  The saw-tooth scaling investigations of work functions (WF) in hydrogenated
graphene are theoretically performed by density functional theory. The
positions of hydrogen atoms and the H/C ratios affect WF. With the comparison
of different graphene structures by adsorbed two hydrogen atoms, WF is larger
with less negative charges of the graphene. With different H/C ratios, WF is
controlled by two parts: the graphene surface and hydrogen groups. When the
ratio is smaller than 0.5, the work func-tion is more dependent on the Mulliken
charge of graphene. With more hydrogen atoms, the surface of graphene is more
negative, resulting in a smaller work function. When the ratio is larger than
0.5, the effect of hydrogen groups cannot be ignored. When two sides of
graphene have different numbers of hy-drogen atoms, a dipole exists, making the
movement of electron from Fermi level to vacuum level more difficult, thus WF
is larger than that with the same hydrogen atoms of each side. Therefore the
scaling of work function acts like a saw-tooth dependent on H/C ratio.
