Mathematical models for thermionic emission current density of graphene emitter

Abstract

In this study, five mathematical models were fitted in the absence of space charge with experimental data to find a more appropriate model and predict the emission current density of the graphene-based thermionic energy converter accurately. Modified Richardson Dushman model (MRDE) shows that TEC's electron emission depends on temperature, Fermi energy, work function, and coefficient of thermal expansion. Lowest Least square value of $$S=\sum {\left({J}_{th}-{J}_{exp}\right)}^{2}=0.0002 \,\text{A}^{2}/\text{m}^{4}$$ S = ∑ J th - J exp 2 = 0.0002 A 2 / m 4 makes MRDE most suitable in modelling the emission current density of the graphene-based TEC over the other four tested models. The developed MRDE can be adopted in predicting the current emission density of two-dimensional materials and also future graphene-based TEC response.

Surfaces with Lowered Electron Work Function: Problems of Their Creation and Theoretical Description. A Review

“…( 4) obtained for a sufficient number of the wave vector values. It is also worth paying attention to the inapplicability of three-dimensional electron emission models to twodimensional materials [47] and to the recent appearance of a modified Richardson-Dushman equation for two-dimensional materials, in particular, graphene and carbon nanotubes [48,49]. Deviations from the Richardson-Dushman formula are also possible as a result of non-equilibrium effects [50].…”

Progress in the experimental and computational methods of work function evaluation of materials: A review

“…And by extension it is known as a periodic function of an atomic number [120] . Its dependence on physical factors such as temperature, surface dipole, doping, and electric field cannot be underestimated as investigated by the authors of the twentieth century [7] , [8] , [9] , [10] that image potential contributes to the work function of materials and this work function depends on temperature [11] , [12] , [13] , [14] , [15] , [16] . Also, experimental and theoretical findings revealed that work function is dependent on electronic heat capacity [17] , thermal expansion of the lattice [17] , Young's modulus [17] , [18] , [19] , friction [20] , adhesion [21] surface energy [22] , fracture toughness [19] , [20] , [23] , corrosion [15] , [21] , [24] , and yield strength and hardness [26] .…”