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INTRODUCTION TO ISOTROPIC/ANISOTROPIC ETCHING:
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One common MEMS (Micro-Electro Mechanical Systems) fabrication technique
is the anisotropic etching of crystalline silicon, where etch rate is a 
function of orientation. The fundamental problem studied here is how to 
model the shape transformations from initial mask to final output shape. 

CRYSTAL PLANES:
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In isotropic etching all orientations or planes etch at the same rate,
shapes evolve in a relatively simple fashion. For example a square hole 
would get rounded corners in isotropic etching.

Anisotropic etchants have different rates for different orientations.
For example, common anisotropic silicon etchants have very slow rates at 0,
90, 180, and 360 degrees, while the planes at 45 degree intervals are an
order of magnitude faster. This difference in rate can drastically change
the evolving shape.

The demo directory has a few sample rate files: iso.rate, aniso.rate, etc.

CORNERS:
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Because of the differences in rates, some planes grow, while others
disappear. There are two main classifications that describe how the
initial mask shape will evolve into the final etched shape:

Firstly, etched shapes may be classified as either pegs or holes.
Holes are lower than the surface of the wafer and pegs are higher than the 
wafer. Holes enlarge with time while pegs shrink. After long times, holes 
are dominated by slow planes, while pegs become dominated by fast planes.

Secondly, within a shape (be it a peg or a hole), there can be two types 
of corners: convex (peg-like) and concave (hole-like). For example, an 'L'
shaped hole has five concave corners and one convex corners.
While etching convex corners fast planes dominate: fast planes increase
in length while slow planes decrease in length. For concave
corners, slow planes dominate.

Rules of thumb:

  Isotropic: holes are rounded off; pegs stay sharp

  Silicon: holes get squared off; pegs become faceted

  Anisotropic: holes have symmetry of minimum rates;
               pegs have symmetry of maximum rates