Size-dependent resistivity of metallic wires in the mesoscopic range

Abstract

As the lateral dimension of conductors approaches the mesoscopic regime, deviations of electric resistivity from that of bulk material are observed. Size effects come into play as the lateral dimension of the wire is in the range of the mean free path of the conduction electrons and below. In order to probe the size effects in systems confined in both lateral dimensions copper wires with widths ranging from 40 to 800 nm were prepared in a ${\mathrm{SiO}}_2$ matrix. The resistance of the wires was measured in the temperature range from 77 to 573 K. A size-dependent increase of the resistivity was found for decreasing wire widths. For the narrowest wires the resistivity is a factor of $2.6$ higher than the copper bulk value $\left(1.75\mathrm{}\hspace{0.5em}\mu \Omega \mathrm{cm}\right).\mathrm{}$ The experimental data was compared to theoretical predictions over the whole investigated range of size and temperature using a semiclassical model. The model includes diffusive scattering of the conduction electrons at the surface and the grain boundaries of the wire. Very good agreement of theory with experimental data was found. In this way a coherent picture of the size dependent resistivity has been obtained.