Amanda M. Loveless

Scaling laws for gas breakdown for nanoscale to microscale gaps at atmospheric pressure

Electronics miniaturization motivates gas breakdown predictions for microscale and smaller gaps, since traditional breakdown theory fails when gap size, d, is smaller than ∼15 μm at atmospheric pressure, patm. We perform a matched asymptotic analysis to derive analytic expressions for breakdown voltage, Vb, at patm for 1 nm ≤ d ≤ 35 μm. We obtain excellent agreement between numerical, analytic, and particle-in-cell simulations for argon, and show Vb decreasing as d → 0, instead of increasing as predicted by Paschens law. This work provides an analytic framework for determining Vb at atmospheric pressure for various gap distances that may be extended to other gases.

A universal theory for gas breakdown from microscale to the classical Paschen law

While well established for larger gaps, Paschens law (PL) fails to accurately predict breakdown for microscale gaps, where field emission becomes important. This deviation from PL is characterized by the absence of a minimum breakdown voltage as a function of the product of pressure and gap distance, which has been demonstrated analytically for microscale and smaller gaps with no secondary emission at atmospheric pressure [A. M. Loveless and A. L. Garner, IEEE Trans. Plasma Sci. 45, 574–583 (2017)]. We extend these previous results by deriving analytic expressions that incorporate the nonzero secondary emission coefficient, γSE, that are valid for gap distances larger than those at which quantum effects become important (∼100 nm) while remaining below those at which streamers arise. We demonstrate the validity of this model by benchmarking to particle-in-cell simulations with γSE = 0 and comparing numerical results to an experiment with argon, while additionally predicting a minimum voltage that was mask...

Design, characterization and experimental validation of a compact, flexible pulsed power architecture for ex vivo platelet activation

Electric pulses can induce various changes in cell dynamics and properties depending upon pulse parameters; however, pulsed power generators for in vitro and ex vivo applications may have little to no flexibility in changing the pulse duration, rise- and fall-times, or pulse shape. We outline a compact pulsed power architecture that operates from hundreds of nanoseconds (with the potential for modification to tens of nanoseconds) to tens of microseconds by modifying a Marx topology via controlling switch sequences and voltages into each capacitor stage. We demonstrate that this device can deliver pulses to both low conductivity buffers, like standard pulsed power supplies used for electroporation, and higher conductivity solutions, such as blood and platelet rich plasma. We further test the effectiveness of this pulse generator for biomedical applications by successfully activating platelets ex vivo with 400 ns and 600 ns electric pulses. This novel bioelectrics platform may provide researchers with unprecedented flexibility to explore a wide range of pulse parameters that may induce phenomena ranging from intracellular to plasma membrane manipulation.

Demonstration of field emission driven microscale gas breakdown for pulsed voltages using in-situ optical imaging

While multiple studies have explored the mechanism for DC and AC microscale gas breakdown, few have assessed the mechanism for pulsed voltage gas breakdown at the microscale. This study experimentally and analytically investigates gas breakdown for gap widths from 1 μm to 25 μm. Using an electrical-optical measurement system with a spatial resolution of 1 μm and a temporal resolution of 2 ns, we measure the breakdown voltages and determine breakdown morphology as a function of the gap width. An empirical fit shows that the breakdown voltage varies linearly with the gap distance at smaller gaps, agreeing with an analytical theory for DC microscale gas breakdown coupling field emission and Townsend avalanche that shows that the slope is a function of field emission properties. Furthermore, the curved breakdown paths captured between 5 μm and 10 μm demonstrate a similar effective length (∼11.7 μm) independent of the gap width, which is consistent with a “plateau” in breakdown voltage. This indicates that Townsend avalanche alone is insufficient to drive breakdown for these gaps and that ion enhanced field emission must contribute, in agreement with theory. The overall agreement of measured breakdown voltage with theoretical predictions from 1 μm to 25 μm indicates the applicability of DC microscale gas breakdown theory to pulsed breakdown, demonstrating that pulsed voltages induce a similar transition from Townsend avalanche to field emission as DC and AC voltages at the microscale.While multiple studies have explored the mechanism for DC and AC microscale gas breakdown, few have assessed the mechanism for pulsed voltage gas breakdown at the microscale. This study experimentally and analytically investigates gas breakdown for gap widths from 1 μm to 25 μm. Using an electrical-optical measurement system with a spatial resolution of 1 μm and a temporal resolution of 2 ns, we measure the breakdown voltages and determine breakdown morphology as a function of the gap width. An empirical fit shows that the breakdown voltage varies linearly with the gap distance at smaller gaps, agreeing with an analytical theory for DC microscale gas breakdown coupling field emission and Townsend avalanche that shows that the slope is a function of field emission properties. Furthermore, the curved breakdown paths captured between 5 μm and 10 μm demonstrate a similar effective length (∼11.7 μm) independent of the gap width, which is consistent with a “plateau” in breakdown voltage. This indicates that Tow...

Scaling laws for AC gas breakdown and implications for universality

The reduced dependence on secondary electron emission and electrode surface properties makes radiofrequency (RF) and microwave (MW) plasmas advantageous over direct current (DC) plasmas for various applications, such as microthrusters. Theoretical models relating molecular constants to alternating current (AC) breakdown often fail due to incomplete understanding of both the constants and the mechanisms involved. This work derives simple analytic expressions for RF and MW breakdown, demonstrating the transition between these regimes at their high and low frequency limits, respectively. We further show that the limiting expressions for DC, RF, and MW breakdown voltage all have the same universal scaling dependence on pressure and gap distance at high pressure, agreeing with experiment.

Sensitivity of modeled microscale gas breakdown voltage due to parametric variation

Device miniaturization increases the importance of understanding and predicting gas breakdown and electrical discharge thresholds. At gap sizes on the order of ten microns at atmospheric pressure, field emission drives breakdown rather than Townsend avalanche. While numerical and analytical models can demonstrate this transition, a quantitative understanding of the relative importance of each parameter remains unclear. Starting from a universal model for gas breakdown across the field emission and Townsend avalanche regimes [A. M. Loveless and A. L. Garner, Phys. Plasmas 24, 113522 (2017)], this paper applies the concept of error propagation from ionizing radiation measurements to determine the relative impact of each factor on the predicted breakdown voltage. For limits of both large and small products of the dimensionless ionization coefficient, α ¯ , and gap distance, d ¯, the electrode work function has the largest relative effect on the predicted breakdown voltages with a deviation of 50% in the work function resulting in an uncertainty in the calculated breakdown voltage of ∼84% for both α ¯ d ¯ ≫ 1 and α ¯ d ¯ ≪ 1. This quantifies the significance of nonuniformities in material surfaces and changes in the surface structure during multiple electric field applications and help predict the breakdown voltage for small gaps, motivating better electrode characterization both initially and during repeated operation.Device miniaturization increases the importance of understanding and predicting gas breakdown and electrical discharge thresholds. At gap sizes on the order of ten microns at atmospheric pressure, field emission drives breakdown rather than Townsend avalanche. While numerical and analytical models can demonstrate this transition, a quantitative understanding of the relative importance of each parameter remains unclear. Starting from a universal model for gas breakdown across the field emission and Townsend avalanche regimes [A. M. Loveless and A. L. Garner, Phys. Plasmas 24, 113522 (2017)], this paper applies the concept of error propagation from ionizing radiation measurements to determine the relative impact of each factor on the predicted breakdown voltage. For limits of both large and small products of the dimensionless ionization coefficient, α ¯ , and gap distance, d ¯, the electrode work function has the largest relative effect on the predicted breakdown voltages with a deviation of 50% i...

Generalization of scaling laws for gas breakdown to account for pressure

Summary form only given. The increasing importance of electronics miniaturization has motivated research into the behavior of breakdown voltage for microscale and nanoscale gaps1-4; however, the traditional Paschens law for predicting gas breakdown fails for smaller gaps1. Recent studies have developed analytic and numerical approaches to predict these deviations at atmospheric pressure1,2; however, the analytic expressions2 are only valid at atmospheric pressure and cannot be used to predict or explain recent breakdown studies at sub-atmospheric pressures down to vacuum3,4 or deviations from Paschens law at higher pressures.5 In this presentation, we will generalize previously derived expressions2 for breakdown voltage at atmospheric pressure to derive simplified scaling laws valid for any pressure up to the Meeks criterion for streamer discharge. We will compare these results to particle-in-cell simulations, numerical solutions, and experiments3,4. The implications of these expressions for predicting breakdown voltage as a function of pressure and the significance for understanding deviations from the traditional Paschens law will be discussed.

Matched asymptotic analysis of atmospheric pressure gas breakdown from nanoscale to microscale

Summary form only given. Electronics miniaturization for multiple applications, such as microelectromechanical systems1 and electric micropropulsion2, motivates more accurate predictions of gas breakdown voltage. Traditional breakdown theory described by Paschens law fails for gap distances smaller than ~15 μm.3 Multiple studies have obtained expressions for gas breakdown at microscale; however, these equations can only be solved numerically and do not directly predict the behavior for nanoscale gaps.4 We address this challenge by deriving simple analytic expressions to predict breakdown voltage by conducting a matched asymptotic analysis. We obtained excellent agreement between numerical solutions, analytic solutions, and particle-in-cell simulations for gap distances from 1 nm to 35 μm which corresponds to the Meeks criterion for streamer discharge. Moreover, the analytic expression for small gap distance shows that the breakdown voltage continues to decrease with decreasing gap distance rather than increasing as predicted by Paschens law. Furthermore, the limiting behavior shows regions where the conventional dependence of breakdown voltage as a function of the product of pressure and gap distance fails, motivating further analysis on pressure dependence. The implications of these results on system miniaturization and design at pressures above and below atmospheric pressure will be discussed.