Nonlinear Feedback Control of a Coupled Kinetic Monte Carlo-Finite Difference Code

Abstract Product quality variables for many electronics and materials processes are set at the nanoscale and smaller length scales. Although the control of these processes is of scientific and industrial interest, there is a shortage of feedback controller design methods based on the noncontinuum models that describe such nanoscopic phenomena. In this study, linear, gain-scheduled, and nonlinear feedback controllers are designed for a coupled kinetic Monte Carlo-finite difference code that simulates the manufacture of copper interconnects. The feedback controller designs incorporate a low order stochastic model constructed from the coupled continuum-noncontinuum code

[1]  S. Decoutere,et al.  Transient enhanced diffusion of Boron in Si , 2002 .

[2]  C. Kleijn,et al.  Transport Phenomena in Tungsten LPCVD in a Single‐Wafer Reactor , 1991 .

[3]  Ingrid Moerman,et al.  Study of GaN and InGaN films grown by metalorganic chemical vapour deposition , 1997 .

[4]  Alan Bratschun,et al.  The application of rapid thermal processing technology to the manufacture of integrated circuits—An overview , 1999 .

[5]  K. Kobe The properties of gases and liquids , 1959 .

[6]  C. Kleijn,et al.  A Mathematical Model for LPCVD in a Single Wafer Reactor , 1989 .

[7]  Gou-Chung Chi,et al.  Growth and characterization of GaN by atomsphere pressure metalorganic chemical-vapor deposition with a novel separate-flow reactor , 1999 .

[8]  P. Dewilde,et al.  Singular value decomposition: an introduction , 1989 .

[9]  Evgeni P. Gusev,et al.  Structure and stability of ultrathin zirconium oxide layers on Si(001) , 2000 .

[10]  A. Agarwal Ultra-shallow junction formation using conventional ion implantation and rapid thermal annealing , 2000, 2000 International Conference on Ion Implantation Technology Proceedings. Ion Implantation Technology - 2000 (Cat. No.00EX432).

[11]  D. R. Coughanowr,et al.  Process systems analysis and control , 1965 .

[12]  A. T. Fiory,et al.  Effect of ramp rates during rapid thermal annealing of ion implanted boron for formation of ultra-shallow junctions , 1999 .

[13]  Egbert Oesterschulze,et al.  Low temperature remote plasma-enhanced deposition of thin metal oxide films by decomposition of metal alkoxides , 1991 .

[14]  H. Iwai,et al.  Ultra-thin gate oxides-performance and reliability , 1998, International Electron Devices Meeting 1998. Technical Digest (Cat. No.98CH36217).

[15]  Daniel F. Downey,et al.  Effects of “fast” rapid thermal anneals on sub-keV boron and BF2 ion implants , 1999 .

[16]  A. Striganov,et al.  Tables of spectral lines of neutral and ionized atoms , 1968 .

[17]  Yaman Arkun,et al.  Principal components analysis in estimation and control of paper machines , 1996 .

[18]  Antonios Armaou,et al.  Feedback control of plasma etching reactors for improved etching uniformity , 2001 .

[19]  M. Morari,et al.  ON THE STABILITY OF SYSTEMS WITH MIXED TIME-VARYING PARAMETERS , 1997 .

[20]  Jane P. Chang,et al.  Spectroscopic study of plasma using zirconium tetra-tert-butoxide for the plasma enhanced chemical vapor deposition of zirconium oxide , 2001 .

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

[22]  Yiming Lou,et al.  A method for real-time control of thin film composition using OES and XPS , 2003, Proceedings of the 2003 American Control Conference, 2003..

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

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

[25]  T. Cale,et al.  Multiple scale integrated modeling of deposition processes , 2000 .

[26]  S. C. Palmateer,et al.  Flow visualization studies for optimization of OMVPE reactor design , 1986 .

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

[28]  C. Kleijn,et al.  Modeling of Chemical Vapor Deposition of Tungsten Films , 1993 .

[29]  C. Cabral,et al.  Mechanisms for microstructure evolution in electroplated copper thin films near room temperature , 1999 .

[30]  Jane P. Chang,et al.  Metalorganic precursor decomposition and oxidation mechanisms in plasma-enhanced ZrO2 deposition , 2002 .

[31]  Richard Pollard,et al.  A Mathematical Model for Chemical Vapor Deposition Processes Influenced by Surface Reaction Kinetics: Application to Low‐Pressure Deposition of Tungsten , 1991 .

[32]  W. R. Angus The Identification of Molecular Spectra , 1941, Nature.

[33]  P. J. Ireland,et al.  High aspect ratio contacts: A review of the current tungsten plug process , 1997 .

[34]  Constantinos Theodoropoulos,et al.  Design of gas inlets for the growth of gallium nitride by metalorganic vapor phase epitaxy , 2000 .

[35]  Hh Hidde Brongersma,et al.  Mechanism of the reaction of WF6 and Si , 1994 .

[36]  Mohamed Henini,et al.  Handbook of Semiconductor Manufacturing Technology , 2001 .

[37]  Fred Roozeboom,et al.  Effect of heating ramp rates on transient enhanced diffusion in ion-implemented silicon , 2001 .

[38]  T. E. Haynes,et al.  Physical mechanisms of transient enhanced dopant diffusion in ion-implanted silicon , 1997 .

[39]  Chris R. Kleijn,et al.  Computational modeling of transport phenomena and detailed chemistry in chemical vapor deposition : a benchmark solution , 2000 .

[40]  F. Maury,et al.  Selection of metalorganic precursors for MOCVD of metallurgical coatings: application to Cr-based coatings , 1996 .

[41]  Richard C. Alkire,et al.  Simulation of Shape Evolution during Electrodeposition of Copper in the Presence of Additive , 2001 .

[42]  P. A. Stolk,et al.  Interactions of ion‐implantation‐induced interstitials with boron at high concentrations in silicon , 1996 .

[43]  J. Autran,et al.  Tantalum pentoxide (Ta2O5) thin films for advanced dielectric applications , 1998 .

[44]  M. Kushner,et al.  Trench filling by ionized metal physical vapor deposition , 2001 .

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

[46]  David J. Duquette,et al.  Mass Transfer Models for the Electrodeposition of Copper with a Buffering Agent , 2001 .

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

[48]  Richard C. Alkire,et al.  Electrodeposition of Copper: The Effect of Various Organic Compounds* , 1999 .

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

[50]  N. S. Barnett,et al.  Private communication , 1969 .

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

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

[53]  Ioannis G. Kevrekidis,et al.  Model identification of a spatiotemporally varying catalytic reaction , 1993 .

[54]  F. Maury,et al.  A Thermodynamic Approach to the CVD of Chromium and of Chromium Carbides Starting from Cr(C6H6)2 , 1998 .

[55]  G. Stewart Perturbation theory for the singular value decomposition , 1990 .

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

[57]  Tao Wang,et al.  Cluster formation during annealing of ultra-low-energy boron-implanted silicon , 2000 .

[58]  Y. Taur,et al.  Quantum-mechanical modeling of electron tunneling current from the inversion layer of ultra-thin-oxide nMOSFET's , 1997, IEEE Electron Device Letters.

[59]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .