  Materials with reduced dimensionality often exhibit exceptional properties
that are different from their bulk counterparts. Here we report the emergence
of a commensurate 2 $\times$ 2 charge density wave (CDW) in monolayer and
bilayer SnSe$_2$ films by scanning tunneling microscope. The visualized spatial
modulation of CDW phase becomes prominent near the Fermi level, which is pinned
inside the semiconductor band gap of SnSe$_2$. We show that both CDW and Fermi
level pinning are intimately correlated with band bending and virtual induced
gap states at the semiconductor heterointerface. Through interface engineering,
the electron-density-dependent phase diagram is established in SnSe$_2$. Fermi
surface nesting between symmetry inequivalent electron pockets is revealed to
drive the CDW formation and to provide an alternative CDW mechanism that might
work in other compounds.
