10.25394/PGS.12746651.v1
Amanda M Loveless
Unified Electron Emission and Gas Breakdown Theory Across Length, Pressure, and Frequency
2020
Purdue University Graduate School
gas breakdown
electron emission
plasma discharge
microscale breakdown
2020-07-31 17:46:23
article
https://hammer.figshare.com/articles/thesis/Unified_Electron_Emission_and_Gas_Breakdown_Theory_Across_Length_Pressure_and_Frequency/12746651
<p>As electronic device dimensions
decrease to micro and nanoscale, Paschen’s law (PL)—the standard theory used to
predict breakdown voltage (<i>V<sub>b</sub></i>)
governed by Townsend avalanche (TA)—fails due to ion-enhanced field emission
(FE). Analytic models to predict <i>V<sub>b </sub></i>at
these scales are necessary to elucidate the underlying physics driving
breakdown and electron emission in these regimes. Starting from a
previously-derived breakdown criterion coupling TA and FE, this dissertation
derives a universal (true for any gas) breakdown equation. Further simplifying
this equation using a matched asymptotic analysis, dependent on the product of
the ionization coefficient and the gap distance, yields an analytic theory for
dimensionless <i>V<sub>b</sub></i>. This
analytic model unifies the coupled FE/TA regime to a universal PL derived by applying
scaling parameters to the standard PL. This model enables parametric analyses
to assess the effects of different parameters (such as pressure, gap distance, and
field enhancement factor) on breakdown and quantify the relative contribution
of FE and TA to identify the transition to the universal PL. This dissertation
applies this general theory to experimental cases of different gap width, gap
pressure and electrode surface roughness before exploring unification across
electron emission regimes, validation with molecular dynamics simulations, and
extensions to alternating current (AC).</p>
<p> </p>
<p>One application of this theory to
experimental data used data from a collaborator at Xi’an Jiaotong University,
who used an electrical-optical measurement system to measure the breakdown
voltage and determine breakdown morphology as a function of gap width. An
empirical fit showed that the breakdown voltage varied linearly with gap
distance at smaller gaps as in vacuum breakdown. This dissertation demonstrates
that applying the matched asymptotic theory in the appropriate limits recovers
this scaling with the slope as a function of field emission properties. </p>
<p> </p>
<p>Pressure also plays a critical role
in gas breakdown behavior. This dissertation derives a new analytic equation
that predicts breakdown voltage <i>V<sub>b</sub></i>
within 4% of the exact numerical results of the exact theory and new
experimental results at subatmospheric pressure for gap distances from 1-25
. At atmospheric pressure, <i>V<sub>b</sub></i> transitions to PL near the product of pressure and
gap distance, <i>pd</i>, corresponding to
the Paschen minimum; at lower pressures, the transition to PL occurs to the
left of the minimum. We further show that the work function plays a major role
in determining whether <i>V<sub>b</sub></i> transitions from the coupled FE/TA
equation back to the traditional PL to the right or the left of the Paschen
minimum as pressure increases, while field enhancement and the secondary
emission coefficient play smaller roles. These results indicate that
appropriate combinations of these parameters cause <i>V<sub>b</sub></i> to transition to PL to the left of the Paschen
minimum, which would yield an extended plateau similar to some microscale gas
breakdown experimental observations. </p>
<p> </p>
<p>Finally, the importance of
electrode surface structure on microscale gas breakdown remains poorly
understand. This dissertation provides the next step at assessing this by
applying the asymptotic theory to microscale gas breakdown measurements for a
pin-to-plate electrode setup in air at atmospheric pressure with different
cathode surface roughness. Multiple discharges created circular craters on the
flat cathode up to 40 μm deep with more pronounced craters created at smaller
gap sizes and greater cathode surface roughness. The theory showed that
breakdown voltage and ionization coefficient for subsequent breakdown events
followed our earlier breakdown theory when we replaced the gap distance <i>d</i> with an effective gap distance <i>d<sub>eff</sub></i> defined as the sum of
cathode placement distance and crater depth. Moreover, the theory indicated
that <i>d<sub>eff</sub></i> could become
sufficient large to exceed the Meek criterion for streamer formation, motivating
future studies to assess whether the cathode damage could drive changes in the
breakdown mechanism could for a single electrode separation distance or the
Meek criterion requires modification at microscale. </p>
<p> </p>
<p>We next unified field emission with
other electron emission mechanisms, including Mott-Gurney (MG), Child-Langmuir
(CL), and quantum space-charge-limited current (QSCL) to develop a common
framework for characterizing electron emission from nanoscale to the classical
PL. This
approach reproduced the conditions for transitions across multiple mechanisms,
such as QSCL to CL, CL to FE, CL to MG to FE, and microscale gas breakdown to
PL using a common nondimensional framework. Furthermore, we demonstrated the
conditions for more complicated nexuses where multiple asymptotic solutions
matched, such as matching QSCL, CSCL, MG, and FE to gas breakdown. A
unified model for radiofrequency and microwave gas breakdown will be compared
to experimental results from Purdue University to elucidate breakdown
mechanism. </p>
<p>The results from this dissertation
will have applications in microscale gas breakdown for applications including
microelectromechanical system design, combustion, environmental mitigation,
carbon nanotube emission for directed energy systems, and characterizing
breakdown in accelerators and fusion devices.</p>