Fabrication and Control of Sodium Concentration in Cobaltate Na$_{x}$CoO$_{2}$ thin films ($x $= 0.68, 0.75) by Thermal Diffusion

We have fabricated Na$_{x}$CoO$_{2}$ ($x\sim $0.68 {\&} 0.75) thin films on sapphire (0001) substrates via lateral diffusion of sodium into Co$_{3}$O$_{4}$ (111) epitaxial films. The environment of thermal diffusion is key to the control of the sodium concent in thin films. From the results of x-ray diffraction and in-plane resistivity \textit{$\rho $}$_{ab}$, the epitaxial growth and the sodium contents of these Na$_{x}$CoO$_{2}$ thin films were identified. The thermoelectric measurements show a large thermoelectric power in our films, similar to that of single crystals. The quasiparticle scattering rate is found to approach zero, consistent with the small residual resistivity, indicating high quality of the Na$_{x}$CoO$_{2}$ thin films.