No abstract

A n umerical solution procedure combining several weighted residual methods and based on global trial function expansion is developed to solve a model for the steady state gas ow eld and temperature distribution in a low-pressure chemical vapor deposition reactor. The enthalpy ux across wafer gas boundary is calculated explicitly and is found to vary signi cantly as a function of wafer position. An average heat transfer coe cient is estimated numerically and is compared to typical radiative heat transfer rates in these system. The convergence properties of the discretization method developed are also discussed.

Experimental measurements of wafer temperature in a single-wafer, lamp-heated chemical vapor deposition system were used to study the wafer temperature response to gas composition. A physically based simulation procedure for the process gas and wafer temperature was developed in which a subset of parameter values were estimated using a nonlinear, iterative parameter identification method, producing a validated model with true predictive capabilities. With process heating lamp power held constant, wafer temperature variations of up to 160 K were observed by varying the feed gas H2/N2 ratio. Heat transfer between the wafer and susceptor was studied by shifting the instrumented wafer off the susceptor axis, exposing a portion of the wafer backside to the chamber floor. Model predictions and experimental observations both demonstrated that the gas velocity field had little influence on the observed wafer and predicted gas temperatures.

ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, distributed-parameter system models. Four industrially relevant examples taken from electronic materials and chemical processing applications are used to demonstrate the simulation approach developed.

ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract: A model of a tungsten chemical vapor deposition (CVD) system is developed to study the CVD system thermal dynamics and wafer temperature nonuniformities during a processing cycle. We develop a model for heat transfer in the system's wafer/susceptor/guard ring assembly and discretize the modeling equation with a multiple-grid, nonlinear collocation technique. This weighted residual method is based on the assumption that the system's dynamics are governed by a small number of modes and that the remaining modes are slaved to these slow modes. Our numerical technique produces a model that is effectively reduced in its dynamical dimension, while retaining the resolution required for the wafer assembly model. The numerical technique is implemented with only moderately more effort than the traditional collocation or pseudospectral techniques. Furthermore, by formulating the technique in terms of a collocation procedure, the relationship between temperature measurements made on the wafer and the simulator results produced with the reduced-order model remain clear.