**Physical Effects/Overview of Mechanism:**-
Under photolithography, a pattern mask is placed on a silicon wafer, and
exposed to light. The aerial image determines the cross-linking bond
strength at various spots. This yields an etch rate as a function of
position, Under the final step, known as photolithography development, the
material is etched away, thus the speed function F which gives the
speed of the interface in its normal direction is purely a function of
position.

**Fast Marching Methodology:**-
In this case, we may use the
fast marching method, which
provides for an extremely fast solution of the Eikonal equation.

**Sample Simulations:**-

In the figure on the left, we use a model Gaussian function which is radially symmetric of the form

exp(-64.0*((x-0.5)*(x-0.5)+(y-0.5)*(y-0.5)))*cos(12.0*z)

In the figure on the right, we use a masking pattern given in the figure, using an I-line stepper, numerical aperture 0.6. The rate function is calculated using the three-dimensional exposure and post-exposure bake modules of TMA's Depict 4.0, and this is coupled to our fast marching level set method.

(72K) (286K) Evolution of single contact hole Evolution under mask pattern Model Gaussian rate function Rate calculated using TMA's Depict

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