Transcript Field Solvers

Detailed Device Simulators
Commercial simulators: EM,
semiconductor devices, Comsol
Commercial Simulator for Detailed
Device Modeling
• A lot of very powerful device level tools.
• Commercial tools that handle meshing,
solution and analysis
• Three examples
– EM – Finite Difference Time Domain and HFSS
– Comsol – multi-physics
– Semiconductors – Sentuarus
First Example is Maxwell’s Equations
 The basic set of equations describing the electromagnetic world
Gauss’s law
Gauss’s law for magnetism
Faraday’s law
Ampere’s law
Constitutive relations
  D  v
 B  0
B
E  
t
D
H  J 
t
D   E and B   H
Commercial software packages
 Commercial software packages
Finite element method (FEM)
Method of Moments (MoM)
ADS Momentum
HFSS
Transmission line matrix (TLM)
CST Microstripes
Finite-difference time-domain (FDTD)
FDTD Overview – Cells
 A three-dimensional problem space is composed of cells
5/60
FDTD Overview – Material grid
 A three-dimensional problem space is composed of cells
6/60
Transformation from Time-Domain to Frequency-Domain
 Results can be obtained for frequency domain using Fourier Transform
A low-pass filter
S11
S21
Incident plane wave
8/60
Scattering Problems

   H inc  H scat     Einc  Escat 
t
A dielectric sphere
9/60
  H inc

  0 Einc
t
Scattering from a Dielectric Sphere
10/60
Wireless Personal Communications Devices
Source: Allen Taflove, “A Perspective on the 40-Year History of FDTD Computational Electrodynamics,”
Applied Computational Electromagnetics Society (ACES) Conference,
Miami, Florida, March 15, 2006.
11/60
Can be found at http://www.ece.northwestern.edu/ecefaculty/Allen1.html
Also for optics: Focusing Plasmonic Lens
Source: Allen Taflove, “A Perspective on the 40-Year History of FDTD Computational Electrodynamics,”
Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, 2006.
Can be found at http://www.ece.northwestern.edu/ecefaculty/Allen1.html
Different Methods of
Electromagnetic Analysis
MOM
13
Example of Adaptive meshing
Waveguide Filter at right (symmetry along top
face) shows effect of mesh adaptation. The
region between posts has a denser mesh, due to
the superposition of reflected energy found in
the solution process.
Post
Post
14
Some Typical High-Frequency Electromagnetic
Applications
Waveguide Components
RF Integrated Circuits
Antenna
EMC
15
EM Summary
• Lots of choices – you will use Maxwell-2D
• Lots of data
– Fields
– Terminal currents/voltages
– S parameters
• Typically slow
• Often hard to learn
Multi-physics - Comsol
• Multi-physics is the
combination of several physics
phenomena when describing a
process
• In modeling and simulations,
these descriptions are based
on the laws of physics
• There is one precise way to
present the laws of physics,
and that is by means of
differential equations*
* Feynman “Famous Lectures”
The description of a loudspeaker involves
electromagnetic fields and forces, structural
analysis, and acoustic pressure fields in the
one model.
COMSOL’s Methodology for Modeling Multiphysics
Phenomena
• Development goals:
– To create a software where
scientists and engineers can
formulate any system of partial
differential equations (PDEs)
based on the laws of physics
– To formulate user interfaces,
based on the above methods,
for the most common areas in
applied physics and engineering
Microwave-thermal-structural
multiphysics couplings in a
waveguide circulator
COMSOL’s Methodology for Modeling Multiphysics Phenomena
Example: Fully Coupled Physics with Joule Heating and CFD
•
•
•
Definition in the
graphical user interface
Automatic assembly
using equation interpretation
and then discretization
Solution with direct or
iterative solvers using a fully
coupled system utilizing a
damped Newton method
Fluid dynamics
and heat transfer
Thermal analysis
in solids
Assembling of equations
and discretization
using FEM
Solution of the
coupled system
Electromagentic
fields
COMSOL’s Methodology for Modeling Multiphysics Phenomena
Example: Fully Coupled Physics with Joule Heating and CFD
•
•
•
Temperature field defined in both solid and fluid domains
The fluid flow equations are only defined in the fluid domain
The static electric field is only defined in the solid domain
Outlet
Metal wire heated
using an electric current
Inlet
Automatic meshing with
tetrahedral elements.
Quadrilateral and prism
elements are also available as
well as manual settings and
adaptive meshing.
The slice plot shows
temperature.
The arrows show the
velocity field. Note the
expansion due to the
temperature increase.
The boundary plot on the
hot wire shows the electric
potential.
The solution takes 12
minutes on a Toshiba Tecra
laptop. It requires about
600 Mb of RAM including a
300 Mb footprint.
The deformation and
stresses are mostly caused
by thermal expansion. The
fluid forces have little
effect.
Other Multiphysics Coupling Examples in COMSOL
• Electromagnetic wave propagation and
structural analysis
– Stress-optical effects
After annealing at
high temperatures,
mismatch in thermal
expansion between
the silica and silicon
layers results in
thermally induced
stresses at the
operating
temperature. These
stresses influence the
refractive index.
Other Multiphysics Coupling Examples in COMSOL
• Equation-based modeling of semiconductors
– Electrons and hole concentration fields coupled to
Poisson’s equations
Distributed
SPICE model of
an integrated
bipolar
transistor. The
model couples
the electric
potential for
four different
layers (four
equations) with
a circuit model.
Model of a MOS
transistor including
drift-diffusion of
electron (n) and
hole (p)
concentrations,
coupled to the
Poisson equation.