Thermionic emission from monolayer graphene, sheath formation and its feasibility towards thermionic converters

Abstract

A formalism describing the thermionic emission from a single layer graphene sheet operating at a finite temperature and the consequent formation of the thermionic sheath in its proximity has been established. The formulation takes account of two dimensional densities of state configuration, Fermi-Dirac (f-d) statistics of the electron energy distribution, Fowler's treatment of electron emission, and Poisson's equation. The thermionic current estimates based on the present analysis is found to be in reasonably good agreement with experimental observations (Zhu et al., Nano Res. 07, 1 (2014)). The analysis has further been simplified for the case where f-d statistics of an electron energy distribution converges to Maxwellian distribution. By using this formulation, the steady state sheath features, viz., spatial dependence of the surface potential and electron density structure in the thermionic sheath are derived and illustrated graphically for graphene parameters; the electron density in the sheath is seen to diminish within ∼10 s of Debye lengths. By utilizing the graphene based cathode in configuring a thermionic converter (TC), an appropriate operating regime in achieving the efficient energy conversion has been identified. A TC configured with the graphene based cathode (operating at ∼1200 K/work function 4.74 V) along with the metallic anode (operating at ∼400 K/ work function 2.0 V) is predicted to display ∼56% of the input thermal flux into the electrical energy, which infers approximately ∼84% of the Carnot efficiency.