Power-Law Degradation and Lifetime Interpretation in Microelectronics Reliability

Reliability degradation in semiconductor devices originates from microscopic stochastic processes such as defect motion, diffusion, bond rearrangement, and charge trapping occurring under electrical and thermal stress. Experimental degradation measurements, however, often exhibit smooth empirical scaling behavior, particularly power-law time dependences extending across many orders of magnitude in time. This tutorial reviews the thermodynamic and kinetic foundations underlying these observations and explains how empirical power-law degradation behavior can emerge from the collective interaction of many microscopic stochastic processes. The discussion begins with irreversible thermodynamics, random walk transport, diffusion, and Arrhenius kinetics and then connects these microscopic concepts to the macroscopic degradation trends commonly observed in semiconductor reliability experiments. Attention is given to the interpretation of stress-dependent power-law degradation kinetics and their implications for accelerated lifetime extrapolation. Practical limitations associated with conventional logarithmic degradation analysis are examined, including baseline sensitivity, logarithmic instability near the measurement floor, and systematic curvature that may remain hidden despite high goodness-of-fit metrics. Methods based on transformed-coordinate linearization and curvature-sensitive extraction are discussed together with their implications for time-to-failure extrapolation and activation-energy interpretation. Experimental studies of phenomena such as bias temperature instability frequently show degradation behavior in which the time exponent depends systematically on voltage and temperature stress conditions. Under such conditions, the reciprocal exponent m=1/n can significantly amplify stress acceleration during lifetime extrapolation. This work provides a conceptual framework connecting microscopic stochastic degradation physics with the empirical methods commonly used in practical semiconductor reliability analysis and long-term lifetime prediction.