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Chapter 6:
Scattering Models for Discrete Surface Features
Author(s): John C. Stover
Published: 2012
DOI: 10.1117/3.975276.ch6

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. - Albert Einstein

The ability to accurately model scatter from discrete surface features has huge advantages over having to actually take the measurements. Beyond the problems associated with building (or buying) a scatterometer (see Chapter 7) and using it to measure defect scatter in the presence of surface scatter (see Section 7.7), there is the issue of sample preparation. How do you determine that your sample really is, for example, a 95-nm spherical silicon particle and not something else that has ended up on the sample substrate? Or, if it is silicon - is it spherical? Or, maybe it is not a particle at all but a surface pit, and the particle of interest is another 100 μm to the left. What if you want to determine the relative effects of variations in particle index on variations in surface index - how would you prepare those samples? Modeling is obviously the practical solution to answer questions like these - if you can get a confirmed model.

Because scatter models of localized surface features are calculation intensive (and often privately owned), there is no attempt here to derive or even give equations - that is handled in the literature. Instead, this chapter reviews a couple of approaches that have been used to create models for particle scanners used in the semiconductor industry, discusses model confirmation, and gives some example results. A source of publicly available code is also given. Confirmation techniques are discussed in Section 7.7.

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Spherical lenses

Mathematical modeling

Semiconducting wafers


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