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Chapter 1:
Appendix A: Coherence
Author(s): Harry J. Levinson
Published: 2011
DOI: 10.1117/3.865363.ap1

Coherence refers to the degree that light waves are correlated. Coherence has been the subject of entire books on optics, or at least lengthy chapters. A few essential elements are summarized in this Appendix. There are two types of coherence-temporal coherence and spatial coherence, both of which are relevant to lithography.

Temporal coherence refers to the correlation of light in time. There are several situations in lithography where temporal coherence is relevant. Consider the situation depicted in Fig. A.1. A beam of light is incident on a resist-coated silicon surface. Consider, for the moment, very transparent resist. The instantaneous amplitude of the incident wave at x is given by A(t). The amplitude of the reflected light is given by the amplitude of the light after the time it has propagated to the interface and reflected:


where ρ is the reflectivity of the resist-silicon interface, c is the speed of light, and n is the index of refraction of the resist.

The time-averaged intensity at point x is given by:


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Spatial coherence

Temporal coherence


Lithographic illumination


Excimer lasers

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