Size effect in the in-plane electrical resistivity of very thin graphite crystals

Abstract

In order to investigate the effect of film thickness of thin graphite crystals on the electrical properties, we prepared thin graphite films by cleaving a kish graphite (KG) crystal with the rrr value of 32.3. The values of the thickness of the graphite films were ranging from around 300 to 1000A. Keeping these graphite films free from strain, we measured the temperature dependence of the in-plane resistivity between liquid helium and room temperatures. The experimental results could be expressed by a simple two band model and the Sugihara's theory for lattice vibration in thin-carbon films. By using these expressions, we estimated the overlap energy E0 of conduction and valence bands for the thin graphite films with various thicknesses. It was found that E0 decreases with decreasing film thickness. We also estimated the reciprocal of the relaxation time due to lattice defects or surface scattering l/τi and that due to lattice vibration l/τi for the thin films with various thicknesses. Consequently, it was found that the effect of l/τi increases rapidly, as the film thickness decreases. KEYWORDS graphite, thin film, resistivity, size effect, band overlap energy