Modeling of material parameters of transparent electrode films with near-zero permittivity

Aim. We investigate the effect of the material parameters of a transparent metal oxide electrode (N is the electron density, and τ is the average electron scattering time) on the frequency at which the dielectric constant of the material ε (epsilon) becomes close to zero (the so-called ENZ materials).

Methodology. Using the Drude model, the parameters N, τ and the plasma frequency ω0 are calculated in the range of parameters of materials used in electronics, as well as for composite materials with different geometries of inclusions. The parameters of materials based on zinc oxide and methods of their formation are presented, in which the described regime of the dielectric constant of the material close to zero can be realized.

Results. For a number of materials of transparent electrode films used in near-IR radiation control devices, the influence of material parameters (N and τ) on the frequency at which the dielectric constant of the material ε (epsilon) becomes close to zero (ENZ materials) is studied. The technologies of materials in which the ENZ mode can be implemented are described.

Research implications. The described mode is implemented for a number of transparent electrode film materials used in near-IR radiation control devices.

1. Silveirinha M. G., Alù A., Edwards B., Engheta N. Overview of Theory and Applications of Epsilon-Near-Zero Materials. In: URSI General Assembly (Chicago, IL, USA, August 8-16, 2008). Available at: https://www.ursi.org/proceedings/procGA08/papers/B01p6.pdf (accessed: 16.12.2022)

2. Ni J. H., Sarney W. L., Leff A. C., Cahill J. P., Zhou W. Property Variation in Wavelength-thick Epsilon-Near-Zero ITO Metafilm for Near-IR Photonic Devices. In: Scientific Reports, 2020, vol. 10, pp. 713. DOI: 10.1038/s41598-020-57556-z.

3. Lotkov E. S., Baburin A. S., Ryzhikov I. A., Sorokina O. S., Ivanov A. I., Zverev A. V., Ryzhkov V. V., Bykov I. V., Baryshev A. V., Panfilov Yu. V., Rodionov I. A. ITO film stack engineering for low-loss silicon optical modulators. In: Scientific Reports, 2022, vol. 12, article number: 6321. DOI: 10.1038/s41598-022-09973-5.

4. Kim J., Dutta A., Naik G. V., Giles A. J., Bezares F. J., Ellis C. T., Tischler J. G., Mahmoud A. M., Caglayan H., Glembocki O. J., Kildishev A. V., Caldwell J. D., Boltasseva A., Engheta N. Role of epsilon-near-zero substrates in the optical response of plasmonic antennas. In: Optica, 2016, vol. 3, iss. 3, pp. 339–346. DOI: 10.1364/OP-TICA.3.000339.

5. Argyropoulos C., Chen P.-Y., D’Aguanno G., Engheta N., Alú A. Boosting optical nonlin-earities in epsilon-near-zero plasmonic channels. In: Physical Review B, 2012, vol. 85, iss. 4, article: 045129. DOI: 10.1103/PhysRevB.85.045129.

6. Alam M. Z., De Leon I., Boyd R. W. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. In: Science, 2016, vol. 352, iss. 6287, pp. 795–797. DOI: 10.1126/science.aae0330.

7. Engheta N. Pursuing Near-Zero Response. In: Science, 2013, vol. 340, iss. 6130, pp. 286–287. DOI: 10.1126/science.1235589.

8. Ma Z., Li Z., Liu K., Ye C., Sorger V. J. Indium-Tin-Oxide for High-performance Electro-optic Modulation. In: Nanophotonics, 2015, vol. 4, iss. 2, pp. 198–213. DOI: 10.1515/nanoph-2015-0006.

9. Silveirinha M., Engheta N. Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials. In: Physical Review Letters, 2006, vol. 97, iss. 15, article: 157403. DOI: 10.1103/PHYSREVLETT.97.157403.

10. Silveirinha M. G., Engheta N. Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using epsilon-near-zero metamaterials. In: Physical Review B, 2007, vol. 76, iss. 24, article: 245109. DOI: 10.1103/PhysRevB.76.245109.

11. Liu R., Cheng Q., Hand T., Mock J., Cui T. Experimental Demonstration of Electromagnetic Tunneling Trough an Epsilon-Near-Zero Metamaterial at Microwave Frequencies. In: Physical Review Letters, 2008, vol. 100, iss. 2, article: 023903. DOI: 10.1103/PhysRevLett.100.023903.

12. Feng S., Halterman K. Coherent perfect absorption in epsilon-near-zero metamaterials. In: Physical Review B, 2012, vol. 86, iss. 16, article: 165103. DOI: 10.1103/PhysRevB.86.165103.

13. Edwards B., Alu A., Young M. E., Silveirinha M., Engheta N. Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave wave-guide. In: Physical Review Letters, 2008, vol. 100, iss. 3, article: 033903. DOI: 10.1103/PhysRevLett.100.033903.

14. Yang X., Hu C., Deng H., Rosenmann D., Czaplewski D. A., Gao J. Experimental demonstration of near-infrared epsilon-near-zero multilayer metamaterial slabs. In: Optics Express, 2013, vol. 21, iss. 20, pp. 23631–23639. DOI: 10.1364/OE.21.023631.

15. Gao J., Sun L., Deng H., Mathai C. J., Gangopadhyay S., Yang X. Experimental realization of epsilon-near-zero metamaterial slabs with metal-dielectric multilayers. In: Applied Physics Letters, 2013, vol. 103, iss. 5, pp. 051111. DOI: 10.1063/1.4817678

16. West P. R., Ishii S., Naik G. V., Emani N. K., Shalaev V. M., Boltasseva A. Searching for better plasmonic materials. In: Laser & Photonics Review, 2010, vol. 4, iss. 6, pp. 795–808. DOI: 10.1002/lpor.200900055.

17. Boltasseva A., Atwater H. A. Low-Loss Plasmonic Metamaterials. In: Science, 2011, vol. 331, no. 6015, pp. 290–291. DOI: 10.1126/science.1198258.

18. Vasudev A., Kang J., Park J., Liu X., Brongersma M. Electro-optical modulation of a silicon waveguide with an epsilon-near-zero material. In: Optics Express, 2013, vol. 21, iss. 22, pp. 26387–26397. DOI: 10.1364/OE.21.026387.

19. Tiwald T. E., Tompson D. W., Woollam J. A., Paulson W., Hance R. Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles. In: Thin Solid Films, 1998, vol. 313–314, pp. 661–666. DOI: 10.1016/S0040-6090(97)00973-5.

20. Kinsey N., Khurgin J. Nonlinear epsilon-near-zero materials explained: opinion. In: Optical Materials Express, 2019, vol. 9, iss. 7, pp. 2793–2796. DOI: 10.1364/OME.9.002793.

21. Wu J., Xie Z. T., Sha Y., Fu H. Y., Li Q. Epsilon-near-zero photonics: infinite potentials. In: Photonics Research, 2021, vol. 9, iss. 8, pp. 1616–1643. DOI: 10.1364/PRJ.427246.

22. Zagrubskiy A. A., Chernova A. P. Statistika nositelei zaryada i kineticheskie protsessy [Statistics of Charge Carriers and Kinetic Processes]. St. Petersburg, St. Petersburg State University Publ., 2007. 223 p.

23. Secondo R., Khurgin J., Kinsey N. Absorptive loss and band non-parabolicity as a physical origin of large nonlinearity in epsilon-near-zero materials. In: Optical Materials Express, 2020, vol. 10, iss. 7, pp. 1545–1560. DOI: 10.1364/OME.394111.

24. Pchelintsev A. N., Shishin V. A. [Relaxation time of electron conduction in metal]. In: Vestnik Tambovskogo gosudarstvennogo tekhnicheskogo universiteta [Transactions of the Tambov State Technical University], 2003, vol. 9, no. 3, pp. 464–468.

25. Borisenko S. I. [Scattering of electrons at impurity ions at low temperatures in a superlattice with doped quantum wells]. In: Fizika i tekhnika poluprovodnikov [Semiconductors], 2003, vol. 37, no. 9, pp. 1117–1122.

26. Gintilas Sh. Z., Denis V. I., Martunas Z., Shetkus A. P. [Temperature dependence of intervalley relaxation time in electronic silicon]. In: Fizika i tekhnika poluprovodnikov [Semiconductors], 1984, vol. 18, no 2, pp. 324–326.

27. Gantmakher V. F., Petrashov V. T. [Scattering of conduction electrons in pure metals]. In: Metally vysokoi chistoty [Metals of high purity]. Moscow, Nauka Publ., 1976, pp. 31–59.

28. Gantmakher V. F., Levinson I. B. Rasseyanie nositelei toka v metallakh i poluprovodnikakh [Scattering of current carriers in metals and semiconductors]. Moscow, Nauka Publ., 1984. 352 p.

29. Litvinov E. A., Vozianova A. V., Khodzitsky M. K. Epsilon-Near-Zero metal-dielectric composite for terahertz frequency range. In: Journal of Physics: Conference Series, 2018, vol. 1062: IX International conference “Basic Problems of Optics” BPO'2016 (17–21 October 2016, Saint-Petersburg, Russian Federation), pp. 012010. DOI: 10.1088/1742-6596/1062/1/012010.

30. Kroger F. Khimiya nesovershennykh kristallov [Chemistry of imperfect crystals]. Moscow, Mir Publ., 654 p.

31. Ozgur U., Alivov Y. I., Liu C., Tekeb A., Reshchikov M. A., Doğanc S., Avrutin V., Cho S.-J., Morkoçd H. A comprehensive review of ZnO materials and devices. In: Journal of Applied Physics, 2005, vol. 98, iss. 4, article: 041301. DOI: 10.1063/1.1992666.

32. Ellmer K., Mientus R. Carrier Transport in Polycrystalline ITO and ZnO:Al II: The Influence of Grain Barriers and Boundaries. In: Thin Solid Films, 2008, vol. 516, iss. 17, pp. 5829–5835. DOI: 10.1016/j.tsf.2007.10.082.

33. Gilmer G. H., Huang H., de la Rubia T. D., Torre J. D., Baumann F. H. Lattice Monte Carlo models of thin film deposition. In: Thin Solid Films, 2000, vol. 365, iss. 2, pp. 189–200. DOI: 10.1016/S0040-6090(99)01057-3.

34. Abduev A., Akhmedov A., Asvarov A., Kamilov I., Sulyanov S. Growth Mechanism of ZnO Layers. In: Nickel N. H., Terukov E., eds. Zinc Oxide – A Material for Micro- and Optoelectronic Applications: Proceedings of the NATO Advanced Research Workshop on Zinc Oxide as a Material for Micro- and Optoelectronic Applications (St. Petersburg, Russia, from 23 to 25 June 2004). Dordrecht, Springer, 2005, pp. 15–24 (NATO Science Series II: Mathematics, Physics and Chemistry. Vol. 194).

35. Ellmer K., Klein A., Rech B., eds. Transparent conductive zinc oxide: basics and applications in thin film solar cells. Berlin, Springer, 2008. 443 p. (Springer Series in Materials Science (SSMATERIALS), vol. 104).

36. Asvarov A., Abduev A., Akhmedov A., Kanevsky V. On the Effect of the Co-Introduction of Al and Ga Impurities on the Electrical Performance of Transparent Conductive ZnO-Based Thin Films. In: Materials (Basel), 2022, vol. 15, iss. 17, pp. 5862. DOI: 10.3390/ma15175862.

37. Cohen D. J., Barnett S. A. Predicted electrical properties of modulation-doped ZnO-based transparent conducting oxides. In: Journal of Applied Physics, 2005, vol. 98, iss. 5, pp. 053705. DOI: 10.1063/1.2035898.