Institute for Systems Research Technical Reports

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.

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.

We offer a method for computing a workingapproximation to the controllability energy function, one of the mainobjects involved in the method. Moreover, we show that for a class ofsecond-order mechanical systems with dissipation, under certain conditionsrelated to the dissipation, an exact formula for the controllabilityfunction can be derived. We then present an algorithm for a numericalimplementation of the Morse-Palais lemma, which produces a local coordinatetransformation under which a real-valued function with a non-degeneratecritical point is quadratic on a neighborhood of the critical point.

Application of the algorithm to the controllabilty function plays a key rolein computing the balanced representation. We then apply our methods andalgorithms to derive balanced realizations for nonlinear state-space modelsof two example mechanical systems: a simple pendulum and a double pendulum.

The second part (Chapter 5) deals with modeling of rapid thermal chemicalvapor deposition (RTCVD) for growth of silicon thin films, viafirst-principles and empirical analysis. We develop detailedprocess-equipment models and study the factors that influence depositionuniformity, such as temperature, pressure, and precursor gas flow rates,through analysis of experimental and simulation results. We demonstratethat temperature uniformity does not guarantee deposition thicknessuniformity in a particular commercial RTCVD reactor of interest.

In thethird part (Chapter 6) we continue the modeling effort, specializing to acontrol system for RTCVD heat transfer. We then develop and apply ad-hocversions of prominent model reduction approaches to derive reduced modelsand perform a comparative study.

The overallobjective is to improve manufacturing effectiveness for epitaxial growth ofsilicon and silicon-germanium (Si-Ge) thin films on a silicon wafer. Growthtakes place in the ASM Epsilon-1 chemical vapor deposition (CVD) reactor, aproduction tool currently in use at ESSS. Phase II project results includedevelopment of a new comprehensive process-equipment model capable ofpredicting gas flow, heat transfer, species transport, and chemical mechanismsin the reactor under a variety of process conditions and equipment settings.

Applications of the model include prediction and control of deposition rate andthickness uniformity; studying sensitivity of deposition rate to processsettings such as temperature, pressure, and flow rates; and reducing the use ofconsumables via purge flow optimization. The implications of varioussimulation results are discussed in terms of how they can be used to reducecosts and improve product quality, e.g., thickness uniformity of thin films. We demonstrate that achieving deposition uniformity requires some degree oftemperature non-uniformity to compensate for the effects of other phenomenasuch as reactant depletion, gas heating and gas phase reactions, thermaldiffusion of species, and flow patterns.