Sondheimer Theory Research Articles

Size effect on the electrical conductivity and longitudinal gauge factor of thin metal films

The electrical and piezoresistive properties of vacuum deposited films of copper, tungsten, platinum and gold were investigated in the thickness range from 100 to 1000 A. Both the conductivity and the longitudinal strain coefficient of resistance exhibit a size dependence, that was interpreted by applying the Sondheimer theory of charge transport in thin films on the assumption that the reflection of electrons by the film surfaces is partially specular. The proportion of electrons elastically scattered has been deduced from considerations based on the anomalous skin effect. The calculations are in reasonable agreement with the observations; the discrepancies can be attributed to the chemical contamination of the samples and to departures of the surface structure from the idealized flat configuration assumed in the theoretical treatment.

Measurement of strain coefficient of resistance in silver films

Epitaxial silver films (300–1400 Å) have been vacuum deposited onto mica substrates in order to assess the effect of strain on resistivity. The experimental procedure for determining the strain coefficient of resistance 1/ R(d R/dε) is described in detail. The results for 1/ R(d R/dε) have been compared with those derived from Sondheimer's theory of thin film conduction. It is concluded that the experimental values for 1/ R(d R/dε) show qualitative agreement with this theory.

ELECTRICAL CONDUCTION IN SINGLE-CRYSTAL ALUMINUM THIN FILMS

Electrical conduction in thin (400−1500 Å) single-crystal aluminum films vacuum evaporated on NaCl substrates is explained by a simple model and verified by experimental results. The resistivity of the inter-island boundaries is accounted for by considering the film structure as a metal—insulator matrix and calculating its equivalent resistivity. An unambiguous comparison can then be made with the Fuchs—Sondheimer theory of size-affected conduction in thin metal films only after subtracting off the resistivity contribution due to interisland boundaries.

Thickness dependence of the electrical conductivity in vacuum deposited copper films

The size dependence of the conductivity observed in vacuum condensed copper films 200-1500 A thick was interpreted by applying the Sondheimer theory on the assumption that the scattering of the carriers by the film boundaries is partially elastic. The fraction of electrons specularly reflected at the surfaces was determined by a method based on the anomalous skin effect.

Hall Effect in Thin Metal Films

Hall coefficient RH and Hall mobility μ have been measured for annealed polycrystalline and epitaxially grown gold, silver, and copper films at 296° and 77°K. At thicknesses above about 600 Å, nearly bulk values are obtained for RH and μ. Below 600 Å, a film-thickness dependence (size effect) was observed. This dependence is weak for epitaxially grown films, indicating a predominantly specular reflection of conduction electrons. On the other hand, the dependence is marked for polycrystalline films. Results on polycrystalline gold and silver films fit a predominantly diffuse scattering behavior. Data on carefully prepared polycrystalline films of copper agree well with Sondheimer's theory for perfect diffuse scattering so that best fit mean free path values can be calculated. In general, however, contrary to the theoretical predictions, RH was found to show a slight size effect even for film thicknesses greater than the electron mean free path (t>l). This departure may be the result of an oversimplified theory. The sharper decline of the Hall mobility for t<l in polycrystalline films than is expected theoretically may be attributed to enhanced crystallite-size boundary scattering.

The Influence of the Size Effect on Electrical Resistivity Measurements in Irradiated Metals

AbstractTwo high purity Al foils of thickness 40 μm and 5.6 μm are simultaneously irradiated. The initial resistivity increments per unit defect concentration for the foils differ by a factor of two due to the size effect. Sondheimer's theory is in good agreement with the experimental data. The calculations are presented for a range of parameters so that the magnitude of this effect can be estimated for other experiments.

Sondheimer oscillations in the hall effect of aluminium

Abstract The Hall coefficient in thin aluminium films has been measured. The bulk variation of the Hall coefficient was found to obey an analogy to Kohler's rule for the magnetoresistivity, with some reservations. The size dependent part of the Hall coefficient was found to be in general agreement with Sondheimer's theory.

On the Theory of Thermal Conductivity of Monovalent Metals

Sondheimer's theory of thermal conductivity contradicts in two points with experimental results. i) The theoretical values of the conductivity at low temperatures are too small compared with expermental values. ii) At intermediate temperatures, the theory predicts the existence of a minimum of the conductivity which is not observed. We criticize Sondheimer's theory in several points, and confining ourselves only to the problem of thermal conductivity, we obtain on a new basis satisfactory results. The main results are as follows : i) Bloch's hypothesis that the phonon system is in thermal equilibrium in all temperature regions is applicable in the case of thermal conductivity. ii) Sondheimer solved Bloch equation by expanding C(E) in a power series of E, but this type of function does not give a correct solution in the case of the second order phenomena. By using a more reasonable variational function, we obtain a more correct lower limit of thermal conductivity which is about 20% larger than Klemens' result. Further, we obtain an upper bound by a certain method and thus determine the bour.ds of the correct solution. iii) By considering exchange field and correlation field, it is shown that the method of self.consistent field gives fairly large resistivity at high temperatures. The ratio Cft: becomes 1.22. By this effect, the theoretical values of thermal conductivity becomes more consistent with experimental values, and the minimum of the conductivity at intermediate temperatures disappears. iv) Debye temperature determined by comparing with experimental values agrees very well with the Debye temperature of longitudinal sound waves calculated by Toya.