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# Arrhenius Lifetime Acceleration of an Integrated Circuit

The Arrhenius equation predicts failure acceleration rate due to temperature increase. Although originally developed to describe chemical reactions due to temperature, it applies equally well to electronic assembly failure rates. The Arrhenius activation energy, ΔH, is all that is needed to calculate temperature-related acceleration.

Swedish chemist Svante Arrhenius provided a physical justification and interpretation for his observation back in 1899. His equation can be used to model the temperature-variance of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. A useful generalization borne out by the Arrhenius equation is that for many common chemical reactions at room temperature, the reaction rate doubles for every 10 °C increase in temperature.

Arrhenius Model for Integrated Circuits

 F = x1x2 = eα {Lifetime Acceleration Factor}
 Where: x1 = Failure rate at junction temperature T1x2 = Failure rate at junction temperature T2T = Junction temperature in degrees KΔH = Thermal activation energy in eVk = Boltzmann's constant    