A Thermodynamic Framework for Reliability Kinetics

Empirical power-law relationships are widely used in reliability physics to describe degradation kinetics and predict lifetime. Such behavior appears across diverse failure mechanisms, including time-dependent dielectric breakdown (TDDB), hot-carrier injection (HCI), bias temperature instability (BTI), electromigration (EM), and fatigue. In this work, a thermodynamic framework for reliability kinetics is developed from Gibbs free energy and entropy partitioning, leading to a generalized kinetic equation that incorporates thermal activation, stress acceleration, and accumulated degradation. The formulation introduces two parameters: a stress coefficient, γ, which describes the influence of externally applied stress, and a correlation coefficient, χ, which describes how accumulated degradation influences subsequent degradation. Negative values of χ correspond to self-limiting evolution, positive values correspond to self-amplifying evolution, and χ=0 represents statistically independent accumulation. Representative reliability mechanisms are interpreted within this framework, with TDDB approaching independent evolution, HCI exhibiting weak self-limiting behavior, BTI showing strong self-limiting behavior, and fatigue exhibiting self-amplifying behavior. Electromigration illustrates the complementary role of stress acceleration through γ. The proposed framework provides a common thermodynamic interpretation of empirical power-law degradation kinetics and introduces degradation correlation as a complementary descriptor for reliability modeling and lifetime prediction.