Automatic differentiation is applied to the optimal design of microelectronics manufacturing equipment. The performance of nonlinear, leastsquares optimization methods is compared between numerical and analytic gradient approaches. The optimization calculations are performed by running large finite-element codes in an object-oriented optimization environment. The Adifor automatic differentiation tool is used to generate analytic derivatives for the finite-element codes. The performance results support previous observations that automatic differentiation becomes beneficial as the number of optimization parameters increases. The increase in speed, relative to numerical differences, has a limiting value and results are reported for two different analysis codes.
Most physically based modeling software accepts input in the form of geometry definition, physical parameters, initial conditions, and boundary conditions; and then, on the basis of solving physical conservation equations, predicts the steady-state or transient behavior of a system or process. There is a growing need to create software tools that can themselves control or manipulate the physically based models in certain ways to enhance the usability of models for equipment design and process optimization. These required tools can be described broadly in the following categories: sensitivity analysis, parameter estimation, inverse problems, dynamic optimization, and real-time control. This paper discusses generally the development and application of such modeling tools, drawing examples from a specific RTP reactor design. These techniques accelerate significantly the optimal design of processes and the concurrent engineering of real-time process-control algorithms.
A concurrent-engineering approach is applied to the development of an axisymmetric rapidthermal- processing (RTP) reactor and its associated temperature controller. Using a detailed finite-element thermal model as a surrogate for actual hardware, we have developed and tested a multiinput multi-output (MIMO) controller. Closed-loop simulations are performed by linking the control algorithm with the finite-element code. Simulations show that good temperature uniformity is maintained on the wafer during both steady and transient conditions. A numerical study shows the effect of ramp rate, feedback gain, sensor placement, and wafer-emissivity patterns on system performance.
The insertion of single-wafer thermal and CVD technologies into the front- and back-end of the line processing starts with study of the integrated circuits manufacturing and device performance requirements. Relying upon the lessons learned and using the concurrent engineering approach, next generation processing equipment design architecture is then defined. In order to meet the process performance, throughput, and cost of ownership requirements of semiconductor IC manufacturing as defined in the SIA road map, heavy emphasis must be put on sensor fusion and model-based process control. In the existing semiconductor IC manufacturing equipment, process control is usually accomplished by control of equipment settings, qualification wafer runs and ex-situ measurements of the various wafer properties, as well as design architecture for stable equipment performance. The conventional approach, however, suffers from slow drifts of various equipment state parameters such as infrared absorbing quartz media causing thermal memory effects, or deposition of films on the reactor walls causing variation in the optical characteristics of the reactor as well as chemical and particle memory effects. Using model-based real-time control in conjunction with implementation of various in-situ and ex-situ sensors, these effects can be well monitored and controlled. This paper is to discuss various production related issues with single-wafer thermal and CVD technologies.
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