Computational nanometrology of nanostructures: the challenge of spatial complexity

Institute of Nanoscience and Nanotechnology, NCSR Demokritos, Aghia Paraskevi, 15341 Greece

Abstract

Several applications of nanotechnology are based on the surface nanopatterning of materials and the new functionalities it brings about. Not surprisingly, the novel material properties are tightly linked to nanostructure morphology and very sensitive to its geometrical characteristics. Therefore, the measurement and characterization of nanostructure morphology is very critical in order to get control of the added value of nanopatterning on material properties and functionalities. In other words, there is an emergent need for accurate and concise metrology of all kinds of nanostructures.

Up to now, the main tools for imaging and measuring the nanostructures are the well-known and widely used probe microscopes (AFM, SEM, TEM). However, due to the minute size of the measured structures, the measurement results are strongly dependent on the effects of measuring device and process. In order to get as more accurate measurement as possible, it is necessary to deconvolute the true structure from the effects of measurement. This can be made through the development and implementation of mathematical modeling methods able to get control of the measurement effects on the result and aid the acquisition of the true morphology. Furthermore, novel mathematical and computational methods are required in the characterization of complex surface nanostructures created by deposition, etching, ion bombardment or laser treatment of surfaces. The mathematical and computational methods needed to aid the accurate and complete metrology of surface nanostructures are collectively defined by the term computational nanometrology.

In this paper, first we shortly introduce the field of computational nanometrology and define its content. Then we focus on two specific applications to demonstrate the benefits of computational nanometrology. In the first, a new mathematical transform is proposed to enable the simultaneous characterization of both periodicity and feature width in almost periodic arrangements of nanodots on a surface. In the second, the multifractal spectrum of complex nanomorphologies is calculated to quantify their multiscale hierarchical structuring. Both methodologies are motivated and applied to the characterization of polymer surfaces after their treatment in plasma reactors.