Zeeman Effect of Impurity Levels in Silicon

Abstract

Completely resolved Zeeman spectra for the bismuth donor in silicon including optical transitions from the $1s$ donor ground state to the excited states $2p_0$, $2p_{\pm }$, $3p_0$, $4p_0$, $3p_{\pm }$, $5p_0$, $4p_{\pm }$, and $5p_{\pm }$ are presented. The transitions were observed at liquid helium temperature, using linearly polarized radiation alternately parallel and perpendicular to the magnetic field, and field intensities up to 38.9 kilogauss oriented along each of the three principal crystallographic axes. Both linear splitting of the $p_{\pm }$ states and a quadratic dependence on field were observed. The use of impurity Zeeman spectra is demonstrated for evaluating effective mass parameters, determining the nature of energy bands and finding and identifying impurity excited states. The transverse effective mass for the electron in silicon was found to be (0.186±0.006) $m_0$ in agreement with recent cyclotron resonance results. From Zeeman splitting, electron effective masses up to 0.5 $m_0$ can be measured to within ±½% at infrared frequencies in a field of 40 kilogauss. The behavior in a magnetic field of the first two donor excited states could be explained by treating the magnetic terms of the Hamiltonian as a perturbation to first order. Interactions among the higher closely-spaced Zeeman levels were observed above 20 kilogauss and were evaluated with a second-order treatment. The Zeeman structure for the aluminum acceptor reflected the complexity of the valence bands and the acceptor ground state and was in qualitative agreement with the theoretical results of Kohn and Schechter. Transitions were observed to eight excited states converging to the series limit. Evidence is given for the degeneracy of each state.