One of my research interests
includes RF and Microwave circuits and components; microwave and millimeterwave
semiconductor devices, semiconductor device simulations, wavedevice
interactions, electromagnetics, and numerical techniques applied to
monolithic microwave integrated circuits.
The topic of my Ph.D.
dissertation was "Implementation
and improvement of the
fullwave analysis and global modeling
of active microwave/mmwave devices and circuits".
Usually in the submillimeter and upper millimeter wave
range, the transistors width becomes comparable to the
wavelength. Therefore, the transistor cannot be treated
as a point or a lumped element any more. The high
frequency aspects, including distributed effects,
propagation delays, electron transmit time, parasitic
elements, and discontinuity effects become important and
have to be thoroughly investigated. In addition,
coupling the energy from the device to the circuit, (i.e.
the matching problem), becomes an involved issue,
and
approaching it using a simple circuit concept that
neglects the distributed effects of the feeding and
output lines can be a very limited approach. This
process is more complicated when the characteristic
impedance of some transmissionlines utilized becomes
either undefined or not uniquely defined, when not
operated in a pure TEM mode.
As it was mentioned, when semiconductor devices are
operated under high frequency conditions the device
modeling problem becomes more involved. In such cases,
quasistatic semiconductor device models are not
adequate, and the wave effects have to be incorporated.
These added effects become important for the following
reasons:

The short wave period is comparable to the electron
relaxation times.

The electrons need a finite time to adjust their
velocities to the changes in field.

The processes inside the devices are dynamic.

In largesignal problems, the AC electric field is
comparable to the DC field.

Large magnetic fields exit inside the device.

Electromagnetic coupling between electrodes (parasitic
elements) is enhanced.

Discontinuity problem is created when coupling signal
to and out of the device.
The electromagnetic waves interact with the free
carriers inside the device and affect carrier transport.
The carriers, in turn, become a source of
electromagnetic fields making the need to couple the two
systems justified. Another requirement for high
frequency modeling is that some simplifying assumptions
in the solidstate model are no longer valid. In the
conservation equations, for example, spatial and
temporal variations are significant in the domain of the
problem.
So, the only acceptable method for presenting these
various forces is to combine the dynamic field solution
with a semiconductor device model called "fullwave
method".
The fullwave simulation of active devices (transistors)
couples a three dimensional timedomain solution of
Maxwell's equations to the active device model. The
active device model is based on the moments of the
Boltzmann's transport equation. The coupling between the
two models is established by using fields obtained from
the solution of Maxwell's equations in the active device
model to calculate the current densities inside the
device. These current densities are used to update the
electric and magnetic fields.
The circuit aspect, the microwave and millimeterwave
circuits consist of closely spaced active and passive
devices, many levels of transmission lines and
discontinuities. The circuit performance may be
adversely affected by the high density, due to unwanted
effects such as crosstalk, caused by coupling, surface
waves, and unintended radiation, to name just a few.
Evidently, careful circuit designs must be developed
based on advanced design tools that take the
electromagnetic wave effects into considerations. This
creates a need for comprehensive analysis and design
tools that consider all the circuit elements
simultaneously, including the active devices, the
passive components, the radiation elements, and the
package. So, the accurate approach is to simulate the
whole highfrequency circuit by coupling the physical
equations representing the semiconductor devices with
the electromagnetic fields in the other passive
components. This simulation and modeling approach for
high frequency circuits called the "global modeling".
In fullwave analysis of very highfrequency transistors
the Maxwell's equations in conjunction with the
semiconductor equations must be solved. These equations
form a highly nonlinear Partial Differential Equations
(PDE's) system which must be numerically solved. So,
fullwave analysis and global modeling are tremendous
tasks that involve advanced numerical techniques and
different algorithms. As a result, it is computationally
expensive. Therefore, there is an urgent need to present
a new approach to reduce the simulation time, while
maintaining the same degree of accuracy presented by
global modeling techniques.
In the most cases, the numerical scheme used in the
simulation is based on the finitedifference timedomain
(FDTD) method. But using the standard FDTD scheme takes
a long time for simulation. In this dissertation, I want
to improve and decrease the simulation time of physical
based analysis and global modeling of active microwave
devices. In fact, the most important part of my research
is proposition of a new mathematical approach (for
example, using another numerical scheme) or improvement
of the used conventional numerical scheme,
i.e.
FDTD method (for example, using the nonuniform mesh or
increasing the time steps).
One approach (to reduce simulation time) is to
adaptively refine grids in locations where the unknown
variables vary rapidly. Such a technique is called
multiresolution time domain (MRTD), and a very
attractive way to implement it is to use wavelets. The
nonuniform grids are obtained by applying wavelet
transforms followed by hard threshold. This allows
forming fine and coarse grids in locations where
variable solutions change rapidly and slowly,
respectively.
One of my proposed methods is using filter bank
transforms. Solving elliptic Partial Differential
Equations (PDE's), or using implicit methods for solving
timedependent PDE's, results in large system of linear
equations Ax = b. Size of the problems is
often too large for using a direct solver, and one has
to relay on iterative methods. Such methods are
dependent on the condition numbers of the operator
matrices, A, in the sense that small condition
numbers guarantee a fast convergence to the solution,
whereas large condition numbers often imply that the
convergence will be slow. For instance, solving the
Poisson’s equation on a large or nonuniform grid leads
to a matrix with the large condition number. In this
case, an effective preconditioning of the matrix A
is usually required in order to keep the number of
iterations small. In one of my papers, I proposed to use
an efficient method that not only guarantees obtaining
the solution but also increases the speed of the
convergence. It is important to note that in fullwave
analysis of active devices, the Poisson’s equation must
always be solved in excitation plane where the input
voltage is applied. For example, for the
electromagneticwave analysis of MEFET transistor, an
excitation voltage, V_{gs}(t),
is applied between the gate and the source electrodes at
a plane. This excitation is applied as a plane wave
corresponds to the solution of the Poisson’s equation of
the applied voltage at each time step. Then, the
electric and magnetic fields are obtained in other
sections by solving Maxwell’s equations. In conventional
approach for implementing of global modeling using FDTD
method, all the equations which include time derivative
(hydrodynamic and Maxwell’s equations) are represented
by explicit FD schemes and have straightforward
solutions. Only, solving the Poisson’s equation leads to
a large system of linear equations, Ax = b.
Therefore, one of the most important approaches for
simulation time reduction of global
modeling of active microwave devices is decreasing the
solving time of the equation system, Ax = b,
which obtained from the Poisson’s equation.
Some good dissertations on the FullWave
Analysis and Global Modeling of active microwave devices

S. M. ElGhazaly, “Analysis
and Improvement of mmWave GaAs MESFET's,” Ph.D. dissertation, Department of Electrical
Engineering, The University of Texas at Austin, 1988.

M. A. AlSunaidi, “Simulation
of HighFrequency Semiconductor Devices Using a Full
Electromagnetic Wave Model,” Ph.D. dissertation, Department of Electrical
Engineering, Arizona State University, Tempe, AZ, 1995.

S. M. S. Imtiaz, “Physical
Simulation of High Frequency Semiconductor Devices and Amplifier
Circuits,” Ph.D. dissertation, Department of Electrical
Engineering, Arizona State University, Tempe, AZ, 1997.

S. Hammadi, “Time
Domain Methods for the Global Simulation of MillimeterWave Transistors
and Circuits,” Ph.D. dissertation, Department of
Electrical Engineering, Arizona State University, Tempe, AZ, 1999.

Y. A. Hussein, “Electromagnetic
Physical Modeling of Microwave Devices and Circuits,”
Ph.D. dissertation, Department of Electrical Engineering,
Arizona State University, Tempe, AZ, 2003.

J. S. AyubiMoak, “Gloal
Modeling of Microwave Transistors Using a FullBand Cellular
Monte Carlo/FullWave Maxwell Simulator,”
Ph.D. dissertation, Department of Electrical Engineering,
Arizona State University, Tempe, AZ, 2008.
Fullwave analysis and global modeling in progress

Basic paper about the fullwave
analysis of highfrequency active devices:
Electromagnetic wave effects on microwave
transistors using a fullwave timedomain model,
1996.

Global modeling of highfrequency
active circuits:
Global modeling of millimeterwave
circuits: electromagnetic simulation of amplifiers,
1997.

Using the fullwave analysis for
simulation and analysis of different devices:
Performance of MODFET and MESFET, a
comparative study including equivalent circuits using combined
electromagnetic and solidstate simulator, 1998.

Using the fullwave analysis for
simulation of a highfrequency transistor with new structure:
Airbridged gate MESFET: a new structure
to reduce wave propagation effects in highfrequency transistors,
1999.

A review of fullwave analysis and
global modeling:
A review of global modeling of charge
transport in semiconductors and fullwave electromagnetics,
1999.

Using artificial neural network
for simulation time reduction:
A practical largesignal global modeling
simulation of a microwave amplifier using artificial neural
network, 2000.

Using interpolating wavelet
applied to the DriftDiffusion model for simulation time
reduction:
Electromagnetic and semiconductor device
simulation using interpolating wavelets, 2001.

Using interpolating wavelet
applied to the full hydrodynamic transport model for
simulation time reduction:
Extending multiresolution timedomain
(MRTD) technique to the simulation of highfrequency active
devices, 2003.

and:
An efficient electromagneticphysicsbased
numerical technique for modeling and optimization of
highfrequency multifinger transistors, 2003.

Using genetic algorithms for the
fullwave analysis improvement:
Modeling and optimization of microwave
devices and circuits using genetic algorithms, 2004.

Using alternatingdirection
implicit (ADI) method for simulation time reduction:
Efficient numerical methods for simulation
of highfrequency active devices, 2006.
