Applied Mathematics Program


People and Departments Research Topics Graduate Program

Faculty Research Profile
Richard D. BraatzRichard D. Braatz
Professor
Department of Chemical and Biomolecular Engineering
University of Illinois at Urbana-Champaign

93 RAL

600 S. Mathews Ave. , Urbana, IL 61801

217-333-5073

braatz@uiuc.edu

http://www.scs.uiuc.edu/chem_eng/Faculty/braatz.html

Research Summary

New applications in materials, medicine, and computers are being discovered where the control of events at the molecular and nanoscopic scales is critical to product quality, although the primary manipulation of these events during processing occurs at macroscopic length scales. This drives our research program in the creation of tools for the design and control of multiscale systems that have length scales ranging from the atomistic to the macroscopic.

Research Projects

  • Multiscale Systems and Control
    The challenges to building such tools include uncertainties in the physicochemical mechanisms as well as the values of thermodynamic and kinetic parameters, complexities in the simulation of model equations that can span the subatomic to the macroscopic scales, lack of direct real-time manipulations and measurements of most properties at the nanoscale during processing, and the inapplicability of most existing mathematical systems tools to address systems described by noncontinuum and dynamically coupled continuum-noncontinuum models.

    These challenges are being addressed by a systematic approach to multiscale systems engineering that includes stochastic parameter sensitivity analysis, Bayesian parameter estimation applied to ab initio calculations and experimental data, hypothesis mechanism selection, and multiscale optimization. This enables multiscale systems to be designed based on the simulation codes that are most appropriate for simulating the various time and length scales of the process.

    New developments in multiscale systems theory are driven by applications to a variety of complex chemical systems including the crystallization of pharmaceuticals and proteins, the extrusion of thin polymer films, the formation of transistor junctions in advanced CMOS devices (in collaboration with Prof. E. Seebauer), and the manufacture of copper interconnects in electronic devices (in collaboration with Prof. R. Alkire). For pharmaceutical crystallization, an integrated system incorporating ATR-FTIR spectroscopy, process video microscopy, and laser backscattering has been created to reduce time to production. For polymer film extrusion, first-principles models are being created for incorporation into novel algorithms to control the film uniformity. For ultrashallow junctions, the results provide specific recommendations for microelectronics tool manufacturers on how to optimize processes to produce shallower junctions. For copper interconnects, systems principles are used to suppress numerical instabilities in multiscale simulation codes, gain fundamental insights into surface reaction mechanisms, and design nonlinear feedback controllers.

    Most of our research is in collaboration with industry, where algorithms have been implemented and are currently in use.


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