1. Robust Synthesis of Nanostructures C.F.Jeff Wu* Georgia Institute of Technology (joint with Tirthankar Dasgupta*, Christopher Ma +, Roshan Joseph*, Z L Wang + ) Available at www.isye.gatech.edu/~jeffwu/presentations. * Industrial and Systems Engineering, Georgia Tech + Material Sciences and Engineering, Georgia Tech

2. What are nanostructures ? Nanotechnology is the construction and use of functional structures designed from atomic or molecular scale with at least one characteristic dimension measured in nanometers (1 nm = 10 -9 meter; about 1/50,000 of the width of human hair). Size allows nanostructures to exhibit novel and significantly improved physical, chemical and biological properties, phenomena and processes. Can provide unprecedented understanding about materials and devices. Likely to impact many fields, e.g., –Expand range of performance of chemicals and materials. –New generation of chemical and biological sensors. –Improved computer storage and operation capacity. –Higher ductility and strength of nanostructured ceramics and metals.

3. Role of statistics in nanomaterial research Nanomaterial research –Shift from laboratory-level experimentation to controlled and large scale synthesis. –High yield and reproducibility. Role of statistical methodology –Systematically investigating the experimental conditions for achieving the desired nanostructures. –Building empirical models to express yields and properties of various types of nanostructures as functions of process variables. –Developing robust synthesis processes for producing nanostructures with high yield and minimal variation. Reference : Dasgupta, Ma, Joseph, Wang and Wu (2006), submitted to JASA.

4. Importance of Cadmium Selenide (CdSe) in nanomaterial research Investigated over the past decade for applications in optoelectronics, luminescent materials, lasing materials and biomedical imaging. The most extensively studied quantum-dot material. Regarded as the model system for investigating a wide range of nano-scale processes. Exhibits 1D morphologies of nanowires, nanobelts and nanosaws (Ma and Wang 2005), often with the three morphologies being intimately intermingled together within the as-deposited material.

5. Different CdSe nanostructures NANOSAWS NANOWIRES NANOBELTS Synthesized through a thermal evaporation process in a single-zone horizontal tube furnace. CdSe nanosaws and nanobelts synthesized for the first time by Z.L.Wang and his team at GT (2004).

6. Synthesis process Two main control variables –Source temperature (T) –Pressure (P) Distance (D) of the substrate from the source is a covariate. On each substrate –A deposition is obtained. – 180 individual nanostructures counted using Scanning Electron Microscopy (SEM). Cooling Water Source Material Pump Substrate Carrying Gas

7. A schematic description Y 1 + Y 2 + Y 3 + Y 4 = 180. (Y 1, Y 2, Y 3, Y 4 ) is multinomial (180, p 1, p 2, p 3, p 4 ). SYNTHESIS SOURCE TEMPERATURE (T) PRESSURE (P) DISTANCE FROM SOURCE (D) Y 2 : # Nanowires Y 3 : # Nanobelts Y 4 : # No growth Y 1 : # Nanosaws Internal noiseExternal noise

8. Experimental data (partial)

9. Response graphs Quadratic response surface appropriate

10. Modeling strategy : multinomial GLM

11. Existing methods Use a Poisson surrogate model –Create a pseudo factor with a level for each data point. –Cumbersome for large datasets (Faraway 2006). Direct maximization of multinomial likelihood using neural network (Venebles and Ripley, 2002) –S-PLUS and R modules available. –Separate evaluation of sub-models not available in current implementation.

12. New iterative method :

13. Initialization of parameter estimates (  i2 and  i3 ) in the algorithm

14. Fitted models

15. Achieving robustness : optimization of process parameters

16. The optimization problem

17. Optimal conditions

18. Other salient findings For nanosaws and nanowires, robustness of the synthesis process depends more on the choice of pressure rather than temperature. For nanobelts, temperature affects robustness strongly. There is a large temperature-pressure region that promotes high and consistent yield of nanowires. Highest yields of nanobelts and nanowires are achieved at higher distance (i.e., lower local temperature) as compared to nanosaws. Nanoscientists could provide plausible and in-depth physical interpretations of most of the above phenomena.

19. Impact of the study An early instance of application of statistical techniques in nanotechnology research. Significant advancement over the rudimentary data analysis methods that have been reported in nanomaterial research. –Slight changes in the growth can be overlooked in the current methodology of nanomaterial characterization, possibly leading to inaccurate conclusions regarding the control of growth mechanism. –Offers the advantage of observing and quantifying subtle changes in the growth of a particular nanostructure as a function of the processing variables. An important step towards large-scale controlled synthesis of CdSe nanostructures.

20. Further Challenges The profile of some of the experimental factors (e.g., temperature) change over time and this plays a crucial role in synthesis of nanostructures. –From functional response to functional factors ? Challenges in both design and analysis. Complete disappearance of morphology in some experimental regions makes exploration of optima extremely difficult. –This would require a new design strategy. A combination of sequential and space-filling designs? Work in progress.

21. Modeling mean and variance of log-odds ratios in terms of set-values