A three-dimensional model for thermionic emission from graphene and carbon nanotube

Graphene and carbon nanotube (CNT) have been proposed to be good materials for thermionic energy converter (TEC). For accurate simulation of performance of TEC, it is important to know the correct equation for temperature dependence of thermionic emission current density ( J ) from graphene and carbon nanotube. In this paper we first consider the existing theory of electron energy dispersion relation in graphene to reconsider the relations between Fermi energy and Fermi velocity in relation to some form of electron mass in graphene. We then consider existing various models of temperature dependence of J versus T ( J ( T )) and their applicability to nano-materials. We find that no model exists to date that fully conforms to the available experimental data on J ( T ) of nano materials. By providing justifications for three components of electron momentum vector during thermionic emission from graphene, we then find a three-dimensional model that fits the experimental thermionic emission data from graphene and carbon nanotube far better than any existing model. We present a detailed comparison of our model with existing models of thermionic emission. The work function determined using our model also agrees very well with independent experimental results. This model is expected to be very effective in modelling TEC with graphene or CNT.