Multifractal analysis of line-edge roughness

Vassilios Constantoudis; George Papavieros; Gian Lorusso; Vito Rutigliani; Frieda van Roey; Evangelos Gogolides

doi:10.1117/12.2306508

13 March 2018 Multifractal analysis of line-edge roughness

Vassilios Constantoudis, George Papavieros, Gian Lorusso, Vito Rutigliani, Frieda van Roey, Evangelos Gogolides

Proceedings Volume 10585, Metrology, Inspection, and Process Control for Microlithography XXXII; 1058534 (2018) https://doi.org/10.1117/12.2306508
Event: SPIE Advanced Lithography, 2018, San Jose, California, United States

Abstract

In this paper, we propose to rethink the issue of LER characterization on the basis of the fundamental concept of symmetries. In LER one can apply two kinds of symmetries: a) the translation symmetry characterized by periodicity and b) the scaling symmetry quantified by the fractal dimension. Up to now, a lot of work has been done on the first symmetry since the Power Spectral Density (PSD), which has been extensively studied recently, is a decomposition of LER signal into periodic edges and quantification of the ‘power’ of each periodicity at the real LER. The aim of this paper is to focus on the second symmetry of scaling invariance. Similarly to PSD, we introduce the multifractal approach in LER analysis which generalizes the scaling analysis of standard (mono)fractal theory and decomposes LER into fractal edges characterized by specific fractal dimensions. The main benefit of multifractal analysis is that it enables the characterization of the multi-scaling contributions of different mechanisms involved in LER formation. In the first part of our work, we present concisely the multifractal theory of line edges and utilize the Box Counting method for its implementation and the extraction of the multifractal spectrum. Special emphasis is given on the explanation of the physical meaning of the obtained multifractal spectrum whose asymmetry quantifies the degree of multifractality. In addition, we propose the distinction between peak-based and valley-based multifractality according to whether the asymmetry of the multifractal spectrum is coming from the sharp line material peaks to space regions or from the cavities of line materis (edge valleys). In the second part, we study systematically the evolution of LER multifractal spectrum during the first successive steps of a multiple (quadruple) patterning lithography technique and find an interesting transition from a peak-based multifractal behavior in the first litho resist LER to a valley-based multifractality caused mainly by the effects of etch pattern transfer steps.

Citation Download Citation

Vassilios Constantoudis, George Papavieros, Gian Lorusso, Vito Rutigliani, Frieda van Roey, and Evangelos Gogolides "Multifractal analysis of line-edge roughness", Proc. SPIE 10585, Metrology, Inspection, and Process Control for Microlithography XXXII, 1058534 (13 March 2018); https://doi.org/10.1117/12.2306508

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available