Experimental study of the Zeeman splitting of boron levels in silicon

The Zeeman effect of the first four photoexcitation lines of boron in silicon has been investigated in crystals with low boron concentration (∼${10}^{14}$ atoms/${\mathrm{cm}}^3$) and for magnetic fields up to 64 kG with $\overrightarrow{\mathrm{E}}\perp \overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{B}}$. As many as eleven discrete components have been resolved for line 1 for ${\overrightarrow{\mathrm{B}}}_{\parallel }〈100〉$. No quadratic shift is observed for lines 1 and 2, but a small interaction is found between the excited sublevels of line 3 and other excited sublevels. Line 4 exhibits a characteristic upwards shift which can be fitted for most components to a quadratic law. By comparison with behavior of boron in germanium, it is found that the observed splitting is mainly due to the splitting of the ground state, which is about twice that of the excited states and this accounts for the thermalization effect observed at high fields. The results can be explained by assuming for the excited states of lines 1 and 2 the ${\Gamma }_8$ symmetry as deduced from piezospectroscopic measurements. The symmetry of the excited state of line 3 cannot be obtained with certainty from our experimental results and the data for line 4 can be partially explained on the basis of a ${\Gamma }_6+{\Gamma }_7$ symmetry. With the assumption of a symmetric splitting of the ground state, it has been found that the splitting of the excited states of line 1 is asymmetric and anisotropic, in contrast to the corresponding splitting for line 2. The $g$ factors obtained for the ground state are in qualitative agreement with the experimental determinations by magneto-Raman effect. The results obtained for the excited states of lines 1 and 2 are quantitatively self-consistent with respect to the anisotropy of the $g$ factors and to the selection rules given by Bhattacharjee and Rodriguez. It has also been possible to estimate for line 1 the parameters $u$ and $v$ governing the relative intensities of the allowed transitions. A comparison with theory for line 4 shows its partial breakdown due to the failure to meet the prerequisite for group-theoretical analysis.