Modeling feedback effects in metal under ESD stress

The feedback model of on-chip interconnect metal heating during electrostatic discharge (ESD) is extended to capture and simplify overall behavior of the metal. Of greatest interest to risk assessment is the peak temperature T
_max
reached during an ESD event, and it is discovered that T
_max
for Human Body and Charged Device Model (HBM, CDM) events follows its own simplified feedback equation with constant parameters. These constants are a function of the electrical and thermal properties of the metal layer. The result is a simple relation between T
_max
and current density for the HBM or CDM event under consideration, a valuable aid to risk assessment and design rule checks. The summary equations capture the results of many detailed finite element and numerical convolution calculations of heat flow for on-chip metal.