Thickness dependent lattice expansion in nanogranular Nb thin films

We report on the dependence of the lattice parameter on thickness (t) and grain size (D) in nanogranular Nb thin films deposited on Si (100) substrates by using dc magnetron sputtering. The lattice parameter is found to exponentially increase with decreasing thickness as well as grain size. We analyze the lattice expansion in terms of the excess free volume in the grain boundaries, which is found to decrease with the grain size in large thickness limit. The thickness dependence of the lattice expansion and the grain size dependence of the excess free volume are discussed in terms of the oxygen content in the grain boundaries.