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

Abstract

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. I. INTRODUCTIONEstimation of the effects of process variations on device performance has long been a concern. The computational complexity of current simulators precludes incorporation of process variations to device performance. This can be attributed to the lack of accurate methods and models for process variations. Designers have been trying to cope with this absence through worstcase analysis, Monte Carlo techniques or through the invocation of Gaussian distribution assumptions. But these approaches can no longer be counted upon to provide sufficiently accurate and fast results, as deep sub-micron silicon technologies rapidly push manufacturers to device parameter characterizations of increased accuracy in order to obviate the increasing number of design iterations.The effects of process variations on device parameters further indicate that the relationships between factors causing process variations and device parameters are deviating from a linear approximation even for a small input domain. This implies that the Gaussian distribution assumption attributed to device performance parameters is no longer accurate. Therefore, a more accurate methodology is necessary to estimate the effects of mismatch on high-level parameters.The paper presents a methodology to deterministically estimate the results of process variations on device parameters

Statistical Compact Modeling and Si Verification Methodology

“…If this is not possible or too costly, for example for circuit timing simulations, then the models should incorporate the variations in the physical parameters. At this step, the physical parameters, such as width and height, will likely be correlated, and hence necessary computational methods such as principal component analysis [9] or alternatives [10] should be implemented in order to reduce or eliminate the inaccuracies caused by correlation between parameters.…”

Monte Carlo-Alternative Probabilistic Simulations for Analog Systems

“…Besides these, almost all designers count on Monte Carlo methods for probabilistic simulations. We have introduced a computationally expensive hierarchical version of the proposed method for probabilistic device simulations in [31].…”

Early, Accurate and Fast Yield Estimation through Monte Carlo-Alternative Probabilistic Behavioral Analog System Simulations

“…An accurate yet computationally expensive hierarchical version of the proposed method has been introduced for probabilistic device simulation [31] and preliminary algorithms for analog systems were presented as a poster at [29]. In this paper, we introduce new algorithms for blackbox type of system simulations suitable for very fast analog behavioral simulations specialized in accurate density and yield estimation.…”