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RESEARCH PAPERS: Processes Equipment and Devices

A Total Concentration Fixed-Grid Method for Two-Dimensional Wet Chemical Etching

[+] Author and Article Information
P. Rath

Department of Mechanical Engineering, National Institute of Technology, Rourkela, India 769008

J. C. Chai1

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singaporemckchai@ntu.edu.sg

Y. C. Lam, V. M. Murukeshan

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

H. Zheng

 Singapore Institute of Manufacturing Technology, Singapore 638075, Singapore

1

Corresponding author.

J. Heat Transfer 129(4), 509-516 (Oct 21, 2006) (8 pages) doi:10.1115/1.2709654 History: Received June 15, 2005; Revised October 21, 2006

A total concentration fixed-grid method is presented in this paper to model the two-dimensional wet chemical etching. Two limiting cases are discussed, namely—the diffusion-controlled etching and the reaction-controlled etching. A total concentration, which is the sum of the unreacted and the reacted etchant concentrations, is defined. Using this newly defined total concentration, the governing equation also contains the interface condition. A new update procedure for the reacted concentration is formulated. For demonstration, the finite-volume method is used to solve the governing equation with prescribed initial and boundary conditions. The effects of reaction rate at the etchant–substrate interface are examined. The results obtained using the total concentration method, are compared with available results from the literature.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the two-dimensional wet chemical etching problem

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Figure 2

Sketch for evaluation of normal concentration gradient at the interface

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Figure 3

Etching control volumes undergoing etching

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Figure 4

Grid-independent test for nondimensional etching parameter β=100 and Sh=1

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Figure 5

Comparison of etch profiles for: (a) reaction-controlled etching (Sh=1); and (b) diffusion-controlled etching (Sh=1000) with β=100

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Figure 6

Etchant concentration contours near the etchfront for β=100: (a) reaction-controlled etching (Sh=1); and (b) diffusion-controlled etching (Sh=1000)

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Figure 7

Comparison of two update procedures of reacted concentration (cR) for diffusion-controlled etching (Sh=1000) with β=10

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Figure 8

Evolution of etch profiles at different time levels for finite reaction at the interface with β=10

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Figure 9

Effect of reaction rate on etch profile shape

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Figure 10

Concentration contours at t*=20 for β=10: (a) contours for Sh=0.1; and (b) contours for Sh=1.0

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