Experimental investigation of the optical spin-selection rules in bulk Si and Ge/Si quantum dots

We study the relationship between the circular polarization of photoluminescence and the magnetic-field-induced spin polarization of the recombining charge carriers in bulk Si and Ge/Si quantum dots. First, we quantitatively compare experimental results on the degree of circular polarization of photons resulting from phonon-assisted radiative transitions in intrinsic and doped bulk Si with calculations which we adapt from recently predicted spin-dependent phonon-assisted transition probabilities in Si. The excellent agreement of our experiments and calculations quantitatively verifies these spin-dependent transition probabilities and extends their validity to weak magnetic fields. Such magnetic fields can induce a luminescence polarization of up to 3%/T. We then investigate phononless transitions in Ge/Si quantum dots as well as in degenerately doped Si. Our experiments systematically show that the sign of the degree of circular polarization of luminescence resulting from phononless transitions is opposite to the one associated with phonon-assisted transitions in Si and with phononless transitions in direct-band-gap semiconductors. This observation implies qualitatively different spin-dependent selection rules for phononless transitions, which seem to be related to the confined character of the electron wave function.

Figure 1

${\sigma }^{+}$- and ${\sigma }^{-}$-polarized PL spectra of the intrinsic Si sample in a magnetic field of $-7$ T. The inset is a closeup for the TA-related luminescence. Both the TO and TA free-exciton peaks exhibit a positive DCP. See the text for a definition of “TO”.

Figure 2

Magnetic-field dependence of the DCP of the “TO” PL peak of bulk Si of different doping type. The symbols give experimental values while the solid lines represent the theoretical calculations presented in the text.

Figure 3

Circular-polarization-resolved spectra of the phononless PL of the Ge QD sample. The spectra were acquired at a temperature of about 10 K and in a magnetic field of (a) $+7$ T and (b) $-7$ T.

Figure 4

Circular-polarization-resolved PL spectra of an $n$-type doped Si sample. The spectra were acquired at a temperature of about 5 K and in a magnetic field of (a) $+7$ T and (b) $-7$ T. The insets are closeups of the high-energy regions of the spectra, containing the TA peak around 1110 meV and the phononless peak, labeled NP, at 1130 meV. The phononless NP peak has an opposite polarization compared to the TA and “TO” peak.