Effect of temperature-dependent work function and fermi energy on thermionic emission current density in graphene

The analytical equation for thermionic emission current density for graphene is modified to include the effect of temperature dependent work function and Fermi energy. It is a well-established fact that thermal expansion occurs in graphene and hence work function and Fermi energy should be affected by it. The earlier proposed analytical equation ignored this fact and was fitted with the reported experimental data, Nano Res. 7(4), 553-560 (2014) to get the temperature independent work function and Fermi energy of single layer graphene (4.514 eV and 0.083 eV respectively). The work function and Fermi energy (chemical potential) were temperature independent in their case which is clearly an approximation. We find that temperature-dependent work function and temperature-dependent Fermi energy has significant effect on the thermionic emission current density of substrate-free single layer graphene and hence cannot be ignored.