Emergent faces in crystal etching

Author

Hubbard, Ted J. ; Antonsson, Erik K.

Author_Institution

Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA

Volume

3

Issue

1

fYear

1994

fDate

3/1/1994 12:00:00 AM

Firstpage

19

Lastpage

28

Abstract

The time development of emergent faces in crystal etching is investigated. We present and discuss a novel computational approach, based on an intuitive geometrical derivation, for predicting an etched shape given an initial polygonal (mask) shape and a diagram of etch rate as a function of orientation. A two-dimensional geometric model is derived which determines the etched shape as a function of time. The model is both intuitive and easy to implement manually or by computer. Because the model is intuitive in nature, some results can be obtained from only partial information. In addition, the model is a first step in the transition from analysis to design. Rather than predicting the etched shape for a given original shape, often what is desired is the original mask shape needed to produce a particular etched shape. This inversion process is carried out for some special cases. The concepts of equilibrium or eigen shapes (Eshapes), limit shapes, and time scaling are introduced. Model predictions are compared with experimental results. The extension from two dimensions to three is also introduced

Keywords

eigenvalues and eigenfunctions; etching; micromechanical devices; semiconductor device models; semiconductor process modelling; semiconductor technology; Eshapes; MEMS design; MEMS fabrication; computational approach; crystal etching; eigen shapes; emergent faces; equilibrium; etch rate; etched shape; geometric model; initial polygonal mask shape; intuitive geometrical derivation; limit shapes; microelctromechanical systems; micromechanicalelctrical systems; orientation; original mask shape; partial information; time development; time scaling; Anisotropic magnetoresistance; Crystallization; Design engineering; Design methodology; Etching; Fabrication; Micromechanical devices; Shape; Silicon; Very large scale integration;

fLanguage

English

Journal_Title

Microelectromechanical Systems, Journal of

Publisher

ieee

ISSN

1057-7157

Type

jour

DOI

10.1109/84.285721

Filename

285721