Bayesian Analysis for Robust Synthesis of Nanostructures
Nanomaterials, because of their unique properties such as extremely small size and increased ratio of surface area to volume, have a great potential in many industrial applications that involve electronics, sensors, solar cells, super-strong materials, coatings, drug delivery, and nanomedicine. They have the potential also to improve the environment by direct applications of these materials to detect, prevent and remove pollutants. While nanomaterials present seemingly limitless possibilities, they bring with them new challenges. Among them is the precise control of the morphology of nanomaterials, which is extremely critical to the development of advanced nanodevices with various functionalities. The one-dimensional nanostructures of Cadmium Selenide (CdSe) have been found to represent morphologies of nanowires, nanobelts, and nanosaws, however, their synthesis is by trial and error. Predictive modeling and control methods are essential to process yield and productivity improvement. The process yield (response) is a vector whose elements correspond to the number of appearances of the different types of nanostructures, namely nanosaws, nanowires, and nanobelts. The goal in this paper is to apply existing Bayesian methodologies to describe the growths of these nanostructures in terms of process variables and to predict the probability of transition from one nanostructure to another when changes are made to one or more process variables. We also propose a Bayesian algorithm to identify the optimal process conditions that maximize the predicted probability of each type of nanostructure.
- 62.23.Eg: Nanodots
- 87.15.A-: Theory, modeling, and computer simulation
- 73.63.Fg: Nanotubes
- 62.25.-g: Mechanical properties of nanoscale systems(for structure of nanoscale systems, see 61.46.-w; for structural transitions in nanoscale materials, see 64.70.Nd; for electronic transport in nanoscale systems, see 73.63.-b)
- 42.62.Be: Biological and medical applications(see also 87.50.W-, 87.63.L-, and 87.80.Cc in biological and medical physics)
- B. Bhushan, Handbook of Nanotechnology (second edition). Springer, New York (2007).
- A. Mansoori, P. Araujo, E. Araujo, Diamondoid Molecules with Applications in Biomedicine, Materials Science, Nanotechnology & Petroleum Science. World Sci Pub Co, Hackensack, NJ (2012).
- Khataee, A., Mansoori, A. Nanostructured Titanium Dioxide Materials: Properties, Preparation and Applications. World Sci Pub Co, Hackensack, NJ (2012).
- C. Ma, Z. Wang, Road Map for Controlled Synthesis of CdSe Nanostructures. Advanced Materials 17, 1 (2005).
- L. Zhang, Y. Jia, S. Wang, Z. Li, C. Ji, J. Wei, H. Zhu, K. Wang, D. Wu, E. Shi, Y. Fang, and A. Cao, Carbon Nanotube and CdSe Nanobelt Schottky Junction Solar Cells. Nano Letter 10, 3583 (2010). [WoS]
- T. Dasgupta, C. Ma, V. Roshan Joseph, Z. L. Wang, C. F. J. Wu, Statistical Modeling and Analysis for Robust Synthesis of Nanostructures. Journal of the American Statistical Association 103, 594 (2008). [WoS][Crossref]
- M. C. Kennedy, and A. O’Hagan, Bayesian calibration of computer models (with discussion). Journal of Royal Statistical Society-Series B 63, 425 (2001).
- C. S. Reese, A. G. Wilson, M. Hamada, H. F. Martz, and K. J. Ryan, Integrated analysis of computer and physical experiments. Technometrics 46, 153 (2004). [Crossref]
- M. J. Bayarri, J.O. Berger, R. Paulo, J. Sacks, J. Cafeo, J. Cavendish, C. H. Lin, and J. Tu, A framework for validation of computer models. Technometrics 49, 138 (2007). [Crossref][WoS]
- Q. Huang, Physics-driven Bayesian hierarchical modeling of the nanowire growth process at each scale. IIE Transactions 43, 1 (2011). [WoS]
- P. McCullagh, J.A. Nelder, Generalized Linear Models. Chapman and Hall: London. (mathematical statistics of generalized linear model) (1989).
- C. P. Robert, G. Casella, Monte Carlo Statistical Methods. Second edition. Springer, New York (2005).
- K. Imai, G. King, O. Lau, Toward A Common Framework for Statistical Analysis and Development. Journal of Computational and Graphical Statistics 17, 892 (2008). [WoS][Crossref]
- K. Imai, G. King, O. Lau, Zelig: Everyone’s Statistical Software. http://gking.harvard.edu/zelig (2009).
- D. J. Spiegelhalter, A. Thomas, N. Best, D. and Lunn, WinBUGS user manual [online], http://www.mrc-bsu.cam. ac.uk/bugs.