Numerical analysis of a SWEAT structure with an improved one dimensional nonlinear model

Abstract

An improved one dimensional (1 − D) nonlinear model of the thermal response of the Standard Wafer-level Electromigration Accelerated Test (SWEAT) structure is described. The major improvement in this model are accurate predictions of the critical current density j o ; according to older models j o is inversely proportional to the “power” I 2R/R(T s) , while our model shows a different (increasing) trend and is confirmed by measurements. The ratio of the maximum temperature increase to the average temperature increase (γ) for the investigated structure depends on the relative change of the resistance and normalized current A 0 1 2 = I/I no , and can be calculated within 1% from basic material and structure parameters. The model includes the edge correction factor α depending on the geometry of the structure (W n/t i) , material parameters and stress current I. Using the corrected values for the edge correction factor, the maximum temperature increase in the SWEAT test structure can be calculated within less than 5°C.