Ultrahigh-resolution photoluminescence studies of excitons bound to boron in silicon in magnetic fields

The Zeeman effect on bound excitons in Si doped with boron has been studied in magnetic fields of up to 12 T, using Fourier-transform photoluminescence spectroscopy with a resolution of 3 μeV. Up to 20 narrow spectral components of the no-phonon boron-bound-exciton line have been resolved in each of the three 〈001〉, 〈111〉, and 〈110〉 sample orientations. In addition to the linear paramagnetic splitting of spectral components, a quadratic diamagnetic splitting was observed, and was attributed to the difference in the diamagnetic shifts of the single-electron states associated with the different conduction-band minima. From the pattern of the bound-exciton splittings, the order of the valley-orbit energy levels has been determined to be ${\mathrm{\Gamma }}_3$,${\mathrm{\Gamma }}_5$,${\mathrm{\Gamma }}_1$, with level ${\mathrm{\Gamma }}_3$ being the lowest and ${\mathrm{\Gamma }}_1$ the highest. A perturbation Hamiltonian, constructed from symmetry considerations, and describing the valley-orbit splitting, interparticle correlations, and interactions with the magnetic field, was used for calculations of the boron-bound-exciton energy levels versus field. Phenomenological parameters, including interparticle-correlation constants, g factors, and diamagnetic-shift constants were determined by simultaneously optimizing the fit between experimentally observed and calculated energy levels in strong magnetic fields and under uniaxial stress.