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The breakdown voltage in a DC glow discharge as function of the pressure in a reactor at low pressure has been studied for more than a century. In 1889 Paschen first plot the sparking voltage as function of the product of the pressure p times the inter-electrode distance d, and wrote the voltage be dependent on the number of gas molecules between the electrodes. In 1910 Townsend brought about an explanation based on collisional ionization probability (related to α, the first Townsend coefficient) and the ion bombardment of the cathode (related to γ, the second Townsend coefficient). In 1915 he proposed an equation relating the breakdown voltage to the product p*d. However the Townsend model has some drawbacks and fails to explain the recent discovery of the dissociation glow by Yasuda in 2000. The authors proposed an alternative model to explain the breakdown voltage of gases, based on surface-state electron transfer from the cathode to the gas. In metal, weakly bound electrons are present at the surface, according to the Drude model (1900). By assuming a perfect metallic surface, it is possible to estimate the electron density in the metal, hence the number of electrons in the surface state of the metal. The voltage is the gradient of the electric field which pulls those electrons out of the cathode. Thus the breakdown voltage builds up the minimum electric field required to extract electrons from the surface state. Those cause the dielectric breakdown of the gas phase and the current increases by several order of magnitude; this is the breakdown current. A plot of the measured breakdown current against the estimated number of electrons in the surface state shows a linear dependency. This shows that the primary electrons that cause the electrical breakdown of the gas originate from the cathode surface. Moreover, as a consequence of the dielectric breakdown of the gas phase, a sudden and drastic change in the electric field profile between the electrode occurs which can then accelerate the electrons to the ionization energy of the gas molecule. A unified curve for different gases, electrode material and sizes linking the breakdown voltage to the pressure is obtained, supporting the above approach.
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