This thesis examines the application of the multigrid method to the semiconductor equations. An overview of semiconductor device modelling in presented, and the multi-grid method is described. Several modifications to the basic multigrid algorithm are evaluated based on their performance for a one dimensional model problem. It was found that using a symmetric Gauss-Seidel relaxation scheme, a special prolongation based on the discrete equations, and local relaxation sweeps near the pn-junctions produced a robust, and efficient code. This modified algorithm is also successful for a wide variety of cases, and its performance compares favourably with other multigrid algorithms that have been applied to the semiconductor equations. / Science, Faculty of / Mathematics, Department of / Graduate

Graduation date: 1991

Li Yeping. / "December 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 138-147) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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One of the ways of countering the ever increasing computational requirements in the simulation and modeling of electrical and electromagnetic devices and phenomena, is the development of simulation and modeling tools on parallel computing platforms. In this thesis, a previously developed Monte Carlo parallel device simulator is utilized, enhanced, and evolved, to render it applicable to the modeling and simulation of certain key applications. A three-dimensional Monte Carlo simulation of GaAs MESFETs is first presented to study small-geometry effects. Then, a finite-difference time-domain numerical solution of Maxwell's equations is developed and coupled to Monte Carlo particle simulation, to illustrate a photoconductive switching experiment. As the third and major application of the Monte Carlo code, high-field electron transport simulations of the ZnS phosphor of AC thin film electroluminescent devices are presented. A full band structure (of ZnS) computed using a nonlocal empirical pseudopotential technique is included in the Monte Carlo simulation. The band structure is computed using a set of form factors, that were tuned to fit experimentally measured critical point transitions in ZnS. The Monte Carlo algorithms pertaining to the full band model are developed. Most of the scattering mechanisms, pertinent to ZnS are included to model the electron kinetics. The hot electron distributions are computed as a function of the electric field in the ZnS phosphor layer, to estimate the percentage of hot electrons that could potentially contribute to excitation of luminescent impurity centers in the ZnS phosphor layer. Impact excitation, a key process in electroluminescence, is included in the Monte Carlo simulation to estimate the quantum yield of the devices. Preliminary results based on the full band k-space model exhibit experimentally observed trends. / Graduation date: 1996

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

The last six years has seen the emergence and rapid development of a new type of field effect transistor, the High Electron Mobility Transistor (HEMT), which offers improved performance in both digital and analogue circuits compared with circuits incorporating either MEtal Semiconductor (MES) or Metal Oxide Semiconductor (MOS) FETs. A new physically-based analytic model for HEMTs, which predicts the DC and RF electrical performance from the material and structural parameters of the device, is presented. The efficacy of the model is demonstrated with comparisons between simulated and measured device characteristics, at DC and microwave frequencies. The good agreement with experiment obtained with the model indicates that velocity overshoot effects are considerably less important in HEMTs than has been widely assumed, and that the electron transit velocity in submicron devices is approximately 10 cm/s, rather than around 2x10 cm/s. The Inverted HEMT, one of the major HEMT structural variants, is emphasized throughout this work because of its potential advantages over other variants, and practical results from 0.5 micron gate length Inverted HEMTs are presented. / Thesis (Ph.D.)-University of Natal, Durban, 1986.

The Jain and Balk analytic model for two-dimensional effects in short channel MOSFETS is investigated. The effects considered are Drain Induced Barrier Lowering, DIBL, and the maximum electric field, Emax, which influences Drain Induced High Field, DIHF. A scaled short channel design is used as the basis for the investigation. Cases are numerically simulated using the MINIMOS program. DIBL and Emax are calculated using the Jain and Balk model. Model values are compared to numerical simulation values. Results show the model consistently overestimates DIBL. Also, the range for which the model closely estimates Emax is found. Variation in Emax with change of junction depth Xj is investigated. The electric field, Ex, as it varies with depth in the channel is investigated, and compared to the Jain and Balk approximation. The deviations suggest that the model must break down for short channels.

The voltage controlled resistance model is developed for a reliable MOS transistor resistance mapping. The model includes both system and local parameters, and incorporates the effect of rise and fall time variations on the gate delay. MOS transistor resistance mapping is applied in logic simulation and timing verification. Also, it can be used in automatic transistor sizing and critical path analysis.

This thesis examines substrate noise coupling for NMOS transistors in heavily doped substrates. The study begins with the analysis of an NMOS transistor switching noise in a digital inverter at the device level. A resistive substrate network for the NMOS transistor is proposed and verified. Coupling between N+- P+ contacts is compared both qualitatively and quantitatively with simulations. The difference between the N-P and P-P coupling is in the cross-coupling parameter. A new N-P model, which requires only five parameters, is proposed by taking advantage of an existing P-P model combined with the concept of a virtual separation. This model has been validated up to 2GHz with Medici simulations. The virtual separation concept has been validated with 2D/3D simulations and measurements from test structures fabricated in a 0.35μm TSMC CMOS heavily doped process. This model is useful when transistor switching noise is the dominant source of substrate noise. Applications of the new N-P model are demonstrated with circuit simulations. / Graduation date: 2004