The Fractal Geometry of TiAlNiAu Thin Film Metal System and Its Sheet Resistance (Lateral Size Effect)

This paper investigates the relation between the geometry of metric space of a TiAlNiAu thin film metal system and the geometry of normed functional space of its sheet resistances (functionals), which are elements of the functional space. The investigation provides a means to describe a lateral size...

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Bibliographic Details
Published in:	Symmetry (Basel) Vol. 13; no. 12; p. 2391
Main Authors:	Torkhov, Nikolay Anatolyevich, Evstigneev, Maxim Pavlovich, Kokolov, Andrey Alexandrocivh, Babak, Leonid Ivanovich
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-12-2021
Subjects:	Approximation Electrical resistivity Fractal geometry Fractals functional space Geometry Investigations Metal films Metric space Size effects thin film Thin films Transistors Workflow
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Summary:	This paper investigates the relation between the geometry of metric space of a TiAlNiAu thin film metal system and the geometry of normed functional space of its sheet resistances (functionals), which are elements of the functional space. The investigation provides a means to describe a lateral size effect that involves a dependency in local approximation of sheet resistance Rsq of TiAlNiAu metal film on its lateral linear dimensions (in (x,y) plane). This dependency is defined by fractal geometry of dendrites, or, more specifically, it is a power-law dependency on fractal dimension Df value. The revealed relation has not only fundamental but also a great practical importance both for a precise calculation of thin film metal system Rsq values in designing discreet devices and ICs, and for controlling results at micro- and nanoscale in producing workflow for thin metal films and systems based on them.
ISSN:	2073-8994 2073-8994
DOI:	10.3390/sym13122391