Spin and energy relaxation in germanium studied by spin-polarized direct-gap photoluminescence

Spin orientation of photoexcited carriers and their energy relaxation are investigated in bulk Ge by studying spin-polarized recombination across the direct band gap. The control over parameters such as doping and lattice temperature is shown to yield a high polarization degree, namely larger than 40$\%$, as well as a fine tuning of the angular momentum of the emitted light with a complete reversal between right- and left-handed circular polarization. By combining the measurement of the optical polarization state of band-edge luminescence and Monte Carlo simulations of carrier dynamics, we show that these very rich and complex phenomena are the result of the electron thermalization and cooling in the multivalley conduction band of Ge. The circular polarization of the direct-gap radiative recombination is indeed affected by energy relaxation of hot electrons via the $X$ valleys and the Coulomb interaction with extrinsic carriers. Finally, thermal activation of unpolarized $L$ valley electrons accounts for the luminescence depolarization in the high temperature regime.

Figure 1

(a) Upper panel: Color-coded map of the PL intensity describing the temperature dependence of the photoluminescence (PL) spectra of $i$-Ge. Lower panel: 4 K PL data. Direct-gap, $c\Gamma -v\Gamma$, and indirect-gap transitions, $cL-v\Gamma$, mediated by longitudinal (LA) and transverse (TA) acoustic phonons are indicated along with the detector cutoff. The 4K PL spectra from all the studied samples are reported in the inset. (b) Energy variation of the direct gap with the temperature. Open dots are the PL peak positions measured in $i$-Ge, whereas the solid line represents Varshni's law according to the parameters of Ref. 28. (c) Temperature dependence of the total excess energy $\Delta E$ for carriers photoexcited in Ge by a laser energy at 1.165 eV (solid black line). The blue squares show the variation of the energy of the split-off band ${\Delta }_{\mathrm{SO}}$ with temperature according to Ref. 29. The inset shows the physical processes underlying the luminescence mechanisms.

Figure 2

Temperature dependence of the modification factor $\lambda$ and linewidth $w$ of the direct-gap PL of $p^{+}$-Ge (open dots) and $i$-Ge (full dots) samples. The shadowed gray area defines the 95$\%$ confidence bound region as obtained from the fitting of the spectra with the exponentially modified Gaussian function reported in Eq. (2).

Figure 3

(a) Modulation of the peak intensity with the analyzer angle measured in $i$-Ge, $p^{-}$-Ge, $n$-Ge, and p${}^{+}$-Ge as a function of temperature. The minima (dark) and maxima (bright) are visible from the color-coded scale. (b) Experimental data for the polarization degree of the studied samples as a function of doping and temperature.

Figure 4

Calculated circular polarization degree of the recombination in the $\Gamma$ valley of bulk Ge excited with ${\mathit{\sigma }}^{-}$.