Unifying Field and Temperature Acceleration in Semiconductor Device Reliability Through Entropic Kinetics.

Abstract

Time-dependent dielectric breakdown (TDDB) is an important failure mechanism that affects semiconductor device reliability. The degradation lifetime depends strongly on both electric field and temperature, yet these dependencies are commonly treated using separate empirical acceleration factors. This work develops a thermodynamic description in which electrical stress changes the accessible microscopic states of the dielectric and therefore contributes an entropic term to the Gibbs free energy. The resulting formulation separates the field-independent activation barrier, Ea, from a field-dependent entropic contribution characterized by α. This relation predicts a linear decrease in apparent activation energy with the logarithm of the electric field. Published TDDB data for SiO₂, high-k, low-k, and Cu/low-k dielectric systems exhibit this behavior. Independent temperature- and field-dependent measurements from the same source yield a common entropic field-energy scale of approximately 1.2 eV. A one-second reference field, E1sec, provides a physical time anchor that allows field and temperature acceleration to be compared without assuming a common pre-exponential factor across temperatures. For an absolute time temperature series, independently extracted values of α vary by 11.9% across three temperatures, while a fixed α produces a normalized relation with R² ≈ 0.97. The parameters Ea, α, and E1sec provide a compact thermodynamic representation of field- and temperature-dependent TDDB kinetics across the datasets examined here.