Field Emission from Bismuth and Tungsten in a Magnetic Field

Abstract

Detailed calculations of magnetic-field-induced quantum effects in bismuth are described. In agreement with previous calculations, it is found that 10% fluctuations in the field-emission current can be expected at moderate fields if only the conduction electrons contribute to the field-emitted current. The magnitude of the fluctuations decreases significantly if other bands contribute to the field-emission current. In particular, when the contribution from the hole band is included in the calculations for a magnetic field parallel to the trigonal axes, the magnitude of the magnetic-field-induced fluctuations is reduced to 0.23%. Two experimental attempts to observe quantum effects are described. In the first, the current was measured as a function of magnetic field for fields up to 45 kG. In the second, the magnetic field was modulated and the in-phase fluctuations of the field-emission current were measured. No dc magnetic-field-induced quantum effects larger than 0.5% were observed from bismuth or tungsten and no fractional current changes larger than 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ were observed for a 40-G-rms field modulation. Both techniques had sufficient sensitivity to measure effects had the conduction band been the only contributor to the field-emission current. These null experimental results support the theoretical prediction that other bands besides the conduction band would reduce the relative magnitude of the magnetic-field-induced effects. Another experimental technique in which the magnetic-field-induced fluctuations would be enhanced to measureable values is proposed.