Cyclotron Absorption in Metallic Bismuth and Its Alloys

Extensive studies of cyclotron absorption in bismuth and in alloys of bismuth with tin and tellurium are reported. Experimentally, a microwave cavity arrangement is used which causes circularly polarized radiation to be incident on the sample. The samples are disks which form part of the cavity wall during the experiment. A signal is observed which is under most conditions proportional to the change in the fractional power absorption of the sample as the magnetic field applied to the sample is changed. The experiment is done with this field in the plane of the sample as well as normal to it. When the magnetic field is normal to the sample surface, circularly polarized radiation distinguishes between the effects of holes and of electrons. Making this distinction is complicated in bismuth by the anisotropy of the band structure, but it is not impossible. In pure bismuth the number of holes equals the number of electrons; alloying with tin increases the relative number of holes and alloying with tellurium increases the relative number of electrons. The experiments have been done both at 24 000 Mc/sec and at 72 000 Mc/sec. The tilted ellipsoid model of the electron band, and the ellipsoid of revolution model for the hole band have been used in a classical magneto-ionic theory of the effect which fits the data taken with magnetic field normal to the sample surface quite satisfactorily. The fit between this theory and the experiment is substantial confirmation of the validity of this band model, and makes it possible with the aid of certain infrared observations to determine the parameters of the model numerically. The mass parameters obtained for an ellipsoid in the electron band are $m_1=0.0088\mathrm{}$, $m_2=1.80\mathrm{}$, $m_3=0.02323\mathrm{}$, $m_4=\pm 0.16$, while those for the hole band are $M_1=M_2=0.068\mathrm{}$ and $M_3=0.92\mathrm{}$. Comparison is made with similar results obtained from magnetoresistance and de Haas-van Alphen experiments. The experiments done with the magnetic field in the plane of the sample have been used to improve the accuracy of the determination of cyclotron resonance fields and therefore of the masses of the charge carriers, although no quantitative theory of the over-all shape of the signal under these conditions is available.