Atomic structure evolution and linear regression fitting models for pre-breakdown electric field strength of FCC, BCC and HCP metal nano-emitters under high electric field from PIC-ED–MD simulations

Abstract

The multi-scale and multi-physics simulations are carried out for the nano-emitters consisting of FCC (Al, Cu and Au), BCC (V, Mo and W) and HCP (Ti, Zn and Zr) metals, using the hybrid electrodynamics coupled with molecular dynamics-particle in cell simulations (PIC-ED-MD). We show that the tilting of nano-emitter at low temperature and small electric field (E-field) is mainly caused either by the movement of partial dislocations at the apex of nanotip or by the elastic local distortions of atomic registries away from their ideal lattice sites (FCC/BCC/HCP). At high E-field, the intense resistive heating due to the strong electron emission leads to the directly melting of the apex of nano-emitters. For nano-emitters consisting of low melting point metals such as Al, Zn and Au, the thermal runaway is driven by the elongation, thinning, and necking of the molten region. Meanwhile, the elongation, thinning, and sharpening produce the nano-protrusion at the apex of metal nano-emitters, and the detaching of atoms or atomic cluster from nano-protrusion mainly contribute to the thermal runaway event for refractor metals such as Ti, Zr, Mo and W. The critical E-field strength of metal nano-emitters is found to be strongly correlated with structural parameters (atomic coordination number of liquid and equilibrium lattice constant), thermodynamic quantities (cohesive energy and enthalpy of evaporation) and phase transition temperatures (melting point and boiling point). Those correlations enable us to establish either the single-variable linear fitting models or multi-variable linear regression models to predict the critical E-field value for metal nano-emitters with good credibility.

Self-consistent numerical solution of quantum regime with exchange-correlation effects of space charges for electron field emission in a nano-gap

“…In Figures 12D,E, we compare the calculated total field emission current and the local E-field strength of nano-emitter during the whole ED-MD-PIC simulation. The large sparks observed in Figures 12D,E after running simulations for certain times within different treatment of the quantum many-body effects of space charges are an indication of electric prebreakdown caused by structural failure [32][33][34]. In Figure 12D, it is found that the initial emission current is highest for PW-LDA method, The fluctuations seen in Figure 12 for either total emission current or E-field value reflect the changes in atomic structure, shape, and geometries of nano-emitter under the electric stress, thermal stress, and interatomic interactions in typical ED-MD-PIC simulation [32][33][34].…”

“…The large sparks observed in Figures 12D,E after running simulations for certain times within different treatment of the quantum many-body effects of space charges are an indication of electric prebreakdown caused by structural failure [32][33][34]. In Figure 12D, it is found that the initial emission current is highest for PW-LDA method, The fluctuations seen in Figure 12 for either total emission current or E-field value reflect the changes in atomic structure, shape, and geometries of nano-emitter under the electric stress, thermal stress, and interatomic interactions in typical ED-MD-PIC simulation [32][33][34]. Finally, it is worth noting that Cabrera and coworkers systematically studied the current versus voltage characteristics of a diode-like tunnel junctions consisting of a sharp W cathode and a planar electrode as the electron collector with the typical nanogap spacing spanning from 3 nm Frontiers in Physics frontiersin.org to 300 nm and the applied voltage between 10 V and 80 V [48].…”

“…In the hybrid simulation algorithm, the multi-scale self-adaptive finite element meshes were generated and updated dynamically with the atomic structure evolution of metal nano-tip which is treated as the cathode in the typical field emission setup. Such methodology has been routinely employed before to understand the correlation between the electron field emission process and the thermal runaway mechanism of metal nano-tips [32][33][34]. For 3-D field emission model, the electric field and the emission current density were obtained locally from a quasi-planar like emitter.…”