Theoretical study of the electron field emission phenomena in the generation of a micrometer scale discharge

The phenomenon of field emission plays a significant role in the deviation of the breakdown voltage from that predicted by Paschen's law within the range of high electric fields. High fields obtained in small gaps may enhance the secondary electron emission and such enhancement could lead to a lowering of the breakdown voltage and a departure from the Paschen curve. In this paper, the dc breakdown characteristics of the discharge in the micrometric regime were extensively studied by the theoretical approach including ion-enhanced field emission. In addition, semi-empirical expressions for the dependence of the breakdown voltage on the gap spacing and on the pressure based on the numerical solutions of the equation that describes the dc breakdown criteria have been proposed.