  Motivated by recent experiments of carrier-doped C$_{60}$ in a field-effect
transistor (FET), effects of spatial single particle potential variations on
Mott-Hubbard (MH) insulators are studied theoretically. It is shown that the
presence of strong random potentials leads to a reduced dependence of
electronic properties on band fillings and to disappearance of the MH
insulating behavior at integer fillings. A simple physical picture to explain
this behavior is given using a notion of self-doping of the MH insulator. Our
results have important implications on some of the puzzling observations of
carrier-doped C$_{60}$ in the FET. It is also discussed that the FET
configuration with Al{$_2$}O{$_3$} dielectric provides an ``ideal'' system with
strong disorders.
