  Electronic density of states (DOS) at Fermi level has been investigated in
ultrathin Ag films grown on Si(111)-(7x7) down to the two dimensional limit of
a single atomic layer. Measurement of DOS at Fermi level by scanning tunneling
spectroscopy shows an approximate (1 - {\gamma}/d) dependence, where {\gamma}
is a constant and d is the film thickness. The results are explained in the
light of an analytical theory as well as our density functional theory (DFT)
calculations. DFT results also show that in the proximity of the interface the
DOS values of the film and the substrate are mutually affected by each other.
