The Influence of AlGaN/GaN Heteroepitaxial Structure Fractal Geometry on Size Effects in Microwave Characteristics of AlGaN/GaN HEMTs

The investigation of size effects appearing in the dependence of AlGaN/GaN HEMT high-frequency characteristics on channel width d and number of sections n is conducted using the notions of measure, metric and normed functional (linear) spaces. In accordance with the results obtained, in local approx...

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Bibliographic Details
Published in:Symmetry (Basel) 2019-12, Vol.11 (12), p.1495
Main Authors: Torkhov, Nikolay A., Babak, Leonid I., Kokolov, Andrey A.
Format: Article
Language:English
Subjects:
Aluminum gallium nitrides
Approximation
Equivalent circuits
Fractal geometry
Fractals
Gallium nitrides
Geometry
High electron mobility transistors
Investigations
Materials science
Mathematical models
Metric space
Optimization
Parameters
Size effects
Structural members
Symmetry
Topology
Transistors
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Summary:The investigation of size effects appearing in the dependence of AlGaN/GaN HEMT high-frequency characteristics on channel width d and number of sections n is conducted using the notions of measure, metric and normed functional (linear) spaces. In accordance with the results obtained, in local approximation the phenomenon of similarity can exist, not only in metric spaces of heteroepitaxial structures, but also in the defined on them functional spaces of the measures of these structures’ additive electrophysical characteristics. This provides means to associate size effects of the HEMTs with their structure material fractal geometry. The approach proposed in the work gives an opportunity, not only to predict the size of the structural elements (e.g., channel width and number of sections) of the transistor with the desired characteristics, but also to reconstruct its compact model parameters, which significantly speeds up the development and optimization of the HEMTs with the desired device characteristics. At transferring to the global approximation, when the topological and fractal dimensions of the structure coincide, its electrophysical characteristics, and subsequently, the values of the compact model equivalent circuit parameters, as well as HEMT high frequency characteristics, follow the classic (linear) laws peculiar to the spaces of integer topological dimensions DT.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11121495