Tunneling current of contact of fractal object with metal and superlattice
https://doi.org/10.17586/2220-8054-2023-14-1-54-58
Abstract
In this paper, we study the features of the electric current under conditions of the tunnel effect in fractal structures. Based on the electron dispersion law for fractal objects, an expression for finding the tunneling current is obtained. Current-voltage characteristics are constructed for the following contacts: fractalfractal, fractal-metal, fractal-superlattice. The influence of the fractal dimension on the characteristics of the tunneling current is revealed.
About the Authors
N. N. Konobeeva
Volgograd State University
Russian Federation
Russian Federation
Natalia N. Konobeeva –
University avenue, 100, Volgograd, 400062.
M. B. Belonenko
Volgograd State University
Russian Federation
Russian Federation
Mikhail B. Belonenko –
University avenue, 100, Volgograd, 400062.
References
1. Hausdorff F. Dimension und au¨ βeres Maβ. Math. Ann., 1919, 79, P. 157–179.
2. Heymans O., Fissette J., Vico P., Blacher S., Masset D., Brouers F. Is fractal geometry useful in medicine and biomedical sciences? Med Hypotheses, 2000, 54(3), P. 360-6.
3. Uahabi K.L., Atounti M. Applications of fractals in medicine. Annals of the University of Craiova, Mathematics and Computer Science Series, 2015, 42(1), P. 167–174.
4. Buldyrev S.V. Fractals in Biology. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, 2009, P. 3779–3802.
5. Criscuoli S., Rast M.P., Ermolli I., Centrone M. On the reliability of the fractal dimension measure of solar magnetic features and on its variation with solar activity. Astronomy and Astrophysics, 2007, 461(1), P. 331–338.
6. Husain A., Reddy J., Bisht D., Sajid M. Fractal dimension of coastline of Australia. Scientific Reports, 2021, 11 Article number 6304.
7. Abed A.T., Abu-AlShaer M.J., Jawad A.M.Fractal Antennas for Wireless Communications. In book:Modern Printed-Circuit Antennas Ed. H. Al-Rizzo. IntechOpen, London, 2020, 176 p.
8. De Nicola F., Puthiya Purayil N.S., Spirito D., Miscuglio M., Tantussi F., Tomadin A., De Angelis F., Polini M., Krahne R., Pellegrini V. Multiband plasmonic Sierpinski carpet fractal antennas. ACS Photonics, 2018, 5, P. 2418.
9. Liu W., Wang Z., Wang G., Zeng Q., He W., Liu L., Wang X., Xi Y., Guo H., Hu C., Wang Z.L. Switched-capacitor-convertors based on fractal design for output power management of triboelectric nanogenerator. Nature Communications, 2020, 11 Article number 1883.
10. Menassel R. Optimization of fractal image compression. In book: Fractal Analysis Ed. R. Koprowski, IntechOpen, London, 2020, 128 p.
11. Tiwari A. Fractal applications in electrical and electronics engineering. International Journal of Engineering Science and Advanced Technology, 2012, 2(3), P. 406–411.
12. Fan J.A., Yeo W.-H., Su Y., Hattori Y., Lee W., Jung S.-Y., Zhang Y., Liu Z., Cheng H., Falgout L., Bajema M., Coleman T., Gregoire D., Larsen R.J., Huang Y., Rogers J.A. Fractal design concepts for stretchable electronics. Nature Communications, 2014, 5, Article number 3266.
13. Alexander S., Laerman C., Orbach R., Rosenberg H.M. Fracton interpretation of vibrational properties of crosslinked polimers, glasses and irradiated quartz. Phys. Rev. B., 1983, 28(8), P. 4615–4619.
14. Yoshida B. Exotic topological order in fractal spin liquids. Phys. Rev. B, 2013, 88, P. 125122.
15. Vijay S., Haah J., Fu L. A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations. Phys. Rev. B, 2015, 92, P. 235136.
16. Williamson D.J. Fractal symmetries: Ungauging the cubic code, Phys. Rev. B, 2016, 94, P. 155128.
17. Ma H., Schmitz A.T., Parameswaran S.A., Hermele M., Nandkishore R.M. Topological entanglement entropy of fracton stabilizer codes. Phys. Rev. B, 2018, 97, P. 125101.
18. Slagle K., Kim Y.B. Fracton topological order from nearest-neighbor two-spin interactions and dualities. Phys. Rev. B, 2017, 96, P. 165106.
19. Anderson P.W. Absence of diffusion in certain random lattices, Physical Review, 1958, 109(5), P. 1492–1505.
20. Konobeeva N.N., Belonenko M.B. Sensitivity characteristics of germanene. Nanosystems: physics, chemistry, mathematics, 2018, 9(6), P. 770–774.
21. Zosimov V.V., Lyamshev L.M. Fractals and scaling in acoustics. Acoustical Physics, 1994, 40(5), P. 627–653.
22. Zhikharev L.A. Fractal dimensionalities. Geometry and Graphics, 2018, 6(3), P. 33–48.
23. Adams H., Aminian M., Farnell E., Kirby M., Peterson C., Mirth J., Neville R., Shipman P., Shonkwiler C. A fractal dimension for measures via persistent homology. In: Baas N., Carlsson G., Quick G., Szymik M., Thaule M. (eds), Topological Data Analysis. Abel Symposia, vol 15. Springer, 2020.
24. Levitov L.S., Shitov A.V. Green’s functions. Problems with solutions. Fizmatlit, Moscow, 2003, 392 p.
25. Dalrymple K., Strichartz R.S., Vinson J.P. Fractal differential equations on the Sierpinski gasket. The Journal of Fourier Analysis and Applications, 1999, 5(73), P. 203–284.
26. Fukushima M., Shima T. On a spectral analysis for the Sierpinski gasket. Potential Analysis, 1992, 1, P. 1-35.
27. Strichartz R.S. Analysis on Fractals. Notices of the AMS, 46(10), P. 1199–1208.
28. Strichartz R.S. Some properties of Laplacians on fractals. Journal of Functional Analysis, 1999, 164, P. 181–208.
29. Kim M.H., Yoon D.H., Kim I. Lower and upper bounds for the anomalous diffusion exponent on Sierpinski carpets. J. Phys. A Math. Gen., 1993, 26, P. 5655–5660.
30. Reinhardt H., Kroll M., Karstens S.L., Schlabach S., Hampp N.A., Tallarek U. Nanoscaled fractal superstructures via laser patterning – A versatile route to metallic hierarchical porous materials. Adv. Mater. Interfaces, 2020, 8, P. 2000253.
Review
For citations:
Konobeeva N.N., Belonenko M.B. Tunneling current of contact of fractal object with metal and superlattice. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(1):54-58. https://doi.org/10.17586/2220-8054-2023-14-1-54-58
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