Developing a theoretical relationship between electrical resistivity, temperature, and film thickness for conductors

Abstract

Experimental evidence has made it clear that the size of an object can have an effect on its properties. The electrical resistivity of a thin film will become larger as the thickness of that film decreases in size. Furthermore, the electrical resistivity will also increase as the temperature increases. To help understand these relationships, a model is presented, and equations are obtained to help understand the mechanisms responsible for these properties and to give insight into the underlying physics between these parameters. Comparisons are made between experimental data and values generated from the theoretical equations derived from the model. All of this analysis provides validation for the theoretical model. Therefore, since the model is accurate, it provides insight into the underlying physics that relates electrical resistivity to temperature and film thickness. © 2011 Lacy.