Analytical parameter extraction for NBTI reaction diffusion and trapping/detrapping models

Accurate parameters of negative bias temperature instability (NBTI) model are essential to predict the circuit lifetime during circuit design. This paper presents the extraction methods of NBTI model parameters for the NBTI reaction-diffusion (R-D) and trapping/detrapping (T/D) models. The R-D model parameters extraction mainly includes two steps: linear approximation and optimized extraction. In the first step, the term of ΔVth1/2n is described as approximately linear with t0.5 after the coordinate system conversion, where ΔVth is the degradation in threshold voltage and t is elapsing time. Then, the model parameters can be roughly calculated. In the second, an objective function of the genetic algorithm (GA) has been built up and its constraints can be determined by referring the values gotten from the first step. After solving the function, a set of accurate parameters of the NBTI model can be achieved. Similarly, the T/D model parameters extraction involves the curves fitting and further optimization based on the GA. Both the R-D and T-D extraction methods have been validated using a 40-nm CMOS process, and it is easy to implement the extraction procedures in a program extractor.