Spring06 web article1

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Predicting Line Edge Roughness through a Mechanistic Model Mark D. Smith, KLA-Tencor Corporation

As feature sizes continue shrinking, yield-limiting phenomena stemming from the molecular nature of photoresist materials—such as line-edge roughness (LER)—have become evident. This article presents a model that explicitly takes into account the molecular nature of the photoresist during the exposure and post-exposure bake (PEB) processes. A master equation was written that first describes the probability that acid molecules are generated during exposure, and then describes the evolution of the acid, quencher, and blocking-group probability distributions during the bake process. The article also shows how all of the parameters in this model can be derived from the parameters in a calibrated PROLITH continuum model, and used for prediction of LER.

Introduction

LER has received much attention in the literature. Many correlations between process parameters and LER have been investigated experimentally, and two observations seem to shed the most light on the origins of LER. First, the amount of LER is inversely proportional to the square root of the exposure dose. Statistical mechanics tells us that fluctuations are proportional to the square root of the average number of particles. This type of dependence on the dose implies that shot noise leads to a random distribution of acid during the exposure process, and that this propagates through the resist processing to ultimately create LER. The second important observation is that LER is strongly correlated with metrics of image quality, such as aerial image contrast or NILS. For example, both Michaelson1,2 and Nikolsky3 published experimental results for LER that correlated LER with the predicted concentration gradients at the end of PEB. Nikolsky used the concentration gradients predicted by PROLITH simulations, while Michaelson used an aerial image model combined with a model for exposure

and the PEB process. This approach allowed Michaelson to reduce a very large set of LER experiments onto a single curve. The picture of LER that arises from these observations is that while shot noise leads to a random dose distribution, the consequences of this randomness can be mitigated by high contrast images, which are less sensitive to random fluctuations. Michaelson’s papers (and others) also attempt to characterize how the formulation of the photoresist impacts LER. The most dramatic trend is that LER decreases with quencher loading, with LER being especially excessive for resist formulations with no quencher. One possible explanation for this is that increased quencher loading increases the required dose, which would generate a relatively lower amount of fluctuations due to shot noise. However, Michaelson found that LER correlated only with the concentration gradients at the end of PEB – all of the different quencher loadings fell on the same LER versus gradient curve, without an explicit dependence on dose. Several theoretical models for LER have also been proposed. The paper by Gallatin4 is especially outstanding because it explains many of the observed trends. One shortcoming of the model is that it did not include quencher loading. This is the main outstanding issue addressed in this investigation. Spring 2006

www.kla-tencor.com/magazine

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