Physics-driven Bayesian hierarchical modeling of the nanowire growth process at each scale

Despite significant advances in nanoscience, current physical models are unable to predict nanomanufacturing processes under uncertainties. This research work aims to model the nanowire (NW) growth process at any scale of interest. The main idea is to integrate available data and physical knowledge through a Bayesian hierarchical framework with consideration of scale effects. At each scale the NW growth model describes the time–space evolution of NWs at different sites on a substrate. The model consists of two major components: NW morphology and local variability. The morphology component represents the overall trend characterized by growth kinetics. The area-specific variability is less understood in nanophysics due to complex interactions among neighboring NWs. The local variability is therefore modeled by an intrinsic Gaussian Markov random field to separate it from the growth kinetics in the morphology component. Case studies are provided to illustrate the NW growth process model at coarse and fine scales, respectively.

[1]  Seiji Takeda,et al.  Growth rate of silicon nanowires , 2005 .

[2]  Tao Yuan,et al.  Breakdown phenomena of zirconium-doped hafnium oxide high-k stack with an inserted interface layer , 2006 .

[3]  Wei Lu,et al.  TOPICAL REVIEW: Semiconductor nanowires , 2006 .

[4]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[5]  Donald B. Rubin,et al.  Using Empirical Bayes Techniques in the Law School Validity Studies , 1980 .

[6]  Hirotaro Mori,et al.  In Situ High-Resolution Transmission Electron Microscopy in the Study of Nanomaterials and Properties , 2008 .

[7]  Agus Sudjianto,et al.  Blind Kriging: A New Method for Developing Metamodels , 2008 .

[8]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[9]  James O. Berger,et al.  A Framework for Validation of Computer Models , 2007, Technometrics.

[10]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[11]  Jianjun Shi,et al.  Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes , 2006 .

[12]  Andrej Pázman,et al.  Nonlinear Regression , 2019, Handbook of Regression Analysis With Applications in R.

[13]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[14]  Mihail C. Roco,et al.  Manufacturing at the Nanoscale , 2007 .

[15]  Jye-Chyi Lu,et al.  A Review of Reliability Research on Nanotechnology , 2007, IEEE Transactions on Reliability.

[16]  N. V. Sibirev,et al.  Theoretical analysis of the vapor-liquid-solid mechanism of nanowire growth during molecular beam epitaxy. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Tim Hesterberg,et al.  Monte Carlo Strategies in Scientific Computing , 2002, Technometrics.

[18]  Way Kuo Challenges Related to Reliability in Nano Electronics , 2006 .

[19]  Kazimierz Sobczyk,et al.  Stochastic Modeling of Microstructures , 2001 .

[20]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[21]  C. F. Jeff Wu,et al.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2000 .

[22]  Tirthankar Dasgupta,et al.  Statistical Modeling and Analysis for Robust Synthesis of Nanostructures , 2008 .

[23]  Hashem Rafii-Tabar,et al.  Computational physics of carbon nanotubes , 2007 .

[24]  Alyson G. Wilson,et al.  Integrated Analysis of Computer and Physical Experiments , 2004, Technometrics.

[25]  Janet E. Jones On the determination of molecular fields. —II. From the equation of state of a gas , 1924 .

[26]  Suk Joo Bae,et al.  Statistical Models for Hot Electron Degradation in Nano-Scaled MOSFET Devices , 2007, IEEE Transactions on Reliability.

[27]  Way Kuo,et al.  Dielectric relaxation and breakdown detection of doped tantalum oxide high-k thin films , 2004, IEEE Transactions on Device and Materials Reliability.

[28]  Charles M Lieber,et al.  Semiconductor nanowires , 2006 .

[29]  J. Hirth,et al.  Kinetics of Diffusion-Controlled Whisker Growth , 1964 .

[30]  G. Seber,et al.  Nonlinear Regression: Seber/Nonlinear Regression , 2005 .

[31]  Jye-Chyi Lu,et al.  A Review of Statistical Methods for Quality Improvement and Control in Nanotechnology , 2009 .

[32]  R. S. Wagner,et al.  VAPOR‐LIQUID‐SOLID MECHANISM OF SINGLE CRYSTAL GROWTH , 1964 .

[33]  W. Kuo Assessment for U.S. Engineering Programs , 2006 .

[34]  Douglas C. Montgomery,et al.  Student solutions manual : design and analysis of experiments, seventh edition , 2009 .

[35]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[36]  Brian D. Ripley,et al.  Spatial Statistics: Ripley/Spatial Statistics , 2005 .

[37]  W. Bainbridge,et al.  Societal implications of nanoscience and nanotechnology , 2001 .

[38]  Gang Liu,et al.  Nanostructure morphology variation modeling and estimation for nanomanufacturing process yield improvement , 2009 .

[39]  Jianyu Liang,et al.  Periodic array of uniform ZnO nanorods by second-order self-assembly , 2004 .