In this work, experimental characterization results of indium nano-contacts are presented. The indium nano-contacts are epitaxially grown on a two-dimensional surface of high-resistivity, n-type Cd0.9Zn 0.1Te in ultra-high vacuum. The scaling effect in these contacts is systematic, but not linear. It is shown that the contacts exhibit a profoundly asymmetric behavior. It is argued that the "rectifying" behavior of these contacts is due to tunneling and that the tunneling does not necessarily imply Schottky nature.