- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- A two-dimensional finite element analysis of the stationary...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
A two-dimensional finite element analysis of the stationary semiconductor device equations Chavez, Patrick Pablo
Abstract
The ability to model the steady-state field inside active structures, such as a transistor, is an important aspect of monolithic microwave integrated circuit (MMIC) design. This paper focuses on such an active zone of semiconductor material, and presents a finite element analysis of the classical semiconductor equations. The semiconductor equations are very nonlinear and govern the potential and carrier density distributions in semiconductor materials. A previously developed finite element method (FEM) formulation of these equations, referred to as the current conservation model, is re-introduced and re-derived with compact matrix notation. It is shown how this formulation can be solved with the Newton-Raphson iterative scheme. Then, a newly developed FEM formulation, referred to as the advection-diffusion model, of the continuity equations is described in detail. It is shown by example how this formulation solved with Gummel's iterative technique is very numerically robust. These two different solution methods of the steady-state system of coupled Poisson and continuity equations are combined into a final solution algorithm that exploits their strengths. As a specific example, GaAs MESFETs are the focus of implementation, and the resulting potential field and carrier density distributions are used, to calculate various MESFET parameters such as electrode currents, voltage gain, capacitances, and conductances. Finally, various extensions to the FEM approach involving the application of the method of moments (MoM) are briefly discussed and partially demonstrated. These extensions are intended to compensate for the assumptions and simplifications, mainly with respect to the artificial boundary conditions, used in the original stand-alone FEM formulations.
Item Metadata
Title |
A two-dimensional finite element analysis of the stationary semiconductor device equations
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1997
|
Description |
The ability to model the steady-state field inside active structures, such as a transistor, is an
important aspect of monolithic microwave integrated circuit (MMIC) design. This paper focuses
on such an active zone of semiconductor material, and presents a finite element analysis of the
classical semiconductor equations. The semiconductor equations are very nonlinear and govern the
potential and carrier density distributions in semiconductor materials. A previously developed
finite element method (FEM) formulation of these equations, referred to as the current conservation
model, is re-introduced and re-derived with compact matrix notation. It is shown how this
formulation can be solved with the Newton-Raphson iterative scheme. Then, a newly developed
FEM formulation, referred to as the advection-diffusion model, of the continuity equations is
described in detail. It is shown by example how this formulation solved with Gummel's iterative
technique is very numerically robust. These two different solution methods of the steady-state
system of coupled Poisson and continuity equations are combined into a final solution algorithm
that exploits their strengths. As a specific example, GaAs MESFETs are the focus of
implementation, and the resulting potential field and carrier density distributions are used, to
calculate various MESFET parameters such as electrode currents, voltage gain, capacitances, and
conductances. Finally, various extensions to the FEM approach involving the application of the
method of moments (MoM) are briefly discussed and partially demonstrated. These extensions are
intended to compensate for the assumptions and simplifications, mainly with respect to the artificial
boundary conditions, used in the original stand-alone FEM formulations.
|
Extent |
5902343 bytes
|
Genre | |
Type | |
File Format |
application/pdf
|
Language |
eng
|
Date Available |
2009-03-24
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
DOI |
10.14288/1.0065230
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
1997-11
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.