Statistical Model of Line-Edge and Line-Width Roughness for Device Variability Analysis

The authors propose a model of line-edge and line-width roughness (LER and LWR) of actual device patterns, which received some smoothing steps, for accurate estimation of device variability. The model assumes that LER/LWR has originally an exponential autocorrelation function (ACF) and is smoothed using another exponential function. The power spectrum of this ACF almost completely fits the experimental one of polycrystalline silicon lines, which were formed using plasma etching. The authors investigate the effect of LER/LWR on the current factor of metal-oxide-semiconductor field-effect-transistors, comparing this to conventional models. The Gaussian ACF, which is widely used in device simulations, calculates the variation in the current factor with considerable accuracy as long as accurate LER/LWR statistics are used. However, it alone cannot provide the statistics. The exponential ACF underestimates the variation by a nonnegligible amount. From these results, the authors propose to use the aforementioned smoothed exponential ACF in the device simulations. They also alert to the possibility that a little-known long-range correlation exists universally in the LER/LWR even of the present-day devices and is causing an unexpectedly large mismatching between wide-channel devices.