Modified Richardson-Dushman equation and modeling thermionic emission from monolayer graphene

For the first time we have derived an equation for the temperature (T) dependent work function (W(T)) containing terms up to fifth power of T which gives a modified Richardson-Dushman (MRDE) equation that fits excellently well the experimental data of thermionic current density, J vs temperature, T data for suspended monolayer graphene. It provides a unique technique for accurate determination of work function, W-0, Fermi energy, E-F0 at 0 K and surface density of charge carriers, n(s) of graphene. The corresponding values obtained for monolayer suspended graphene are: W-0 = 4.592 +/- 0.002 eV, E-F0 = 0.203 +/- 0.002 eV; n(s) = 3.16x1012 cm(-2). The model gives us unique method of determination of the Fermi energy of graphene as a function of temperature. The values of thermal expansion coefficient, a and surface density of charge, n(s) obtained with the use of the model are in excellent agreement with experiments. We also find that the model explains fairly well the J vs T data for carbon nanotubes, which is reported in a separate paper.