Further Validation of Spark-Resistance Formula Applied for Human ESD

Micro-gap electrostatic discharge (ESD) events due to a human with charge voltages below 1000 V 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 energy and charge injected into a spark channel, respectively. However, their validity has not well been investigated. To examine which spark-resistance formula could be applied for human 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 200 V and 2000 V, 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 validate the above spark hypotheses, we derived the discharge voltages in closed forms across a spark gap based on the spark-resistance formulae, and compared them with the estimated results from the measured discharge currents. As a result, we found that Rompe-Weizel's formula could well explain initial spark process than Toepler's one regardless of charge voltages.