Quantum size effect in thin bismuth films

The dependence of the resistivity $\rho$, magnetoresistance $\frac{\Delta \rho }{\rho }$, and Hall coefficient $R_H$ of thin Bi films (thickness $d$, 700-2000 Å) on thickness and temperature was studied. Thin Bi films were grown epitaxially on freshly cleaved mica substrates by thermal evaporation in ultrahigh vacuum [(1-5) × ${10}^{-8\mathrm{}}$ 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 (period $\Delta d\sim 400$ Å) 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 had also the oscillatory thickness dependence, and the authors explained these oscillatory behaviors 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. The observed thickness dependence agreed well with the QSE theory.