Quantifying Electron Spin Polarization from Polarized EL in Si spin-LEDs

We analyze the circular polarization (P$_{circ}$) of the electroluminescence (EL) from Si-based spin-LEDs using a recent theory [1] which provides a quantitative relation between the polarization of phonon-assisted optical transitions measured in the EL, and the electron spin polarization electrically injected from Fe/Al2O3 and Fe/SiO2 tunnel barrier contacts [2,3]. EL spectra include features due to transverse acoustic (TA) and transverse optical (TO) phonon-mediated recombination occurring in the p-doped (p$\sim$10$^{19}$cm-3) substrate. P$_{circ}$ of 3.5\% is typical for the TA at 5K, and is systematically higher than that of the TO by a factor $\sim$1.7, consistent with theory. The maximum polarization predicted for the TA is 13\% for recombination of 100\% polarized electrons in p-type Si (10$^{19}$cm-3). Thus the measured P$_{circ}$ 3.5\% corresponds to an electron spin polarization (P$_{spin}$) of 27\% produced by electrical injection from our tunnel barrier contacts. A similar analysis applied to the TO phonon at 80K yields P$_{spin}$ of 25\%. Thus the theory enables quantitative interpretation of optical polarization in indirect gap semiconductors, facilitating future studies of spin injection. [1] P. Li and H. Dery, Phys. Rev. Lett. 105, 037204 (2010). [2] B.T. Jonker, et al., Nature Physics 3, 542 (2007). [3] C.H. Li, et al, Appl. Phys. Lett. 95, 172102 (2009).