Band Structure of Doped Bismuth Using the Shubnikov—de Haas Effect

The band structure of bismuth has been studied using the Shubnikov—de Haas effect. Oscillatory magneto-resistance has been observed in crystals containing up to 0.06 at.% tellurium. The Fermi energy in the most heavily doped crystals was about 95 meV above the bottom of the conduction band at the $L$ point of the Brillouin zone. Extremal values of the cross-sectional areas of the surface and the electron effective masses were combined with measurements of the electron concentration to demonstrate the validity of the two-band models of Lax and Cohen below about 65 meV. Above this energy there are significant deviations from these models as regards both the cross sections and the effective masses. Thus in heavily doped bismuth, where the Fermi energy is relatively large, the two-band models must be modified. The experimental data reported here may be explained most simply in terms of a two-band model in which the mass at the band edge increases with Fermi energy. A distortion of the Fermi surface above about 70 meV is also reported. The amount of distortion apparently increases more rapidly than predicted by the nonellipsoidal nonparabolic model.