Hopping transport of localized pi electrons in amorphous carbon films.

Abstract

The temperature dependence of the dc and ac conductivities has been studied in sputtered arnorphous carbon films. The dc conductivity is proportional to T with n =15— 17 below room temperature. The mechanism is discussed in terms of the mobility-edge conduction, variable-range hopping, and small-polaron hopping. Quantitatively, these models could not interpret the observed behaviors. Instead, the multiphonon tunneling of localized electrons with weak electron-lattice coupling is suggested to be the dominant transport mechanism. This may be attributed to the ~-bonded nature of sputtered amorphous carbon. The ac conductivity is strongly correlated to the dc conductivity, which has never been explained by the current theories based on the pair approximation. Alternatively, the continuous-time random-walk approximation is shown to be a useful approach. I. INTRODUCTION It is believed that amorphous carbon (a-C) prepared by evaporation or sputtering is predominantly sp bonded with an optical gap of 0.4— 0.7 eV. ' At a carbon sp site, there are three strong o. bonds and one weak m bond lying normal to the o. bonding plane. The ~ states will form both the valence- and conduction-band states. ' The sp sites must be clustered together in aromatic units. The large size of such clusters could produce localized states near the Fermi level E+. The eFect of disorder in a ~-electron system is therefore of particular interest. The present authors have shown that the temperature dependence of the dc conductivity in sputtered a-C is empirically described by o. d, =o.oT, with n =15— 17, which may suggest that the nonpolaronic multiphonon tunneling of localized m electrons (weak coupling with lattice) dominates charge transport. Measurement of ac conductivity could provide direct information about the hopping rate of localized electrons. In the present study, the temperature dependences of both dc and ac conductivities are reported. Possible transport mechanisms, mobility-edge conduction, variable-range hopping (single-phonon process), and multiphonon hopping with strongly (small-polaron) and weakly coupled states, are discussed. It is suggested that the conventional mobility-edge conduction or small-polaron conduction could not explain the overall features of transport in a-C. It is also found that the ac conductivity is strongly correlated with the dc conductivity. This feature, which has never been explained by the current theory based on the pair approximation, is interpreted well in terms of the continuous-time random-walk (CTRW) approximation.