  Two dimensional materials are important for electronics applications. A
natural way for electronic structure engineering on two dimensional systems is
on-plane chemical functionalization. Based on density functional theory, we
study the electronic structures of fluorine substituted planar polysilane and
graphane. We find that carbon and silicon present very different surface
chemistry. The indirect energy gap of planar polysilane turns to be direct upon
fluorine decoration, and the gap width is mainly determined by fluorine
coverage regardless of its distribution on the surface. However, electronic
structure of fluorine doped graphane is very sensitive to the doping
configuration, due to the competition between antibonding states and
nearly-free-electron (NFE) states. With specific fluorine distribution pattern,
zero-dimensional and one-dimensional NFE states can be obtained. We have also
studied the chemical modification with -OH or -NH$_2$ group. Carbon seems to be
too small to accommodate big functional groups on its graphane skeleton with a
high concentration.
