### Abstract

We consider a model for chemical vapor deposition, the process of adsorption of gas onto a surface together with the associated deposition of a chemical reactant on the surface. The surface has a microscopic structure which, in the context of semiconductor manufacturing, arises from a preprocessing of the semiconductor wafer. Using singular perturbation analysis, a boundary condition for the corresponding diffusion equation is derived, which allows for the replacement of the microstructured surface by a flat boundary. The asymptotic analysis is numerically verified with a simple test example.

Original language | English (US) |
---|---|

Pages (from-to) | 737-752 |

Number of pages | 16 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 58 |

Issue number | 3 |

State | Published - 1998 |

### Fingerprint

### Keywords

- Asymptotic analysis
- Chemically reacting flows
- Homogenization
- Mass transfer
- Microstructured surfaces
- Partial differential equations
- Singular perturbation
- Time-dependent initial-boundary value problem

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*58*(3), 737-752.

**An Asymptotic Analysis for A Model of Chemical Vapor Deposition on A Microstructured Surface.** / Gobbert, Matthias K.; Ringhofer, Christian.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 58, no. 3, pp. 737-752.

}

TY - JOUR

T1 - An Asymptotic Analysis for A Model of Chemical Vapor Deposition on A Microstructured Surface

AU - Gobbert, Matthias K.

AU - Ringhofer, Christian

PY - 1998

Y1 - 1998

N2 - We consider a model for chemical vapor deposition, the process of adsorption of gas onto a surface together with the associated deposition of a chemical reactant on the surface. The surface has a microscopic structure which, in the context of semiconductor manufacturing, arises from a preprocessing of the semiconductor wafer. Using singular perturbation analysis, a boundary condition for the corresponding diffusion equation is derived, which allows for the replacement of the microstructured surface by a flat boundary. The asymptotic analysis is numerically verified with a simple test example.

AB - We consider a model for chemical vapor deposition, the process of adsorption of gas onto a surface together with the associated deposition of a chemical reactant on the surface. The surface has a microscopic structure which, in the context of semiconductor manufacturing, arises from a preprocessing of the semiconductor wafer. Using singular perturbation analysis, a boundary condition for the corresponding diffusion equation is derived, which allows for the replacement of the microstructured surface by a flat boundary. The asymptotic analysis is numerically verified with a simple test example.

KW - Asymptotic analysis

KW - Chemically reacting flows

KW - Homogenization

KW - Mass transfer

KW - Microstructured surfaces

KW - Partial differential equations

KW - Singular perturbation

KW - Time-dependent initial-boundary value problem

UR - http://www.scopus.com/inward/record.url?scp=0032095623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032095623&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032095623

VL - 58

SP - 737

EP - 752

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -