A physical–statistical model for density control of nanowires

Abstract

In order to develop a simple, scalable, and cost-effective technique for controlling zinc oxide nanowire array growth density, layer-by-layer polymer thin films were used in a solution-based growth process. The objective of this article is to develop a model connecting the thickness of polymer films to the observed density of nanowires that would enable prediction, and consequently control, of nanowire array density. A physical–statistical model that incorporates available physical knowledge of the process in a statistical framework is proposed. Model parameters are estimated using the maximum likelihood method. Apart from helping scientists achieve the basic objective of prediction control and quantification of uncertainty, the model facilitates a better understanding of the fundamental scientific phenomena that explain the growth mechanism.

Keywords:

• Nanotechnology
• diffusion
• Poisson GLM
• maximum likelihood
• Fisher information

Acknowledgement

The research of Joseph was supported by the U.S. National Science Foundation under grants DMS-0706436 and CMMI-0654369. The research of Dasgupta was supported by the U.S. National Science Foundation under grant CMMI-1000720.