Mathematical models for thermionic emission current density of graphene emitter.

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 $$S=\sum {\left({J}_{th}-{J}_{exp}\right)}^{2}=0.0002 \,\text{A}^{2}/\text{m}^{4}$$ 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.