Device Correlation: Modeling using Uncorrelated Parameters, Characterization Using Ratios and Differences

摘要

Partial correlations between parameters of different types of devices, such as effective channel length for PMOS and NMOS devices, are often modeled and simulated statistically via correlation coefficients. However, this is cumbersome and inefficient from a modeling perspective, from a characterization perspective, and from a simulation perspective. We have found that, with physical understanding, it is possible to formulate models with a combination of parameters that are common to, and completely correlated between, different types of devices and parameters that are unique to, and completely independent between, different types of devices. This gives a modeling basis of independent statistical parameters, which is ideal for simple statistical simulation, yet completely encompasses statistical correlations between different device types. The key then is how these underlying parameters, which are not directly observable from measurements of a single type of device or electrical performance, can be characterized. We show that by identifying ratios or differences of electrical measurements between device types these "hidden" physical parameters can be easily characterized statistically. We also show that the technique gives error free values for the variances of the correlated parameters, and allows oxide thickness variation to be characterized from simple DC measurements.