The Resistivity Size Effect in Epitaxial Nb(001) and Nb(011) Layers

Epitaxial Nb(011) and Nb(001) layers are sputter deposited ontoa-plane and r-plane sapphire substrates, respectively, and their resistivity rho measured in situ, ex situ, and at 77 K as a function of layer thickness d = 4-400 nm. The resistivity increase with decreasing d is independent of layer orientation and is described with the model by Fuchs and Sondheimer (FS), providing a value for the bulk electronmean free path lambda = 20 +/- 2 nm at room temperature. Exposure to air causes a 1.5-nm-thick surface oxide and an increase in rho by up to 74%, suggesting a decrease in the surface scattering specularity from p(1) = 0.9 +/- 0.1 at the Nb-vacuum interface to completely diffuse scattering (p(1) = 0) at the oxidized Nb surface. Alternatively, this increase in resistance can be attributed to roughening during surface oxidation while retaining completely diffuse scattering, yielding a lower bound for the room-temperature lambda of 9.0 +/- 0.4 nm. The product of the bulk resistivity rho o times lambda is temperature-independent and, depending on either choosing the roughness or the specularity interpretation, rho o lambda = 14 x 10(-16) or 30 x 10(-16) Omega m(2), respectively. These values are 3.9 and 8.5 times larger than rho o lambda from a previous theoretical prediction, indicating a dramatic break down of the classical FS model for Nb and indicating that the resistivity size effect in Nb is considerably larger than predicted earlier. They are also larger than for W, Ru, and Co, making Nb not promising for high-conductivity narrow interconnect lines.