Forward discrete probability propagation method for device performance characterization under process variations

Process variations are becoming influential at the device level in deep sub-micron and sub-wavelength design regimes, whereas they used to be a few generations away only influential at circuit level. Process variations cause device performance parameters, such as current or output resistance, to acquire a probability distribution. Estimation of these distributions has been accomplished using Monte Carlo techniques so far. The large number of samples needed by Monte Carlo methods adversely affects the possibility of integrating probabilistic device performance at the circuit level due to run-time inefficiency. In this paper, we introduce a novel technique called forward discrete probability propagation (FDPP). This method discretizes the probability distributions and effectively propagates these probabilities across a device formula hierarchy, such as the one present in the SPICE3v3 model. Consequently, probability distributions for process parameters are propagated to the device level. It is shown in the paper that with far fewer number of samples, comparable accuracy to a Monte Carlo method is achieved.