Gaussian process regression approach for robust design and yield enhancement of self-assembled nanostructures

Self-assembled nanostructures are increasingly used for nanoelectronic and optoelectronic applications due to their high surface area to volume ratio and their ability to break traditional lithography limits. However, they suffer due to poor yield and repeatability as the growth process is often not well studied or optimized. Gaussian process regression (GPR) is a machine learning technique that can be used for both regression and classification purpose. In the GPR framework, a probability measure is defined according to one prior belief about the response surface and the Bayesian rule is applied to combine the observations with prior beliefs to form a posterior distribution of the response surface, which is known as the “surrogate model”. We propose here the use of GPR as an effective statistical tool to optimize the growth conditions of nanostructures so as to improve their yield, controllability and repeatability ensuring at the same time that the yield is not affected by process variations at the identified optimum process conditions. In effect, we are proposing a design for reliability and robust design strategy for optimization of self-assembled nanostructure growth. We present here a case study of cadmium selenide nanostructures making use of an extensive design of experiment result (available open source) to illustrate the proposed methodology. The prediction accuracy of GPR is compared with two other commonly used statistical models → binomial and multinomial logistic regression. The use of the GPR method resulted in much better accuracy of probabilistic prediction of the different nanostructures with fewer fitting parameters than the logistic regression method.