Cyclotron Resonance and the Cohen Nonellipsoidal Nonparabolic Model for Bismuth. III. Experimental Results

Complete measurements of the anisotropy of the central-orbit cyclotron effective masses by Azbel'-Kaner cyclotron resonance have been taken at a frequency of 24.03 GHz and a temperature of 1.15 \ifmmode^\circ\else\textdegree\fi{}K for the magnetic field in the three crystallographic planes of Bi. Deviations of up to 10% from ellipsoidal behavior were observed for the electron-effective-mass anisotropies. Except in one instance, the various effective-mass anisotropies give a good fit to the Cohen nonellipsoidal nonparabolic (NENP) model and the fit is clearly superior to the Lax ellipsoidal nonparabolic model fit. The ratio of the Fermi energy to the $L$-point band-gap energy, $\frac{{E}_{F}}{{E}_{g}}$, was determined from fitting the NENP model and found to be 1.5\ifmmode\pm\else\textpm\fi{}0.4, in good agreement with other measurements. The fit to the NENP model also indicated that $\frac{{m}_{2}}{{m}_{2}}$ is approximately 1, implying that the $L$-point valence and conduction bands have identical parameters. The cyclotron effective masses agree within 3% with the values obtained by Edel'man and Khaikin, and disagree by as much as 30% with the values obtained by Kao. Quantum oscillations of the microwave surface impedance similar in nature to de Haas-Schubnikov oscillations have also been observed, but periods arising from the large cross-sectional areas could not be detected and no conclusions regarding the NENP model could be made. Magnetoplasma oscillations due to standing Alfv\'en waves have also been observed. The mass-density values derived from these measurements agree with the values obtained by other investigators. However, the carrier concentration derived from the Alfv\'en-wave periods differs by nearly 12% with the value derived from the Azbel'-Kaner cyclotron-resonance measurements. This difference may be due to nonellipsoidal effects.

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