Scaling law for direct current field emission-driven microscale gas breakdown

Abstract

The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices. V

Electrical characteristics of nanometer gaps in vacuum under direct voltage

“…As a result, the electrical characteristic, which determines the insulating property of microelectronic devices, is critical to the nanometer gaps with the applied voltage of a few volts or dozens of volts. Though there has been a significant volume of experimental work published on the topic of electrical characteristics across micrometer gaps for more than a decade [6][7][8][9], there is not sufficient data about electrical breakdown of vacuum gaps in the nanometer regime [1,[10][11]. Therefore, the understanding of electrical characteristics across nanometer gaps is quite necessary for the design and operation of molecular devices and nano devices.…”

Cathode fall model and current-voltage characteristics of field emission driven direct current microplasmas

“…23 Note that the expression for a does not include the semi-empirical correction 15 proposed recently since the correction was based on simulations of dark discharges as opposed to linearly varying electric fields as in the current scenario. Also, for inert gases, a better fit to experimental data for a can be obtained using the relation…”

“…Venkattraman et al 10 presented particle-in-cell with Monte Carlo collisions (PIC/MCC) simulations and current vs voltage measurements performed on microdevices before breakdown occurs. Several other simulations have been reported dealing with the role of field emission in microdischarges, 11 quantifying the role of various processes in a field emission driven microdischarge, 12 fundamental properties of these microdischarges, 13 and coupling of ion-enhanced field emission and the discharge processes 14 culminating in a scaling law 15 that describes field emission driven gas breakdown without the use of fitting parameters. While most of the above research involved direct current microdischarges, simulations to predict breakdown voltages have also been extended to time-varying fields 16 with different mechanisms contributing to breakdown depending on the applied frequency.…”

Theory and analysis of operating modes in microplasmas assisted by field emitting cathodes

“…4 A recent direction in microdischarge research has been the study of anomalous breakdown [15][16][17] in gaps that are less than 10 lm and the influence of field emission of electrons from the cathode on microscale gas breakdown particularly in the direct current (DC) regime. A combination of theory, [18][19][20][21] particle-in-cell with Monte Carlo collisions (PIC-MCC) [22][23][24] and fluid modeling 25 have been used to propose various models to unify microscale gas breakdown driven by field emission with macroscale gas breakdown driven by secondary electron emission. Numerical results have also been reported for radio frequency microscale gas breakdown driven by field emission.…”