Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals

Abstract

An experimental and theoretical discussion is given of the results of cyclotron resonance experiments on charge carriers in silicon and germanium single crystals near 4\ifmmode^\circ\else\textdegree\fi{}K. A description is given of the light-modulation technique which gives good signal-to-noise ratios. Experiments with circularly polarized microwave radiation are described. A complete study of anisotropy effects is reported. The electron energy surfaces in germanium near the band edge are prolate spheroids oriented along $〈111〉$ axes with longitudinal mass parameter ${m}_{l}=(1.58\ifmmode\pm\else\textpm\fi{}0.04)m$ and transverse mass parameter ${m}_{t}=(0.082\ifmmode\pm\else\textpm\fi{}0.001)m$. The electron energy surfaces in silicon are prolate spheroids oriented along $〈100〉$ axes with ${m}_{l}=(0.97\ifmmode\pm\else\textpm\fi{}0.02)m$; ${m}_{t}=(0.19\ifmmode\pm\else\textpm\fi{}0.01)m$. The energy surfaces for holes in both germanium and silicon have the form $E(k)=A{k}^{2}\ifmmode\pm\else\textpm\fi{}{[{B}^{2}{k}^{4}+{C}^{2}({{k}_{x}}^{2}{{k}_{y}}^{2}+{{k}_{y}}^{2}{{k}_{z}}^{2}+{{k}_{z}}^{2}{{k}_{x}}^{2})]}^{\frac{1}{2}}.$ We find, for germanium, $A=\ensuremath{-}(13.0\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(8.9\ifmmode\pm\else\textpm\fi{}0.1)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(10.3\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$; and for silicon, $A=\ensuremath{-}(4.1\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(1.6\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(3.3\ifmmode\pm\else\textpm\fi{}0.5)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$. A discussion of possible systematic errors in these constants is given in the paper.