De Haas-van Alphen and Galvanomagnetic Effect in Bi and Bi-Pb Alloys

Abstract

The de Haas-van Alphen (dHvA) effect in pure Bi and lightly doped Bi-Pb alloys was studied using a sensitive mutual-induction technique. In pure Bi, we obtained for the electron and hole Fermi surfaces, respectively: Fermi energies ${E}_{n}=25.0$ meV and ${E}_{p}=11.0$ meV; the number densities per ellipsoid $n=0.96\ifmmode\times\else\texttimes\fi{}\frac{{10}^{17}}{\mathrm{cc}}$ and $p=3.00\ifmmode\times\else\texttimes\fi{}\frac{{10}^{17}}{\mathrm{cc}}$, and the Dingle temperatures ${\ensuremath{\kappa}}_{n}=0.68$\ifmmode^\circ\else\textdegree\fi{}K and ${\ensuremath{\kappa}}_{p}=0.2$\ifmmode^\circ\else\textdegree\fi{}K. Additionally, we find that for the conduction band the energy dispersion in the heavy-mass direction is essentially the same as in the lighter-mass direction; i.e., the constant-energy surfaces are very closely ellipsoidal. The data on Bi-Pb alloys show that the relative motion of the conduction and the overlapping valence band is negligible and only the Fermi level shifts with alloying. From the dHvA and the galvanomagnetic data in Bi-Pb alloys in moderate fields, we deduced that the electron and hole mobilities decrease inversely as (${N}_{p}\ensuremath{-}{N}_{n}$) as expected, where the $N$'s are the total carrier densities and we assume that all the Pb atoms scatter independently as ionized impurities.