Enhanced orbital mixing in the valence band of strained germanium

We give a theoretical explanation of the very high electron-spin polarization measured in compressively strained Ge layers through spin-polarized photoemission experiments, based on the enhancement of the band orbital mixing between light-hole (LH) and split-off (SO) bands along the growth direction of Ge thin films. We deduce an increased valence-band mixing, with respect to the bulk case, from the measured spin-polarization values, which exceed the bulk limit when optical transitions away from the $\Gamma$ point of the tetragonally distorted Brillouin zone are taken into account. Furthermore, we show that the degree of LH-SO band orbital mixing is directly proportional to the degree of compressive strain in the Ge layer.

Figure 1

(a) Experimental geometry of the spin-resolved photoemission experiment: electrons are photoemitted from the activated sample with a wave vector $k_{\perp }$ along the [001] crystallographic direction of the strained Ge Brillouin zone. (b) Band structure of Ge/Si${}_{0.31}$Ge${}_{0.69}$, calculated through an $8\times 8\mathbf{k}·\mathbf{p}$ matrix at $T=120$ K (Ref. 18), considering the effective strain ${\epsilon }_{\parallel }=-0.96\%$ and deformation potentials of Ref. 19. The symmetry labels, referring to LH and SO states, take into account band orbital mixing. The broad gray band represents the vacuum energy level $E_v$ within the experimental error.

Figure 2

Character of the LH (a) and SO (b) bands as obtained from $8\times 8\mathbf{k}·\mathbf{p}$ calculations. Full symbols refer to bulk Ge; open circles to the case of Ge/Si${}_{1-x}$Ge${}_x$ with a compressive strain ${\epsilon }_{\parallel }=-0.96\%$.