  The mobility of graphene is very high because the quantum Hall effects can be
observed even at room temperature. Graphene has the potential of the material
for novel devices because of this high mobility. But the energy gap of graphene
is zero, so graphene can not be applied to semiconductor devices such as
transistors, LEDs, etc. In order to control the energy gaps, we propose atomic
monolayers which consist of various materials besides carbon atoms. To examine
the energy dispersions of atomic monolayers of various materials, we calculated
the electronic states of these atomic monolayers using density functional
theory with structural optimizations. The quantum chemical calculation software
"Gaussian 03" was used under periodic boundary conditions. The calculation
method is LSDA/6-311G(d,p), B3LYP/6-31G(d), or B3LYP/6-311G(d,p). The
calculated materials are C (graphene), Si (silicene), Ge, SiC, GeC, GeSi, BN,
BP, BAs, AlP, AlAs, GaP, and GaAs. These atomic monolayers can exist in the
flat honeycomb shapes. The energy gaps of these atomic monolayers take various
values. Ge is a semimetal; AlP, AlAs, GaP, and GaAs are indirect
semiconductors; and others are direct semiconductors. We also calculated the
change of energy dispersions accompanied by the substitution of the atoms. Our
results suggest that the substitution of impurity atoms for monolayer materials
can control the energy gaps of the atomic monolayers. We conclude that atomic
monolayers of various materials have the potential for novel devices.
