Some Details of the Project

Software

• Analysis Codes

  The analysis codes TACO and TWAFER , developed at Sandia National Laboratories, have been used to simulate the thermal properties of CVD reactors.

• Interface Between Analysis Codes and Optimization Codes

  Most analysis codes are not written with the objective to be used for complex design and performance optimization. In an optimization framework, most analysis codes, including TACO and TWAFER , can be used to evaluate objective functions and constraints, but they usually do not provide design sensitivities, essential for derivative based optimization methods. The automatic differentiation tool ADIFOR, developed at Argonne National Laboratories and Rice University, generates derivative code that provides design sensitivities from given analysis codes. While approximate derivatives can also be computed from function values via finite differences, ADIFOR generates `exact' derivatives in significantly less computing time. This leads to better designs and faster design cycles.

• Optimization Codes

  The optimization packages TRICE, developed at Rice University, and OPT++ developed at Sandia National Laboratories, are used. Currently, OPT++ primarily includes codes for nonlinear equations, unconstrained optimization and optimization with simple bound constraints. TRICE is an optimization package designed for nonlinear programming problems arising in optimal control and engineering design problems. (It is planned to include the TRICE algorithms into the OPT++ package.)
  Both packages are object oriented. In the constrained case, they do not insist on specific matrix factorization based subproblem solvers, like many other packages do. This allows users to incorporate their own efficient, application dependent solvers.
  Due to the modular structure of the packages, advancements in the optimization codes and advancements in the application codes are immediately utilized in the design and performance optimization. For example, in typical applications more than 90% of the computing time is spend in application routines. Gains from parallelism in application/analysis codes result in almost equal gains in the optimization procedure.
  The clear separation between optimization and application codes allows novel approaches for distributed computing. Application codes and optimization codes can run on different machines.
  The uniform user interface allows simple exchanges of optimization algorithms.

Some Results

• Performance optimization

  Control variables for performance optimization include heater temperatures (powers), baseplate cooling, and reactor pressure.
  
  A typical performance objective is to bring the wafers close to a desired temperature, while keeping wafer-to-wafer and across-wafer temperatures within prescribed limits to avoid `cracking' of wafers and achieve uniformity of wafers.

  Compute heater powers to achieve uniform temperature distribution on the wafers during steady-state operation.

  Compute heater powers to track given temperature for ramp, hold, and cool-down phase.
  

• Design optimization

  Typical design variables are the number of heater zones, the size and the position of heater zones, the insulation thickness, and the reactor geometry.

  Tools for performance optimization can also aide in the design optimization of CVD reactors, for example in determining the number of heater zones.

Future Work

• Include more complex analysis codes (chemical kinetics).
• Compare optimization approaches (black-box, all-at-once, in-between).
• Include TRICE algorithms into the OPT++ package.