Electric current distribution in thin Ti-Cu base coatings

Abstract

The electrical resistivity of thin layer (film, coating) about 5 microns’ thick has been measured by the classical four-point probes method. The layer includes titanium-copper alloy grains up to 5 microns in size. Unexpectedly we encountered a physical phenomenon that spoils the measurements: the fluctuation of measurement results, i.e. the error of measurement may exceed 1000%.. Under certain conditions such crystals may exert some long-range influence leading to tenfold fluctuations of results of measuring the electrical resistivity, despite of the fact that these crystals are evenly distributed and do not create large-size clusters It was found that the relative scatter of measurement results decreases along with the increase of the distance between the electrodes (probes) due to averaging of currents, however, the error decreasing occurs inversely proportional to the logarithm of the distance between the probes. That is why the scatter remains significant at distances between the applied probes thousands times bigger than crystal grains. It decreases much slower than it occurs in case of one dimensional long strip where the error of measurement is simply inversely proportional to the distance between the probes. It creates huge difficulties for measurement of surface resistance. To overcome these difficulties, the method for the statistical proceeding of the non-uniform results of multiple measurements of electrical resistivity in two-dimensional systems has been proposed, which enable to extract information about average surface resistance even from such confusing set of measurements. By help of such statistic the four probe method can be potentially used in industry, for example, for controlling the quality of metal film coatings, used for heating by electrical current for de-icing of aircrafts or wind turbines.The Paper type: Research paper