Statistical Modeling with the Virtual Source MOSFET Model

A statistical extension of the ultra-compact Virtual Source (VS) MOSFET model is developed here for the first time. The characterization uses a statistical extraction technique based on the backward propagation of variance (BPV) with variability parameters derived directly from the nominal VS model. The resulting statistical VS model is extensively validated using Monte Carlo simulations, and the statistical distributions of several figures of merit for logic and memory cells are compared with those of a BSIM model from a 40-nm CMOS industrial design kit. The comparisons show almost identical distributions with distinct run time advantages for the statistical VS model. Additional simulations show that the statistical VS model accurately captures non-Gaussian features that are important for low-power designs.Masdar Institute of Science and Technolog

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System

Statistical library characterization using belief propagation across multiple technology nodes

In this paper, we propose a novel flow to enable computationally efficient statistical characterization of delay and slew in standard cell libraries. The distinguishing feature of the proposed method is the usage of a limited combination of output capacitance, input slew rate and supply voltage for the extraction of statistical timing metrics of an individual logic gate. The efficiency of the proposed flow stems from the introduction of a novel, ultra-compact, nonlinear, analytical timing model, having only four universal regression parameters. This novel model facilitates the use of maximum-a-posteriori belief propagation to learn the prior parameter distribution for the parameters of the target technology from past characterizations of library cells belonging to various other technologies, including older ones. The framework then utilises Bayesian inference to extract the new timing model parameters using an ultra-small set of additional timing measurements from the target technology. The proposed method is validated and benchmarked on several production-level cell libraries including a state-of-the-art 14-nm technology node and a variation-aware, compact transistor model. For the same accuracy as the conventional lookup-table approach, this new method achieves at least 15x reduction in simulation runs.Masdar Institute of Science and Technology (Massachusetts Institute of Technology Cooperative Agreement