Kinetic properties of electrons in bismuth thin films

Abstract

The resistivity ϱ of bismuth films in the absence of a magnetic field exhibits the following features: it decreases with increasing temperature T; the temperature dependence of the resistance has a maximum at low temperatures for very thin films and a minimum at higher temperatures for films of larger thickness; below 1000 Å the conductivity increases with decreasing film thickness L (anomalous size effect); the classical size effect appears as the film thickness increases. For very thin films the magnetoresistance coefficient (in the region ωτ < 1) changes non-monotonically with rising T: at a certain temperature determined by the film thickness a minimum appears and then an anomalous rise in magnetoresistance. From an analysis of the magnetic field dependence of σ xx and σ yx , calculated from our data on ϱ, Δϱ/ϱ and the Hall e.m.f., and using the formula of the two-band model for strong and weak magnetic fields, we obtained the change in concentration ( n,p) and mobility (μ, ν) of the charge carriers with varying T and L, and hence we were able to explain the observed features of their kinetic properties. The appearance of anomalies results both from the resonance scattering of carriers under size quantization and from the non-uniformity of the distribution through the film thickness of carriers of different sign due to potential bending near the surface. This leads to a shift in the electron spectrum characteristics with decreasing Bi film thickness.