Perspectives on the design and control of multiscale systems

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 motivates the creation of tools for the design and control of multiscale systems that have length scales ranging from the atomistic to the macroscopic. This paper describes a systematic approach that consists of stochastic parameter sensitivity analysis, Bayesian parameter estimation applied to ab initio calculations and experimental data, model-based experimental design, hypothesis mechanism selection, and multistep optimization. 2005 Elsevier Ltd. All rights reserved.

[1]  D. L. Ma,et al.  Robust identification and control of batch processes , 2003, Comput. Chem. Eng..

[2]  L. Petzold,et al.  Adjoint sensitivity analysis for differential-algebraic equations: algorithms and software☆ , 2002 .

[3]  Andreas G. Boudouvis,et al.  Enabling stability analysis of tubular reactor models using PDE/PDAE integrators , 2003, Comput. Chem. Eng..

[4]  William S. Levine,et al.  The Control Handbook , 2005 .

[5]  Panayotis C. Andricacos,et al.  Damascene copper electroplating for chip interconnections , 1998, IBM J. Res. Dev..

[6]  Markos A. Katsoulakis,et al.  Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles , 2003 .

[7]  R. Braatz,et al.  Pair Diffusion and Kick-out: Contributions to Diffusion of Boron in Silicon , 2004 .

[8]  W. E. Stewart,et al.  Sensitivity analysis of initial value problems with mixed odes and algebraic equations , 1985 .

[9]  Linda R. Petzold,et al.  Improved leap-size selection for accelerated stochastic simulation , 2003 .

[10]  Randolph E. Bank,et al.  Transient simulation of silicon devices and circuits , 1985, IEEE Transactions on Electron Devices.

[11]  Dionisios G. Vlachos,et al.  Low-Dimensional Approximations of Multiscale Epitaxial Growth Models for Microstructure Control of Materials , 2000 .

[12]  R. Braatz,et al.  Parameter Sensitivity Analysis Applied to Modeling Transient Enhanced Diffusion and Activation of Boron in Silicon , 2003 .

[13]  H. Fujita,et al.  Micromachines for nanoscale science and technology , 1999 .

[14]  M. Kotrla,et al.  Theory and simulation of crystal growth , 1997 .

[15]  Michael J. Kurtz,et al.  Selection of model parameters for off-line parameter estimation , 2004, IEEE Transactions on Control Systems Technology.

[16]  K. Eric Drexler,et al.  Nanosystems - molecular machinery, manufacturing, and computation , 1992 .

[17]  Costas J. Spanos,et al.  Advanced process control , 1989 .

[18]  C. W. Gear,et al.  'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods , 2002 .

[19]  Jefferson W. Tester,et al.  Incorporation of parametric uncertainty into complex kinetic mechanisms: Application to hydrogen oxidation in supercritical water , 1998 .

[20]  George Stephanopoulos,et al.  Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices , 2003 .

[21]  Constantinos Theodoropoulos,et al.  Effective bifurcation analysis: a time-stepper-based approach , 2002 .

[22]  Alan C. West,et al.  Electrochemical and Fill Studies of a Multicomponent Additive Package for Copper Deposition , 2001 .

[23]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[24]  J. Rawlings,et al.  Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics , 2002 .

[25]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[26]  Lorenz T. Biegler,et al.  Dynamic optimization of the Tennessee Eastman process using the OptControlCentre , 2003, Comput. Chem. Eng..

[27]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[28]  P. Andricacos.  Copper On-Chip Interconnections: A Breakthrough in Electrodeposition to Make Better Chips , 1999, The Electrochemical Society Interface.

[29]  Ioannis G. Kevrekidis,et al.  “Coarse” stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples , 2001, nlin/0111038.

[30]  James E. Butler,et al.  A kinetic Monte Carlo method for the atomic-scale simulation of chemical vapor deposition: Application to diamond , 1997 .

[31]  M. Klein,et al.  Computer simulation studies of biomembranes using a coarse grain model , 2002 .

[32]  Huajian Gao,et al.  A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid , 1999 .

[33]  Richard D. Braatz,et al.  Advanced control of crystallization processes , 2002, Annu. Rev. Control..

[34]  J. Jacquez,et al.  Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design , 1985 .

[35]  Martha A. Gallivan.  Optimization, estimation, and control for kinetic Monte Carlo simulations of thin film deposition , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[36]  Bilal M. Ayyub,et al.  Uncertainty Modeling and Analysis in Civil Engineering , 1997 .

[37]  H. B. Matthews,et al.  Batch crystallization of a photochemical: Modeling, control, and filtration , 1998 .

[38]  R. Braatz,et al.  Effect of near-surface band bending on dopant profiles in ion-implanted silicon , 2004 .

[39]  Richard C. Alkire,et al.  Electrochemical reaction engineering in materials processing , 1994 .

[40]  Shengtai Li,et al.  Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution , 2002, SIAM J. Sci. Comput..

[41]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[42]  Isaac Elishakoff,et al.  Whys and hows in uncertainty modelling : probability, fuzziness and anti-optimization , 1999 .

[43]  T. Duever,et al.  Choosing the right model: Case studies on the use of statistical modeldiscrimination experiments , 1997 .

[44]  Mark E. Law,et al.  Continuum based modeling of silicon integrated circuit processing: An object oriented approach , 1998 .

[45]  Richard M. Murray,et al.  Model reduction and system identification for master equation control systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[46]  I. Kevrekidis,et al.  Coarse molecular dynamics of a peptide fragment: Free energy, kinetics, and long-time dynamics computations , 2002, physics/0212108.

[47]  Haydn N. G. Wadley,et al.  Kinetic Monte Carlo simulation of heterometal epitaxial deposition , 2002 .

[48]  Ioannis G. Kevrekidis,et al.  Computing in the past with forward integration , 2004 .

[49]  Richard M. Murray,et al.  Reduction and identification methods for Markovian control systems, with application to thin film deposition , 2004 .

[50]  John C. Shelley,et al.  Computer simulation of surfactant solutions , 2000 .

[51]  R.K. Kalia,et al.  Multiscale simulation of nanosystems , 2001, Comput. Sci. Eng..

[52]  T. Moffat,et al.  Electrodeposition of Copper in the SPS-PEG-Cl Additive System I. Kinetic Measurements: Influence of SPS , 2004 .

[53]  R. Braatz,et al.  Ramp-Rate Effects on Transient Enhanced Diffusion and Dopant Activation , 2003 .

[54]  Richard D. Braatz,et al.  Mechanism for coupling between properties of interfaces and bulk semiconductors , 2003 .

[55]  D. Vlachos,et al.  Recent developments on multiscale, hierarchical modeling of chemical reactors , 2002 .

[56]  K. Jensen,et al.  A multiscale study of the selective MOVPE of AlxGa1−xAs in the presence of HCl , 2003 .

[57]  Ioannis G. Kevrekidis,et al.  Equation-free: The computer-aided analysis of complex multiscale systems , 2004 .

[58]  Ioannis G. Kevrekidis,et al.  The gap-tooth method in particle simulations , 2003 .

[59]  P. I. Barton,et al.  Parametric sensitivity functions for hybrid discrete/continuous systems , 1999 .

[60]  Richard D. Braatz,et al.  Parameter Sensitivity Analysis of Pit Initiation at Single Sulfide Inclusions in Stainless Steel , 2004 .

[61]  Richard D. Braatz,et al.  Multiscale simulations of copper electrodeposition onto a resistive substrate , 2005, IBM J. Res. Dev..

[62]  Ioannis G. Kevrekidis,et al.  Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice-gas model with lateral interactions , 2002 .

[63]  A. Dollet.  Multiscale modeling of CVD film growth—a review of recent works , 2004 .

[64]  Muruhan Rathinam,et al.  Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method , 2003 .

[65]  J. Harb,et al.  Additive Behavior during Copper Electrodeposition in Solutions Containing Cl − , PEG, and SPS , 2003 .

[66]  Richard D. Braatz,et al.  First-principles and direct design approaches for the control of pharmaceutical crystallization , 2005 .

[67]  P. I. Barton,et al.  Efficient sensitivity analysis of large-scale differential-algebraic systems , 1997 .

[68]  Andrew J. Majda,et al.  Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems , 2003 .

[69]  Richard D. Braatz,et al.  Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems , 2003, IEEE Trans. Control. Syst. Technol..

[70]  Z. Nagy,et al.  Robust nonlinear model predictive control of batch processes , 2003 .

[71]  G. Henkelman,et al.  Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table , 2001 .

[72]  Richard D. Braatz,et al.  A Simplified Picture for Transient Enhanced Diffusion of Boron in Silicon , 2004 .

[73]  M. Kushner,et al.  Monte Carlo Simulation of the Electrodeposition of Copper I. Additive-Free Acidic Sulfate Solution , 2002 .

[74]  D. Vlachos,et al.  Parameter Optimization of Molecular Models: Application to Surface Kinetics , 2003 .

[75]  Richard D. Braatz,et al.  Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis , 2004 .

[76]  Mark J. Kushner,et al.  Monte Carlo Simulation of the Electrodeposition of Copper II. Acid Sulfate Solution with Blocking Additive , 2002 .

[77]  D. Landolt,et al.  Fundamental aspects and applications of electrochemical microfabrication , 2000 .

[78]  David L. Ma,et al.  Worst-case analysis of finite-time control policies , 2001, IEEE Trans. Control. Syst. Technol..

[79]  R. Braatz,et al.  Maximum A posteriori estimation of transient enhanced diffusion energetics , 2003 .

[80]  R.D. Braatz,et al.  Control systems analysis of a multiscale simulation code for copper electrodeposition , 2004, Proceedings of the 2004 American Control Conference.

[81]  D. Gillespie.  Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[82]  I. G. Kevrekidis,et al.  Enabling dynamic process simulators to perform alternative tasks: A time-stepper-based toolkit for computer-aided analysis , 2003 .

[83]  Emile H. L. Aarts,et al.  Simulated annealing and Boltzmann machines - a stochastic approach to combinatorial optimization and neural computing , 1990, Wiley-Interscience series in discrete mathematics and optimization.

[84]  Thomas P. Moffat,et al.  Modeling Superconformal Electrodeposition Using The Level Set Method , 2003 .

[85]  K. Kondo,et al.  Role of Additives for Copper Damascene Electrodeposition Experimental Study on Inhibition and Acceleration Effects , 2004 .

[86]  Sang Yup Lee,et al.  Protein Microarrays and Chips , 2003 .

[87]  I. G. Kevrekidis,et al.  Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation , 2003 .

[88]  Park M. Reilly,et al.  The use of statistical methods to build mathematical models of chemical reacting systems , 1974 .

[89]  David L. Ma,et al.  Coupled mesoscale—continuum simulations of copper electrodeposition in a trench , 2004 .

[90]  Y. Aoyagi,et al.  Carbon nanotube devices for nanoelectronics , 2002 .

[91]  Harry A. Atwater,et al.  Design of a film surface roughness-minimizing molecular beam epitaxy process by reduced-order modeling of epitaxial growth , 2004 .

[92]  K. Jensen,et al.  MULTISCALE MODELING OF THIN FILM GROWTH , 1998 .

[93]  David L. Ma,et al.  Worst‐case performance analysis of optimal batch control trajectories , 1999 .

[94]  Richard D. Braatz,et al.  Systems analysis and design of dynamically coupled multiscale reactor simulation codes , 2004 .

[95]  A. West.  Theory of filling of high-aspect ratio trenches and vias in presence of additives , 2000 .

[96]  Per Linse,et al.  Effect of spatially distributed hydrophobic surface residues on protein-polymer association , 2003 .

[97]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[98]  Dimitrios Maroudas,et al.  Multiscale modeling of hard materials: Challenges and opportunities for chemical engineering , 2000 .

[99]  Richard C. Alkire,et al.  The bridge from nanoscale phenomena to macroscopic processes , 1998 .

[100]  J. Bonevich,et al.  Superconformal Electrodeposition of Copper in 500–90 nm Features , 2000 .

[101]  Richard D. Braatz,et al.  Systems analysis applied to modeling dopant activation and TED in rapid thermal annealing , 2002, 10th IEEE International Conference of Advanced Thermal Processing of Semiconductors.

[102]  George Stephanopoulos,et al.  Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties , 2003 .

[103]  D. Vlachos.  A Review of Multiscale Analysis: Examples from Systems Biology, Materials Engineering, and Other Fluid–Surface Interacting Systems , 2005 .

[104]  James B. Rawlings,et al.  Model identification for crystallization : theory and experimental verification , 1996 .

[105]  P. Christofides,et al.  Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models , 2003 .

[106]  R. Braatz,et al.  Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives , 2004 .

[107]  D. L. Ma,et al.  IDENTIFICATION OF KINETIC PARAMETERS IN MULTIDIMENSIONAL CRYSTALLIZATION PROCESSES , 2002 .

[108]  L. Petzold,et al.  Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem ✩ , 2000 .

[109]  Anthony C. Atkinson,et al.  Optimum Experimental Designs , 1992 .

[110]  Richard D. Braatz,et al.  Optimal control of rapid thermal annealing in a semiconductor process , 2004 .

[111]  R. Braatz,et al.  Electrochemical engineering in an age of discovery and innovation , 2004 .

[112]  Menner A. Tatang,et al.  An efficient method for parametric uncertainty analysis of numerical geophysical models , 1997 .

[113]  P. Christofides,et al.  Feedback control of growth rate and surface roughness in thin film growth , 2003 .

[114]  Richard M. Murray,et al.  THE DYNAMICS OF THIN FILM GROWTH: A MODELING STUDY , 2003 .

[115]  A. Prokop.  Bioartificial Organs in the Twenty‐first Century , 2001 .

[116]  R. Braatz,et al.  Parameter Sensitivity Analysis of Monte Carlo Simulations of Copper Electrodeposition with Multiple Additives , 2003 .

[117]  Timothy O. Drews,et al.  Evolution of Surface Roughness during Copper Electrodeposition in the Presence of Additives Comparison of Experiments and Monte Carlo Simulations , 2003 .

[118]  W. H. Weinberg,et al.  Theoretical foundations of dynamical Monte Carlo simulations , 1991 .

[119]  Menner A. Tatang,et al.  Uncertainty analysis of indirect radiative forcing by anthropogenic sulfate aerosols , 1997 .

[120]  T. Moffat,et al.  Superconformal Electrodeposition of Copper , 2001 .