Length-Dependent Resistance of Thin Wires

The electrical properties of wires with cross-sectional areas of order 1 × ${10}^{-11\mathrm{}}$ ${\mathrm{cm}}^2$ and lengths as small as 0.2 μm have been studied. At temperatures below about 10 K, the resistance of the wires increases with decreasing temperature, as found in previous studies of much longer wires. For wires shorter than about 5 μm, the resistance rise decreases as the length of the wire is decreased. From these results a characteristic length scale of approximately 0.2 μm at 1.5 K is found, in good agreement with the current theory.