Achieving electrothermal stability in interconnect metal during ESD pulses

A feedback model of on-chip interconnect metal heating during electrostatic discharge (ESD) pulses predicts a temperature waveform and its stability given a heat source function and a thermoelectric circuit model or thermal impulse response Z(t). The pulse delivery circuit influences those conditions along with materials and layout. Z(t) can be extracted from pre-silicon modeling (e.g., finite element) or from post-silicon transmission line pulse (TLP) response, then applied to any ESD pulse conditions. For metal lines embedded in a patterned matrix of inactive metal lines at adjoining levels, pulses produce temperatures converging to a constant value, so the related time constants allow thermal impedance Z(t) to be deduced and thermal properties of the materials checked.