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

C.C. McAndrew and P.G. Drennan
Freescale Semiconductor, US

Keywords:
statistical modeling, SPICE modeling, device correlations

Abstract:
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 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,
that nevertheless completely encompasses statistical correlations between different device types.
The key then is how these underlying parameters, which are not directly observable,
can be characterized from measurements. We show that by identifying suitable ratios
and/or differences of electrical measurements between device types, that “hidden” physical parameters,
not observable from direct measurements of a single type of device or electrical performance,
can statistically be effectively and easily characterized. We show that the technique gives error free
values for the variances of correlated parameters, and allows oxide thickness variation to be characterized
from simple DC measurements. As far as we aware, this is the first non-tunneling approach that
allows oxide thickness variations to be determined from DC only measurements.

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