A two-band model for the galvanomagnetic properties of thin semimetal films

Abstract

A two-band model is proposed to describe the galvanomagnetic properties in thin samples of transition metals or of sernimetals such as bismuth which are characterized by two overlapping partially filled bands. The formalism proposed by Sondheimer and Wilson for transition metals and the Cottey model of carrier scattering at the external surfaces are used to solve size effect problems in a thin film subjected to a transverse magnetic field. The general case where the number of carriers per unit volume differs for the two bands is studied. The influence of the temperature is accounted for introducing a parameter x which corresponds to the fraction of the current carried by the conduction electrons. The results of these calculations are presented within the limit of low magnetic fields. Compared with the classical F-S theory, the variation of the Hall effect with film thickness is found to be determined by three essential parameters: the specularity parameterp, the ratio,y, of the number of carriers in the two bands, and the temperature-dependent parameterx. A large scatter of theoretical results is reported; in particular for typical sets of values forp, x andy the size effects can be exactly opposite to those predicted by one-carrier models. Tentative attempts to fit previously published data on the basis of the present model are undertaken. Qualitative agreement is observed, the theory is found to be able to explain the change in the sign of the Hall coefficient with increasing thickness sometimes observed in bismuth films. Difficulties in controlling morphology and geometrical surface properties of films with various thicknesses are outlined. As a consequence, one may find here a possible explanation for quantitative differences between theory and experiments.