Verification of Spark-Resistance Formulae for Micro-Gap ESD

Micro-gap electrostatic discharge (ESD) events due to a human with charge voltages below 1000V cause serious malfunctions in high-tech information devices. For clarifying such a mechanism, it is indispensable to grasp the spark process of such micro-gap ESDs. For this purpose, two types of spark-resistance laws proposed by Rompe-Weizel and Toepler have often been used, which were derived from the hypotheses that spark conductivity be proportional to the internal energies and charges injected into a spark channel, respectively. However, their validity has not well been verified. To examine which spark-resistance formula could be applied for micro-gap ESDs, with a 12-GHz digital oscilloscope, we previously measured the discharge currents through the hand-held metal piece from a charged human with respect to charged voltages of 200V and 2000V, and thereby derived the conductance of a spark gap to reveal that both of their hypotheses are roughly valid in the initial stage of sparks. In this study, to further verify the above spark hypotheses, we derived the discharge voltages in closed forms across a spark gap based on the above spark-resistance formulae, and investigated which spark-resistance formula could be applied for micro-gap ESDs in comparison of spark gaps estimated from the measured discharge currents. As a result, we found that Rompe-Weizel's formula could well explain spark properties for micro-gap ESDs than Toepler's one regardless of charge voltages and approach speeds.