Tunneling, Zero-Bias Anomalies, and Small Superconductors

We have prepared tunnel junctions which contain small Sn particles imbedded in the oxide barrier. The size distribution of the small particles has been determined from electron micrographs. The electrical characteristics of these junctions were measured in the temperature range 1-300\ifmmode^\circ\else\textdegree\fi{}K and in magnetic fields up to 100 kOe. All junctions show a large temperature-dependent resistance peak at zero bias and at low temperatures. The resistance peak increases in magnitude when the Sn particles are made superconducting. A simple model based upon the capacitance of the particles can account quantitatively for this behavior. We believe that a simple extension of this model can account for at least some of the previously reported zero-bias resistance anomalies. From the experiment, it is also possible to extract information about the superconductivity of small particles. We find that Sn particles down to at least a radius $r\ensuremath{\sim}25$ \AA{} are superconducting. The transition temperature of the particles increases with decreasing particle size and reaches 4.2\ifmmode^\circ\else\textdegree\fi{}K for particles with $r\ensuremath{\sim}70$ \AA{}, compared with ${T}_{c}=3.7\ifmmode^\circ\else\textdegree\fi{}$K for bulk Sn. In the radius range $r>100$ \AA{}, the critical field of the particles can be described in terms of a theory by De Gennes and Tinkham. Smaller particles have a much higher critical field, which increases more rapidly with decreasing radius than predicted by that theory.

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