An analytical relation describing the dramatic reduction of the breakdown voltage for the microgap devices

The field-emission–related effects play a significant role in the deviation of the breakdown voltage from that predicted by Paschen's law in the range of micrometer gaps. Beginning from a certain gap spacing, breakdown voltage diverges from the climbing curve seen in the left half of the Paschen curve. In this paper, the equation governing the DC breakdown in microgaps has been solved analytically. The derived analytical relation indicates that the DC breakdown voltage in microgaps depends on the gap size d and the pressure p, particularly, rather than on the product pd. The new theoretical expression allows key features to be identified suggesting that the inclusion of the field emission at micron and submicron gaps is necessary to describe properly the experimental data. The expression presented here can receive a wider interest due to its applicability to the breakdown voltage for a series of gases, gaps and pressures and can serve as ready-to-use guidelines for system engineers and designers