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Computational Electromagnetics and RF Electronics
Full-Wave Analysis and Global Modeling of High-Frequency Active Devices

One of my research interests includes RF and Microwave circuits and components; microwave and millimeter-wave semiconductor devices, semiconductor device simulations, wave-device interactions, electromagnetics, and numerical techniques applied to monolithic microwave integrated circuits.


The topic of my Ph.D. dissertation was "Implementation and improvement of the full-wave analysis and global modeling of active microwave/mm-wave devices and circuits".


Usually in the sub-millimeter 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 transmission-lines 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, quasi-static 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 large-signal 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 solid-state 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 "full-wave method".

The full-wave simulation of active devices (transistors) couples a three dimensional time-domain 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 millimeter-wave 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 high-frequency 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 full-wave analysis of very high-frequency 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, full-wave 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 finite-difference time-domain (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 non-uniform 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 time-dependent 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 full-wave 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 electromagnetic-wave analysis of MEFET transistor, an excitation voltage, Vgs(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 Full-Wave Analysis and Global Modeling of active microwave devices


Full-wave analysis and global modeling in progress



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Last Updated 03/25/2010