Advanced CAD System for Electromagnetic MEMS Interactive Analysis

The level set equation of evolution is:
Φt + V |∇Φ| = 0
where: Φ = scalar function implicitly representing interface (locus where Φ=0)
V = velocity function normal to the propagating interface incorporating
physics of deposition/etching
In this example we utilize the level set kernel inside of Geodesic (detailed in [32]) with two
velocity functions to simulate wet etching and conformal deposition. In the case of conformal
deposition, we assume a constant normal velocity v = 1.0. In the case of etching we assume a
velocity function which simulates selective isotropic etching.
Inside of Geodesic, the setup required to simulate conformal deposition and isotropic selective
etching is very similar. In the case of deposition, we track the top surface of the device using the
scalar field Φ. In etching, on the other hand, we actually track the boundary of the “air” region
surrounding the device (i.e. the scalar field Φ implicitly represents the surface of the air region).
The reasoning behind the difference is simple. We are only using the zero level set (Φ = 0) to
define a material interface, so we can represent only one material with Φ. Since we want the
ability to do selective etches on multiple materials, we represent the boundary of the “air” region.
In the case of isotropic wet etching, this can be thought of physically as tracking the surface of
the etchant.
The following pseudo code highlights the important aspects of performing process simulation
inside of Geodesic using the level set kernel (the actual scripts are included in the examples with
the software distribution):
# define the desired deposition thickness / etch depth
thickness = 1.0
# create a solid with a raised center block in the center
solid_box3d -result box1 -dims {…} -ctr {…}
solid_box3d -result box2 -dims {…} -ctr {…}
solid_union -result input_geom -a box1 -b box2
# create air region
solid_box3d -result tmpair -dims {…} -ctr {…}
solid_subtract -result air -a tmpair -b input_geom
# Set up grid domain
h = {0.500 0.500 0.500}
origin = … (lower left hand corner of solution domain)
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