Quantum size effect in thin bismuth films

TLDR: In this paper, the dependence of the resistivity ρ magnetoresistance Δρ/ρ and Hall coefficient RH of thin Bi films (thickness d: 700-2000 A) on thickness and temperature was studied.

Abstract: The dependence of the resistivity ρ magnetoresistance Δρ/ρ and Hall coefficient RH of thin Bi films (thickness d: 700–2000 A) on thickness and temperature was studied. Thin Bi films were grown epitaxially on freshly cleaved mica substrates by thermal evaporation in ultra-high vacuum (1–5×10-8 Torr). These films had a mosaic structure of equally oriented crystallites (grain size: about 1 µm). The plane of the films was perpendicular to the trigonal axis of Bi. The oscillatory thickness-dependence (its period Δd: 400 A) of the galvanomagnetic coefficients and the decrease of oscillation amplitudes with increasing temperature were observed. The present authors also observed that the temperature at which the resistivity minimum occurred and the rate of the increase of carrier concentration with increasing temperature and also the oscillatory thickness-dependence, and the authors explained these oscillatory behaviours in terms of quantum size effect (QSE). In order to compare the experimental results with the QSE theory, the numerical calculation from this theory for thin Bi films was done. These thickness dependence agreed well with the QSE theory.