Size Effects in the Thermal Variations of the Hall Coefficient

A number of experimental investigations of the temperature T dependence of the Hall coefficient RHF of thin metallic films have been reported1-9 in the past few years, ttowever some data have only been interpreted in terms of the temperature dependence of the electron density r ,9, even if the transport properties of these metallic films agree3,6,7,9,1 0 with the well known FuchsSondheimer theory. 11 In a previous paper we have derived an expression for the correction in the temperature coefficient, 3RH of the Hall coefficient R/4F of thin film arising from the temperature dependence of the bulk mean free path lo. Unfortunately in the case of partially specular scattering of electrons on the external surfaces the expression of/3R/4 is somewhat complicated and its numerical evaluation requires the use of a digital computer. In order to allow an easier calculation this letter proposes an alternative approach to derive an analytical expression for nH: it is taken into account that for nearly specular scattering on external surfaces the surface scattering can be treated with good approximation by the Cottey method 3 which states that the film resistivity PF and its temperature coefficient/F are respectively given by: 3,1 4 PO/PF F(p) t.t{p -1/2 + (1 -u2)ln(1 + p-l)} (1)