### Abstract

Guidelines are given for the development of computer programs for the numerical simulation of semiconductor devices. For this purpose, the basic mathematical results on the corresponding elliptic boundary value problem are reviewed. Particularly, existence, smoothness, and structure of the solutions of the fundamental semiconductor equations are discussed. Various feasible approaches to the numerical solution of the semiconductor equations are described. Much emphasis is placed on constructive remarks to help authors of device simulation programs make decisions on their code design problems. Thus criteria for an optimal mesh generation strategy are given. The iterative solution of the systems of nonlinear and linear equations obtained by discretizing the semiconductor equations is discussed. An example shows the power of these concepts combined with modern numerical methods in comparison to classical approaches.

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

Pages (from-to) | 52-64 |

Number of pages | 13 |

Journal | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |

Volume | CAD-3 |

Issue number | 1 |

State | Published - Jan 1984 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Hardware and Architecture
- Electrical and Electronic Engineering

### Cite this

**IMPLICATIONS OF ANALYTICAL INVESTIGATIONS ABOUT THE SEMICONDUCTOR EQUATIONS ON DEVICE MODELING PROGRAMS.** / Selberherr, Siegfried; Ringhofer, Christian.

Research output: Contribution to journal › Article

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*, vol. CAD-3, no. 1, pp. 52-64.

}

TY - JOUR

T1 - IMPLICATIONS OF ANALYTICAL INVESTIGATIONS ABOUT THE SEMICONDUCTOR EQUATIONS ON DEVICE MODELING PROGRAMS.

AU - Selberherr, Siegfried

AU - Ringhofer, Christian

PY - 1984/1

Y1 - 1984/1

N2 - Guidelines are given for the development of computer programs for the numerical simulation of semiconductor devices. For this purpose, the basic mathematical results on the corresponding elliptic boundary value problem are reviewed. Particularly, existence, smoothness, and structure of the solutions of the fundamental semiconductor equations are discussed. Various feasible approaches to the numerical solution of the semiconductor equations are described. Much emphasis is placed on constructive remarks to help authors of device simulation programs make decisions on their code design problems. Thus criteria for an optimal mesh generation strategy are given. The iterative solution of the systems of nonlinear and linear equations obtained by discretizing the semiconductor equations is discussed. An example shows the power of these concepts combined with modern numerical methods in comparison to classical approaches.

AB - Guidelines are given for the development of computer programs for the numerical simulation of semiconductor devices. For this purpose, the basic mathematical results on the corresponding elliptic boundary value problem are reviewed. Particularly, existence, smoothness, and structure of the solutions of the fundamental semiconductor equations are discussed. Various feasible approaches to the numerical solution of the semiconductor equations are described. Much emphasis is placed on constructive remarks to help authors of device simulation programs make decisions on their code design problems. Thus criteria for an optimal mesh generation strategy are given. The iterative solution of the systems of nonlinear and linear equations obtained by discretizing the semiconductor equations is discussed. An example shows the power of these concepts combined with modern numerical methods in comparison to classical approaches.

UR - http://www.scopus.com/inward/record.url?scp=0021197433&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021197433&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0021197433

VL - CAD-3

SP - 52

EP - 64

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 1

ER -