Institute for Systems Research Technical Reports

Object-Oriented Programming techniques for solvingBVPs are introduced in this work. Object classes are created toencapsulate trial function sequences, discretized differential andquadrature operators, and other data structures used for spectraldiscretization and projection operations. Operator/functionoverloading subsequently is used to numerically implement theGalerkin projection method. Emphasis is placed on developingnumerical methods suitable for discretizing 2- and 3-dimensionalproblems, integrating the resulting ODE/AE systems in time, andreconstructing the solutions in the physical space. A detailed model of anisothermal carbon-carbon chemical vapor infiltration (CVI) systemwas studied as a true test of the ability of the numerical methods.

In this research, an ULVAC ERA-1000 selective tungsten chemical vapor deposition system located at the University of Maryland was studied where a temperature difference as large as 120 ^oC between the system wafer temperature reading and the thermocoupled instrumented wafer measurement was found during the manual processing mode.

The goal of this research was to develop a simplified, but accurate, three-dimensional transport model that is capable of describing the observed reactor behavior.

A hybrid approach combining experimental and simulation studies was used for model development. Several sets of experiments were conducted to investigate the effects of process parameters on wafer temperature.

A three-dimensional gas flow and temperature model was developed and used to compute the energy transferred across the gas/wafer interface. System dependent heat transfer parameters were formulated as a nonlinear parameter estimation problem and identified using experimental measurements.

Good agreement was found between the steady-state wafer temperature predictions and experimental data at various gas compositions, and the wafer temperature dynamics were successfully predicted using a temperature model considering the energy exchanges between the thermocouple, wafer, and showerhead.

To increase the utility of existing simulators, model reduction methods must be used to extract the dominant spatial characteristics of the discharge; numerically efficient spectral projection methods are then used to generated the reduced model. These practical needs motivated the development of a set of simulation tools that provide a framework for process simulation, model reduction, and analysis of simulator predictions.

The goals of this thesis were to build this framework by identifying the computationally common elements of semiconductor device manufacturing process simulation, model reduction, and analysis methods, and to test these tools on the difficult problem of RF plasma simulation. The simulation tools were developed as a library of MATLAB functions; the library and demonstration scripts have been distributed through the MWRtools project website.

With process heating lamp power held constant, wafertemperature variations of up to 160 degrees K were observed by varying feed gasH_2/N_2 ratio. Heat transfer between the wafer and susceptor wasstudied by shifting the instrumented wafer off the susceptor axis,exposing a portion of the wafer backside to the chamber floor. Modelpredictions and experimental observations both demonstrated that the gasvelocity field had little influence on the observed wafer and predictedgas temperatures.

(This work to appear in Proc. 1999 American Control Conference.)

However, these ideas have not yet been adequately exploited inengineering, particularly in the control of smart systems; i.e.,feedback systems having large numbers of actuators and sensors. With dramatic recent improvements in micro-actuator and micro-sensortechnology, there is a need for control schemes betterthan the conventional approach of reading out all of the sensor informationto a computer, performing all the necessary computations in a centralizedfashion, and then sending out commands to each individual actuator.Potential applications for large arrays of micro-actuators includeadaptive optics (in particular, micromirror arrays), suppressingturbulence and vortices in fluid boundary-layers, micro-positioning smallparts, and manipulating small quantities of chemical reactants.

The main theoretical result presented is a Lyapunov functional for thecubic nonlinearity activator-inhibitor model pattern-forming system.Analogous Lyapunov functionals then follow for certain generalizations ofthe basic cubic nonlinearity model. One such generalization is a complex activator-inhibitor equation which, under suitable hypotheses,models the amplitude and phase evolution in the continuum limitof a network of coupled van der Pol oscillators, coupled to a network of resonant circuits, with an external oscillating input. Potentialapplications for such coupled van der Pol oscillator networks includequasi-optical power combining and phased-array antennas.

In addition to the Lyapunov functional, a Lyapunov function for the truncated modal dynamics is derived, and the Lyapunov functional isalso used to analyze the stability of certain equilibria. Basic existence, uniqueness, regularity, and dissipativity properties ofsolutions are also verified, engineering realizations of the dynamicsare discussed, and finally, some of the potential applications areexplored.

This paper was presented at the 32nd CISS, March 18-21, 1998.