A mathematical model for wet-chemical diffusion-controlled mask etching through a circular hole
- H.K. Kuiken
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Asymptotic solutions are presented for diffusion-controlled wet-chemical etching through a round hole in a mask. The three-dimensional diffusion field is assumed to be axisymmetric and fully developed. Two time regimes are considered. The first applies when the etched depth is small in comparison with the width of the mask opening. In the second, the depth of etching is much greater than the width of the mask opening. Explicit solutions are found for the shape of the etched surface as a function of the physical parameters. Among other things it is found that, as long as the etched pits are shallow, etching through small apertures is faster than through larger ones. The opposite is true for deep pits.
- D.M. Allen, The Principles and Practice of Photochemical Machining and Photoetching. Bristol: Hilger (1986) 190pp.
- P.H.L. Notten, J.A.E.M. van den Meerakker and J.J. Kelly, Etching of III-IV Semiconductors. Oxford: Elsevier Adv. Techn. (1991) 349pp.
- M.C. Elwenspoek and H. Jansen, Silicon Micromachining. Cambridge: CUP (1998) 405pp.
- H.K. Kuiken, Etching: a two-dimensional mathematical approach. Proc. R. Soc. London A392 (1984) 199–225.
- H.K. Kuiken, J.J. Kelly and P.H.L. Notten, Etching profiles at resist edges. I. Mathematical models for diffusion-controlled cases. J. Electrochem. Soc. 133 (1986) 1217–1226.
- P.H.L. Notten, J.J. Kelly and H.K. Kuiken, Etching profiles at resist edges. II. Experimental confirmation of models using GaAs. J. Electrochem. Soc. 133 (1986) 1226–1232.
- H.K. Kuiken, Etching through a slit. Proc. R. Soc. London A396 (1984) 95–117.
- C. Vuik and C. Cuvelier, Numerical solution of an etching problem. J. Comp. Phys. 59 (1985) 247–263.
- R.W. Tjerkstra, Isotropic Etching of Silicon in Fluoride Solutions as a Tool for Micromachining. Doctoral Thesis, University of Twente, The Netherlands (1999) 132 pp.
- P. Moon and D.E. Spencer, Field Theory Handbook, third corrected printing. Berlin: Springer (1988) 236pp.
- S.D. Howison and J.R. King, Explicit solutions to six free-boundary problems in fluid flow and diffusion. IMA J. Appl. Math. 42 (1989) 155–175.
- P. Ya. Polubarinova-Kochina, Theory of Groundwater Movement. Princeton: Princeton U. Press (1962) 613pp.
- J.J. Sudirham, Forthcoming PhD Thesis, U. Twente, Enschede, The Netherlands.
- A mathematical model for wet-chemical diffusion-controlled mask etching through a circular hole
Journal of Engineering Mathematics
Volume 45, Issue 1 , pp 75-90
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- oblate spheroidal coordinates
- Industry Sectors
- H.K. Kuiken (1)
- Author Affiliations
- 1. Faculty of Applied Mathematics, Twente University of Technology, P.O. Box 217, 7500 AE, Enschede, The Netherlands