Statistical Modeling and Analysis for Robust Synthesis of Nanostructures

AbstractWe systematically investigate the best process conditions that ensure synthesis of different types of one-dimensional cadmium selenide nanostructures with high yield and reproducibility. Through a designed experiment and rigorous statistical analysis of experimental data, models linking the probabilities of obtaining specific morphologies to the process variables are developed. A new iterative algorithm for fitting a multinomial generalized linear model is proposed and used. The optimum process conditions, which maximize the preceding probabilities and make the synthesis process robust (i.e., less sensitive) to variations in process variables around set values, are derived from the fitted models using Monte Carlo simulations.Cadmium selenide has been found to exhibit one-dimensional morphologies of nanowires, nanobelts, and nanosaws, often with the three morphologies being intimately intermingled within the as-deposited material. A slight change in growth condition can result in a totally different morphology. To identify the optimal process conditions that maximize the yield of each type of nanostructure and, at the same time, make the synthesis process robust (i.e., less sensitive) to variations of process variables around set values, a large number of trials were conducted with varying process conditions. Here, the response is a vector whose elements correspond to the number of appearances of different types of nanostructures. The fitted statistical models would enable nanomanufacturers to identify the probability of transition from one nanostructure to another when changes, even tiny ones, are made in one or more process variables. Inferential methods associated with the modeling procedure help in judging the relative impact of the process variables and their interactions on the growth of different nanostructures. Owing to the presence of internal noise, that is, variation around the set value, each predictor variable is a random variable. Using Monte Carlo simulations, the mean and variance of transformed probabilities are expressed as functions of the set points of the predictor variables. The mean is then maximized to find the optimum nominal values of the process variables, with the constraint that the variance is under control.KEY WORDS: Cadmium selenide nanostructuresGeneralized linear modelMultinomialNanotechnologyRobust designStatistical modeling