Design of an interface between gallium arsenide MESFET physical models and the transmission line matrix method.

The Transmission Line Matrix (TLM) method has been demonstrated to be capable of simulating the electromagnetic propagation in passive components of monolithic microwave integrated circuits (MMICs), such as microstrip lines, air-bridges, and spiral inductors. The full simulation of MMICs by TLM is hindered by the lack of a GaAs MESFET model. Although SPICE-type lumped element models can be embedded, they are not sufficiently accurate to describe the time dependent response, and they defeat the method since TLM distinguishes itself by being capable of simulating physical structures. In addition, the TLM method cannot simulate a physics-based MESFET model since it cannot model fixed charges in the depletion region, nor can it model the highly non-linear field interactions in the conducting region. The TLM method requires a background solver to assist physics-based MESFET modelling. This thesis presents a novel method for enabling the TLM method to simulate the active region of the MESFET. The device is treated as a two-port where the depletion region is the input, and the channel region is the output. The input of the two-port is fed electric field signals from the gate transmission line. An internal GaAs MESFET solver transforms the input electric field into a voltage waveform, and the channel current and the depletion-channel boundary profile are calculated at every time instant by consideration of the channel doping and geometry. Via suitable interface parameters, the calculated outputs are transformed by individual TLM systems filling the channel into output electric and magnetic fields. The first part of the thesis derives a novel two-dimensional formulation of the TLM method enabling it to simulate a vertical section of the MESFET channel whose thickness is chosen small enough such that the electric field can be considered to be uniform. By controlling the TLM pulse energy, nodes conductivities, and section length, these three interface parameters enable the resultant TLM system to transform the physical characteristics of any infinitesimal section of the channel into electric and magnetic fields. The second part of the thesis derives a numerical time-domain quasi two-dimensional model of a GaAs MESFET with several novel aspects. Time-domain simulation is derived from non-stationary electron velocity response to the electric field. A new method is introduced, called the voltage balance method, to numerically solve the Poisson and current continuity equations at every time instant. In addition, a new time-domain treatment of the dielectric relaxation time constants of the drain and gate circuits enable the method to adopt variable time steps. When these three procedures are combined together, they result in a non-linear GaAs MESFET model which can offer sufficient accuracy and substantial time savings over other techniques. Several practical examples are presented showing TLM computations of (i) the non-stationary carrier velocity response to applied field, (ii) the transient field response to an application of biases into the MESFET, and (iii) the field response to an applied electric field sinusoidal waveform at 10 GHZ. The thesis concludes with several recommendations for future work. The key one is to link this work with the 3-dimensional TLM method by augmenting the output channel fields with those computed by TLM for the passive field interactions in the MESFET source, gate, and drain electrodes