In the laser-driven ion acceleration studies, the naturally deposited contaminant layer on the target surface is thought to be a source of energetic ions and protons. Using ellipsometric measurements, we found that the thickness of the surface natural contaminant layer, which cannot be modified without external surface treatment, is on the order of a few nanometers. A conceptual approach is developed where "thick" and "thin" contaminant layer regimes of acceleration are identified and parameterized by the normalized thickness of the contaminant layer. These studies may also help in developing an ion acceleration concept using multilayered targets or through modifications of the target surface.