Advances in manufacturing process technology are key ensembles for the production of integrated circuits in the sub-micrometer region. It is of paramount importance to assess the effects of tolerances in the manufacturing process on the performance of modern integrated circuits. The polynomial chaos expansion has emerged as a suitable alternative to standard Monte Carlo-based methods that are accurate, but computationally cumbersome. This paper provides an overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems.

We present an analysis of the propagation of measurement uncertainty in microwave transistor nonlinear models. As a case study, we focus on residual calibration uncertainty and its effect on modeled nonlinear capacitances extracted from small-signal microwave measurements. We evaluate the uncertainty by means of the polynomial chaos expansion (PCE) method and compare the results with the NIST Microwave Uncertainty Framework, which enables both sensitivity and Monte Carlo (MC) analyses for uncertainty quantification in microwave measurements. We demonstrate that, for the considered application, PCE provides results in agreement with classical MC simulations but with a significant reduction of the computational effort.

We present a novel technique to perform the model-order reduction (MOR) of multiport systems under the effect of statistical variability of geometrical or electrical parameters. The proposed approach combines a deterministic MOR phase with the use of the Polynomial Chaos (PC) expansion to perform the variability analysis of the system under study very efficiently. The combination of MOR and PC techniques generates a final reduced-order model able to accurately perform stochastic computations and variability analysis. The novel proposed method guarantees a high-degree of flexibility, since different MOR schemes can be used and different types of modern electrical systems (e.g., filters and connectors) can be modeled. The accuracy and efficiency of the proposed approach is verified by means of two numerical examples and compared with other existing variability analysis techniques.

Evaluating the robustness of integrated circuits (ICs) against noise and disturbances is of crucial importance in signal integrity (SI) applications. In this work, the addressed challenge is to build a software-based framework allowing for automated detection of failures and fast simulation-based evaluation of designs. In particular, these tasks are here addressed using Anomaly Detection (AD), a branch of Machine Learning (ML) techniques focused on identifying erroneous or deviant data. In the proposed framework, the machine learning model only requires the time-domain waveforms and no additional knowledge about the circuit nor about the errors to be identified. Specifically, a two-step approach to detect anomalous behaviors in output waveforms of digital ICs is proposed, comprising a first phase where machine learning models are trained to learn relevant features describing the data and a second one where those features are used to identify anomalies with unsupervised or semi-supervised anomaly detection techniques. Two relevant application examples validate the performance and flexibility of the proposed method.