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Bias temperature instability (BTI) is a serious reliability concern for MOS transistors. This paper covers theoretical analysis, Monte Carlo simulation, and experimental investigation of the charge trapping component of BTI. An analytical model for both stress and recovery phases of BTI is presented. Furthermore, the model properly describes device behavior under periodic switching, also called AC-BTI or cyclostationary operation. The model is based on microscopic device physics parameters, which are shown to cause statistical variation in transistor BTI behavior. It is shown that a universal logarithmic law describes the time dependence of charge trapping in both stress and recovery phases, and that the time dependence may be separated from the temperature and bias point dependence. Analytical equations for the statistical parameters are provided. The model is compared with experimental data and Monte Carlo simulation results.