GALVANOMAGNETIC STUDIES OF SN-DOPED BI .2. NEGATIVE FERMI ENERGIES

Studies of the Shubnikov-de Haas effect and the Hall effect in single crystals of bismuth doped with tin are extended to excess hole concentration beyond 2×1018 cm-3, the upper limit achieved in earlier reported work. For dopings greater than about 3×1018 cm-3, the Fermi level lies below the bottom of the L-point conduction band, so that the Fermi energy measured from this band edge is negative. The passage of the Fermi level into the forbidden gap at the L point is accompanied by the disappearance of electron quantum oscillations and by a decrease by two orders of magnitude in the magnetoresistance at 4.2°K. At about 5×1018 excess holes/cm3, a large magnetoresistance effect reappears, and low-field quantum oscillations, which are attributed to light holes at the L point, are observed. The dependence of the light-hole periods on magnetic field orientation suggests that the longitudinal mass is smaller for L-point holes [La(3)] than for electrons [Ls(3)], as is predicted by Golin's band-structure calculation. T-point hole oscillations are observed for excess hole concentrations up to 1019 cm-3 and measurements have been extended to fields of 90 kOe to study their anisotropy. The anisotropy is consistent with a T-point hole surface which is a prolate ellipsoid of revolution for excess hole concentrations up to 3×1018 cm-3, but the surface becomes less prolate as tin is added. Data on this surface are compared with the predictions of a six-band k•π calculation derived from Golin's pseudopotential theory, using the matrix elements at T which he calculated; good agreement is obtained. It is pointed out that the analysis of band nonparabolicity in an earlier paper which makes use of the Abrikosov-Falkovski dispersion relation underestimates the magnitude of the T45-(1)-T6+(3) direct gap at T. On the basis of the six-band model, the observed nonparabolicity is found to be consistent with the gap estimated by Golin. © 1969 The American Physical Society.