Total concentration approach for three-dimensional diffusion-controlled wet chemical etching

2006 ◽  
Vol 49 (19-20) ◽  
pp. 3408-3416 ◽  
Author(s):  
P. Rath ◽  
J.C. Chai ◽  
H. Zheng ◽  
Y.C. Lam ◽  
V.M. Murukeshan
Keyword(s):  
Chemical Etching ◽  
Total Concentration ◽  
Three Dimensional ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Wet Chemical ◽  
Wet Chemical Etching

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

2005 ◽  
Author(s):  
P. Rath ◽  
J. C. Chai ◽  
H. Y. Zheng ◽  
Y. C. Lam ◽  
V. M. Murukeshan
Keyword(s):  
Chemical Etching ◽  
Total Concentration ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Concentration Method ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Grid Approach ◽  
Wet Chemical ◽  
Wet Chemical Etching

This article presents a total concentration method for two-dimensional wet chemical etching. The proposed procedure is a fixed-grid approach. It is analogous to the enthalpy method used for modeling melting/solidification problems. The governing equation is formulated using the total concentration of the etchant. It includes the reacted and the unreacted concentrations of the etchant. The proposed governing equation includes the interface condition. The reacted concentration is used to capture the etchant-substrate interface implicitly. Since the grids are fixed, a diffusion problem remains a diffusion problem unlike the moving grid approach where the diffusion problem becomes the convection-diffusion problem due to the mesh velocity. For demonstration purposes, the finite volume method is used to solve for the transient concentration distribution of etchant. In this article, two-dimensional diffusion-controlled wet chemical etching processes are modeled. The results obtained from the proposed total concentration method are compared with available “analytic” solutions and solutions from moving-grid approach.

scholarly journals Three-dimensional structuring of sapphire by sequential He + ion-beam implantation and wet chemical etching

2003 ◽  
Vol 76 (7) ◽  
pp. 1109-1112 ◽  
Author(s):  
A. Crunteanu ◽  
G. Jänchen ◽  
P. Hoffmann ◽  
M. Pollnau ◽  
C. Buchal ◽  
...  
Keyword(s):  
Chemical Etching ◽  
Ion Beam ◽  
Three Dimensional ◽  
Ion Beam Implantation ◽  
Wet Chemical ◽  
Wet Chemical Etching

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

2006 ◽  
Vol 129 (4) ◽  
pp. 509-516 ◽  
Author(s):  
P. Rath ◽  
J. C. Chai ◽  
Y. C. Lam ◽  
V. M. Murukeshan ◽  
H. Zheng
Keyword(s):  
Governing Equation ◽  
Chemical Etching ◽  
Total Concentration ◽  
Grid Method ◽  
Interface Condition ◽  
Two Dimensional ◽  
Fixed Grid ◽  
Concentration Method ◽  
Wet Chemical ◽  
Wet Chemical Etching

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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