Hopping transport in Ag-SnO₂and Mo-SnO₂granular films in the dielectric regime
Ya-Nan Wu2*, Yan-Fang Wei1, Zhi-Qing Li1, Juhn-Jong Lin2
1Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Faculty of Science, Tianjin University, Tianjin, China
2Institute of Physics and Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
* presenting author:Ya-Nan Wu, email:wuyanan@nctu.edu.tw
Over the past several decades, the exp[-√(T₀/T)] behavior of DC conductivity of granular systems in the dielectric regime has been extensively studied, yet the transport mechanisms remain to be fully understood. Recently, a hopping transport process based on co-tunneling processes has been proposed by Beloborodov and coauthors.¹² They described the process as tunneling via virtual electron levels through grains and found electron hopping over large distances exceeding a granule size. The co-tunneling effects have recently been observed in periodic granular arrays,³⁴ but not yet in disordered granular films. This talk will present our work on the variation of conductivity with temperature in two series of insulating Ag-SnO₂and Mo-SnO₂granular films deposited by the co-sputtering method. Our results will be explained in terms of the co-tunneling model.
The bright-field TEM images show that spherical-like Ag particles are embedded in SnO₂matrix, indicating typical granular features of Ag-SnO₂films. On the other hand, the Mo-SnO₂films consist of numerous Mo and SnO₂small substructures with feature sizes varying notably. In both series of films, we have observed that the temperature dependence of conductivity follows the relation σ~exp[-√(T₀/T)] over a wide temperature range of ~10–80 K. By comparing our σ(T) data with co-tunneling conduction, we obtained reasonable values of the localization length ξ and typical hopping distance r*. However, the conductivity does not exhibit an activation dependence on temperature (lnσ∝-1/T) up to 300 K. In this connection, we estimate the number of grains N* involved in a theoretical hopping process. The N* remains larger than 1 in most of our samples until 300 K, indicating that the hops occur not only between adjacent grains and the crossover to simple activated transport will not take place in our measuring range. In summary, our measured exp[-√(T₀/T)] behavior of conductivity can be well described by the hopping conduction based on multiple co-tunneling.

¹I. S. Beloborodov, A. V. Lopatin, V. M. Vinokur, and K. B. Efetov, Rev. Mod. Phys. 79, 469 (2007).
²I. S. Beloborodov, A. V. Lopatin, and V. M. Vinokur, Phys. Rev. B 72, 125121 (2005).
³T. B. Tran, I. S. Beloborodov, X. M. Lin, T. P. Bigioni, V. M. Vinokur, and H. M. Jaeger, Phys. Rev. Lett. 95, 076806 (2005).
⁴A. I. Yakimov, A. V. Dvurechenskiǐ, A. I. Nikiforov, and A. A. Bloshkin, Pis'ma Zh. Eksp. Teor. Fiz. 77, 445 (2003) [JETP Lett. 77, 376 (2003)]

Keywords: Hopping conductivity, Granular films, Multiple co-tunneling, Coulomb gap