As electronic device dimensions
decrease to micro and nanoscale, Paschen’s law (PL)—the standard theory used to
predict breakdown voltage (*V _{b}*)
governed by Townsend avalanche (TA)—fails due to ion-enhanced field emission
(FE). Analytic models to predict

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.

Pressure also plays a critical role
in gas breakdown behavior. This dissertation derives a new analytic equation
that predicts breakdown voltage *V _{b}*
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,

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 *d* with an effective gap distance *d _{eff}* defined as the sum of
cathode placement distance and crater depth. Moreover, the theory indicated
that

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.

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.