measured recombination lifetime due to radiative and nonradiative channels in a $\sim 5\mathrm{nm}$ wide $\mathrm{Ge}/\mathrm{SiGe}$ QW (after 29).