Atomic Scale Modeling and Simulation of Silicon Anisotropic Etching
N. Moldovan
A well-known process in microelectromechanical systems (MEMS) technology involves
etching silicon in alkaline solutions, which produces accurate 3-D silicon structures,
sometimes with atomic smoothness, by taking advantage of the strong dependence
of the etching rate on crystal orientation. Significant experimental effort has
been made to characterize this anisotropy (polar etching rate diagrams, temperature
dependencies, roughness measurements, in situ STM records during etching, electrochemistry
studies etc.). The experimental results were used in complex simulations that
successfully predicted the evolution of the 3-D geometry, starting from the experimentally
measured etching diagrams.
However, until recently, there was only a poor understanding of the causes
of the variation in etching rate with crystal orientation. Recently, two types
of atomic-scale simulations were performed: atom-by-atom removal algorithms and
bond-breaking algorithms. The latter produced simulated etching diagrams that
are very similar to the experimental ones, assuming that the local interatomic
Si-Si bond strength depends on the presence and type of second-order neighbor
atoms. This is especially important at the crystal surface. The theory permits
a genuine parameterization for describing etching behavior and presents a nice
example of explaining macroscopic properties of matter starting from atomic level
properties.
Experimental polar etching diagram for Si in KOH solution (hk0) family of planes |
Simulation with the bond-breaking algorithm of the polar etching diagram for the
(hk0) family of planes at different temperatures of the solution. The temperature
increases from the center (58°C) toward the outside (70°C, 80°C, 95°C).
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Simulated polar etching diagrams for a specific point in the parameter space,
for the (hk0) planes (left) and (hkk) planes (right). Bond-breaking algorithm. |
January 23, 2002
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