One important mechanism in the prebreakdown phase is the quantum tunnelling of electrons from the metal cathode to the gas, lowering the breakdown voltage. Considerable departures from the classical Paschen's curve for pd lower than 1.0 Torr cm in microhollow cathodes with D = 200 μm and electrode spacing of 5 μm and 20 μm in air were observed. Fowler-Nordheim approach was employed to characterize the presence of field emission of electrons which modify the classical voltage versus current curve for pressures lower than 40 Torr.
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Sismanoglu et al. (2008) studied this question.
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