Application of the general thermal field model to simulate the behaviour of nanoscale Cu field emitters

Strong field electron emission from a nanoscale tip can cause a temperature rise at the tip apex due to Joule heating. This becomes particularly important when the current value grows rapidly, as in the pre-breakdown (the electrostatic discharge) condition, which may occur near metal surfaces operating under high electric fields. The high temperatures introduce uncertainties in calculations of the current values when using the Fowler–Nordheim equation, since the thermionic component in such conditions cannot be neglected. In this paper, we analyze the field electron emission currents as the function of the applied electric field, given by both the conventional Fowler–Nordheim field emission and the recently developed generalized thermal field emission formalisms. We also compare the results in two limits: discrete (atomistic simulations) and continuum (finite element calculations). The discrepancies of both implementations and their effect on final results are discussed. In both approaches, the electric field, electron emission currents, and Joule heating processes are simulated concurrently and self-consistently. We show that the conventional Fowler–Nordheim equation results in significant underestimation of electron emission currents. We also show that Fowler–Nordheim plots used to estimate the field enhancement factor may lead to significant overestimation of this parameter especially in the range of relatively low electric fields