Thermal-field and photoemission from meso- and micro-scale features: Effects of screening and roughness on characterization and simulation

Abstract

A methodology of modeling nonplanar surfaces, in which the microscale features of the emission sites can be orders of magnitude smaller than the mesoscale features defining the active emission area, has been developed and applied to both ordered arrays of identical emitters and random variations characteristic of a roughened surface. The methodology combines a general thermal-field-photoemission model for electron emission, a point charge model for the evaluation of field enhancement factors and surface geometry, and a Ballistic-Impulse model to account for the trajectories of electrons close to the cathode surface. How microscale and mesoscale features can both undermine the estimation of thermal-field emission parameters, such as characteristic field enhancement and total current predictions, as well as give rise to changes in the distribution of transverse velocity components used to estimate beam quality features such as emittance that are important to photocathodes, is quantified. The methodology is designed to enable both the proper characterization of emitters based on experimental current-voltage data and the development of a unit cell model of emission regions that will ease the emission model demands in beam optics codes.

Wigner wave packets: Transmission, reflection, and tunneling

“…Accounting for how long an electron takes to pass an emission barrier is difficult for theory, simulations, and experiments on ultrafast processes associated with emission and transmission [32,37,43,56,92,122]. A method to incorporate delays associated with electrons passing a barrier (particularly if tunneling), as occur in field and photoemission studies using quantum mechanical, Monte Carlo, or particle-based methods [17,20,70,94,[123][124][125][126], may profitably use the notion of TARD time introduced here, as it accounts for changes in overall number and current density in a manner that respects their time evolution for a wave packet, but which does not run afoul of interference oscillations associated with Wigner trajectories. A feature that was well-hidden for the gaussian barrier (and will only be slightly better revealed for the parabolic barrier of Section IV D) is the nature of the intersection of the reflected and transmitted dashed white (ballistic) lines.…”

“…Processes associated with the field emission of electrons operate on disparate length scales that span many orders of magnitude [1][2][3]. Tunneling is exquisitely sensitive to the barrier shape [4][5][6], which in turn depends on microscale surface curvature [7][8][9][10][11][12], emitter shape [13][14][15], surface roughness [16][17][18][19][20][21][22] and nearest neighbor (shielding) effects in arrays [23][24][25]. Simulating emission using, for example, particle-in-cell (PIC) or molecular dynamics codes is already challenging because of the difficulty in reconciling particle transport with tunneling (wave) behavior [17,[26][27][28].…”

Dynamics of a Field Emitted Beam From a Microscopic Inhomogeneous Cathode

“…The dynamics of the beam are strongly affected by the conditions at the point of emission, and hence the emitting surface influences the properties of the electron beam greatly. The effects of the cathode surface on the beam can be via the shape of the surface [2,9], roughness or imperfections [10][11][12], temperature [13], or material properties such as the work function [14].…”

The transition from field emission to collisional space-charge limited current with nonzero initial velocity

“…This approach of developing full analytic theories coupling relevant electron emission sources and assessing the transition between dominant mechanisms, referred to more broadly as “nexus theory” 4 , may be extended to other electron emission source mechanisms. For instance, Darr et al 23 replaced FN with the general thermal-field (GTF) emission equation 2 , 24 – 26 , which couples field and thermionic emission, to derive exact and asymptotic solutions linking FN, CL, and the Richardson-Laue-Dushman (RLD) solution for thermionic emission, given by 27 where is the cathode temperature, is the Boltzmann constant, and . Darr et al extended previous studies examining the transition from RLD to CL using Miram curves 28 – 33 by incorporating FN and showing that an increasing contribution of field emission could soften the characteristic “knee” during the transition to CL.…”

“…Darr et al extended previous studies examining the transition from RLD to CL using Miram curves 28 – 33 by incorporating FN and showing that an increasing contribution of field emission could soften the characteristic “knee” during the transition to CL. Lang et al 34 replaced the GTF equation with the general thermo-field photoemission (GTFP) equation 24 , 25 to include the transition to the Fowler-DuBridge (FD) equation for photoemission 2 , 35 . In addition to providing a detailed step-by-step process for developing nexus phase space plots showing the device conditions necessary for the transitions between FD, RLD, FN, MG, CL, and Ohm’s law, Lang et al derived exact solutions for the current density as a function of voltage and demonstrated the transitions to FD, RLD, FN, and CL under appropriate asymptotic conditions of temperature, gap distance, voltage, and laser frequency 34 .…”