Spin-dependent direct gap emission in tensile-strained Ge films on Si substrates

The circular polarization of direct gap emission of Ge is studied in optically excited tensile-strained Ge-on-Si heterostructures as a function of doping and temperature. Owing to the spin-dependent optical selection rules, the radiative recombinations involving strain-split light $\left(c\mathrm{\Gamma }\text{-LH}\right)$ and heavy hole $\left(c\mathrm{\Gamma }\text{-HH}\right)$ bands are unambiguously resolved. The fundamental $c\mathrm{\Gamma }\text{-LH}$ transition is found to have a low temperature circular polarization degree of about 85%, despite an off-resonance excitation of more than 300 meV. By photoluminescence (PL) measurements and tight-binding calculations we show that this exceptionally high value is due to the characteristic energy dependence of the optically induced electron spin population. Finally, our observation of a direct gap doublet clarifies that the light hole contribution, previously considered to be negligible, can dominate the room temperature PL even at low tensile strain values of $\approx 0.2\%$.

Figure 1

Upper panels: Color-coded intensity maps of the photoluminescence (PL) measured as a function of the analyzer angle at 4 K in tensile-strained (a) $n$-Ge, (b) $i$-Ge, and (c) $p$-Ge [15, 30]. Lower panels: 4 K PL spectra of (a) $n$-Ge, (b) $i$-Ge, and (c) $p$-Ge corresponding to ${\sigma }^{-}$ (analyzer angle at ${45}^{\circ }$, black solid line) and ${\sigma }^{+}$ $({135}^{\circ }$, red dashed line) polarization components.

Figure 2

(a) Scheme of the dipole-allowed transitions for right-handed $({\sigma }^{+}$, red lines) and left-handed $({\sigma }^{-}$, black lines) circularly polarized light involving $\mathrm{\Gamma }$-point heavy hole (HH), light hole (LH), and split-off (SO) valence (VB) and conduction (CB) band levels [5]. Fractional values represent the quantum numbers of the component of the angular momentum $J_z$ along the direction of light propagation $z$. (b) Strain-induced LH-HH splitting calculated via the tight-binding method at $\mathrm{\Gamma }$ as a function of a biaxial tensile strain. (c) Low temperature band structure of relaxed bulk Ge (dashed lines) and of Ge with 0.25% biaxial tensile strain (solid lines). The latter mimics the Ge-on-Si heterostructure. Vertical transitions from 1 to 3 are promoted respectively by the absorption of photons at $\hslash {\omega }_p=1.165$ eV from the SO states near $\mathrm{\Gamma }$, the second (V2) and the topmost (V1) out-of-zone-center VB states. (d) Relative population (upper panel) and spin polarization $P_s$ (bottom panel) as a function of the excess energy of CB electrons optically promoted by ${\sigma }^{+}$ excitation. (e) Color-coded map of the photogenerated electronic spin population $\mathrm{\Theta }$ as a function of the components of the electron momentum.

Figure 3

(a) ${\sigma }^{-}$ component of the 4 K PL spectra of $p$-type Ge-on-Si samples with different acceptor concentrations, namely, $3\times {10}^{16}$ (solid blue line), $2\times {10}^{17}$ (dashed magenta line), $5\times {10}^{17}$ (dotted green line), and $9\times {10}^{17}{\mathrm{cm}}^{-3}$ (dashed-dotted red line). (b) Color-coded map as a function of the analyzer angle (upper panel) and corresponding ${\sigma }^{-}$ (black solid line) and ${\sigma }^{+}$ (red dashed line) PL spectra measured at 135 K in $p$-Ge (bottom panel). (c) Temperature dependence of the PL peak positions resolved for the ${\sigma }^{+}$ (red circled dot) and ${\sigma }^{-}$ (black squared dot) components of the emission of $p$-Ge (upper panel), $i$-Ge (middle panel), and $n$-Ge (lower panel). The solid lines account for the expected $c\mathrm{\Gamma }\text{-LH}$ and $c\mathrm{\Gamma }\text{-HH}$ transition energies owing to the corresponding temperature [34], strain [17], and doping [31] contributions.