Energy-Band Parameters and Relative Band-Edge Motions in the Bi-Sb Alloy System near the Semimetal—Semiconductor Transition

We report experimental information which elucidates important features of the ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ alloy system. By means of observations of the Shubnikov-de Haas effect on undoped and doped samples we have followed the transition from a band structure near the Fermi level which is essentially that of pure Bi to one which resembles that of pure Sb. Supplementary information has been obtained from transport measurements. In both Bi and Sb, the conduction band is at the $L$ point in the Brillouin zone. A mirror-image band lies not far below. The upper $L$-point band is the conduction band throughout the alloy system. Our model of the transition involves two processes: (1) The descent of the $T$-point band (the valence band in Bi) relative to the $L$-point bands, a transition to six valence maxima at the nearby $H$ points, and their subsequent rise past the Fermi level to become the valence bands in Sb; (2) the approach, crossing, and separation of the $L$-point bands. At 4.2°K, the descent of the $T$-point maximum below the $T$-point minimum and the $L$-point crossing both occur near $x=8\%$; consequently, there is a transition from semimetallic to direct-gap ($L$-point) semiconducting behavior. The most direct determination of the $L$-point gap is obtained from the nonparabolic behavior of the very small transverse mass components. Strong corroborative evidence is obtained from transport measurements in the temperature range 4°-30°K.