A research group from Kyoto University led by Mahfuzul Islam developed a novel statistical parameter extraction technique that will help LSI (Large Scale Integration) circuit designers to accurately predict their chip performances.

Kensuke Murakami, Mahfuzul Islam, and Hidetoshi Onodera, “CDF Distance Based Statistical Parameter Extraction Using Nonlinear Delay Variation Models,” in 27th IEEE International Symposium on On-Line Testing and Robust System Design (IOLTS), June 2021.

Statistical parameter extraction is a technique to estimate the distributions of underlying physical parameters from a set of distributions of the observed parameters. For example, in the case of a MOS (Metal Oxide Semiconductor) transistor, the observable parameter is its drain current. However, the drain current of a MOS transistor is determined by many physical parameters such as the channel doping density, gate length, oxide thickness, work functions, and so on. The problem is that these parameters are statistical and thus the chip performance also becomes statistical. Estimation of chip’s performance, therefore, refer to estimating the distribution of the chip performance and calculating the worst-case value under certain probability. Thus, it is essential to have accurate statistical models of the physical parameters and simulate the circuit with the accurate models.

Estimation of the distributions of the physical parameters is challenging simply because we cannot measure them directly. We have to calculate their distributions from the distributions of the observable parameters, for example the current or frequency. State-of-the-art extraction techniques, that are often based on simple linear models, worked well under limited scenarios. These techniques also assume that the physical parameters follow normal distributions. However, with the advancement of CMOS technology, we encounter with new phenomena of noise and variation that the assumption of normal distribution does not hold anymore. As a result, there was a need for a new technique that can work with any distributions as well as with nonlinear models. This paper utilizes the concept of comparing two distributions using CDF (Cumulative Distribution Function) distance. We have defined a new CDF distance concept to help converge the extraction process quickly. The work is still ongoing. In the future, we expect the presented technique to be incorporated into the commercial simulation tools.