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Optical Lithography

The simulation of optical lithography involves three steps, namely, Optical computations — calculation of intensity distribution in the resist and elsewhere; Exposure — modeling of changing composition of resist with exposure, and Development — rate of dissolution of resist depending on exposure state and solvent properties.

Optical Computations

The basic approach to calculate the optical intensity in a 2D system assumes separable expression, i.e.

where Iincident(x) is dependent on the imaging system, i.e. wavelength, source, mask and quality of lenses, etc. x-direction is along the surface, у is along the depth, and t is the time.

For /incident (x) calculation, there are several parameters of interest. One of the important parameter is the illumination wavelength к. The other important parameter is the numerical aperture of the objective lenses (NA0). NA is the measure of the ability of a lens to capture diffracted rays. Of course, the mask pattern is also playing a major role in determining the intensity distribution along with defocus denoted by 5. The final important parameter is the degree of coherence a. An incoherent source is a source of infinite dimension (a = to) and coherent source (a = 0) is a point source. A large value of sigma gives a smooth intensity distribution around an edge but has a poor intensity low in the opaque area. Low a typically has a large overshoot in open areas that dampens slowly and may give proximity effect problems. However, open area to adjacent opaque area intensity transition is quite sharp in low a case. Normal acceptable range for a is between 0.4 and 0.9.

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