Transverse Zeeman Effect of the Excitation Spectra of Boron and Thallium Impurities in Germanium

Abstract

The results are presented of an experimental investigation of the transverse Zeeman effect (Voigt configuration) of the excitation spectra of boron and thallium impurities in germanium. These have been studied with the magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$ along $〈100〉$, $〈111〉$, or $〈110〉$ using linearly polarized radiation. The results are compared with the calculations of Lin-Chung and Wallis and the theory of Bhattacharjee and Rodriguez. The $g$ factors given by the former authors have permitted one case out of thirty-two possibilities to be selected for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}\ensuremath{\parallel}〈100〉$. Consequently, the $g$ factors of several of the states of both impurities have been found; this represents the first determination of the $g$ factors for any of the group-III impurities in germanium. The values obtained for the principal $g$ factors, ${g}_{\frac{1}{2}}^{\ensuremath{'}}$ and ${g}_{\frac{3}{2}}^{\ensuremath{'}}$, of the ground states are -1.53\ifmmode\pm\else\textpm\fi{}0.09 and 0.03\ifmmode\pm\else\textpm\fi{}0.04, respectively, for boron, and -1.4\ifmmode\pm\else\textpm\fi{}0.7 and 0.23\ifmmode\pm\else\textpm\fi{}0.04, respectively, for thallium. The values of ${g}_{\frac{1}{2}}^{D}$ and ${g}_{\frac{3}{2}}^{D}$, for example, the $g$ factors of the excited state of the $D$ line are -6.14\ifmmode\pm\else\textpm\fi{}0.13 and 0.07\ifmmode\pm\else\textpm\fi{}0.03, and -5.7\ifmmode\pm\else\textpm\fi{}0.2 and 0.06\ifmmode\pm\else\textpm\fi{}0.23, for boron and thallium, respectively. The difference in value between ${g}_{\frac{3}{2}}^{\ensuremath{'}}$ of boron and thallium is taken to be due to the difference in ground-state wave functions of these two impurities, i.e., a manifestation of the chemical shift. The excited states have essentially the same $g$ factors as is to be expected for effective-mass-like levels. The quadratic factors have not been determined separately for each state. The relative intensities of the $D$ components for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}\ensuremath{\parallel}〈100〉$ are in good agreement with theory. From the results obtained for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}\ensuremath{\parallel}〈100〉$, it is possible to predict the linear splittings and relative intensities of the Zeeman components for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}\ensuremath{\parallel}〈111〉$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}\ensuremath{\parallel}〈110〉$. Good agreement is found with the experimental results for the $D$ components under the latter orientation; the agreement is not as good for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}\ensuremath{\parallel}〈111〉$. Some success is obtained in the interpretation of the $C$ line for all three orientations if this is taken to be due mainly to an excitation to the ${\ensuremath{\Gamma}}_{7}$ state of the ${\ensuremath{\Gamma}}_{7}+{\ensuremath{\Gamma}}_{8}$ combination predicted by the effective-mass theory. The behavior of the $G$ line has not been well understood.