Experimental and simulation studies of resistivity in nanoscale copper films

Abstract

The effect of film thickness on the resistivity of thin, evaporated copper films (approximately 10–150 nm thick) was determined from sheet resistance, film thickness, and mean grain-size measurements by using four-point probe, profilometer, and electron backscatter diffraction (EBSD) and X-ray diffraction (XRD) methods, respectively. The resistivity of these films increased with decreasing film thickness in a manner that agreed well with the dependence given by a versatile simulation program, published earlier, using the measured values for the mean grain size and fitting parameters for surface and grain boundary scattering. Measurements of the change in sheet resistance with temperature of these films and the known change in resistivity with temperature for pure, bulk copper were used to calculate the thickness of these films electrically by using Matthiessen’s rule (this is often referred to as an “electrical thickness”). These values agreed to within 3 nm of those obtained physically with the profilometer. Hence, Matthiessen’s rule can continue to be used to measure the thickness of a copper film and, by inference, the cross-sectional area of a copper line for dimensions well below the mean free path of electrons in copper at room temperature (39 nm).