Influence of the grain size effect on the coefficients of reflection, transmission, and absorption of microwaves by the polycrystalline metal films. Abstract

Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 10
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DOI https://doi.org/10.30898/1684-1719.2020.10.5

UDC 538.975: 539.216.2: 621.371

influence of the grain size effect on the coefficients of reflection, transmission, and absorption of microwaves by the polycrystalline metal films

I. I. Pyataikin

Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia

The paper is received on October 20, 2020

Abstract. The influence of size effect on the , , and coefficients characterizing reflection, transmission, and absorption of microwaves by polycrystalline metal films is studied. Using the example of gold films, the article examines the influence of internal size effect due to their polycrystalline structure on the value of the parameter that determines the dependence of the , and coefficients on the film thickness. It was found that, depending on the value of the reflection coefficient of electrons striking the grain boundaries, parameter calculated using the Mayadas-Shatzkes-Janak (MSJ) theory for grain size effect differs by two to five times from that obtained in calculations based on the use of the Fuchs-Sondheimer theory for thickness size effect. The dependence of on the parameters determining the grain growth rate and limiting grain size has been established, which made it possible to reveal the effect of the film microstructure on the dependence of the , and coefficients on the film thickness. Based on the revealed character of the dependence of on the parameters of the MSJ theory and the structural parameters of the film, recommendations are proposed for choosing the metals that are most optimal for producing coatings for electromagnetic interference shielding.

Key words: size effect, grain size effect, Mayadas-Shatzkes-Janak theory, microwave reflection coefficient, microwave absorption coefficient, coatings for electromagnetic interference shielding.

References

1.     Stratton J.A. Electromagnetic Theory. N.Y., London, McGraw-Hill Book Company. 1941. 631 p.

2.     Kaplan A.E. On the reflectivity of metallic films at microwave and radio frequencies. Radio Engineering and Electronic Physics. 1964. Vol.9. No.10. P.1476-1481. Available at: http://psi.ece.jhu.edu/kaplan1/PUBL/AEK.pubs/RUSS/3.pdf

3.     Kaplan A.E. Metallic nanolayers: a sub-visible wonderland of optical properties. Journal of the Optical Society of America B. 2018. Vol.35. No.6. P.1328-1340. https://doi.org/10.1364/JOSAB.35.001328

4.     Fuchs K. The conductivity of thin metallic ﬁlms according to the electron theory of metals. Mathematical Proceedings of the Cambridge Philosophical Society. 1938. Vol.34. No.1. P.100-108. https://doi.org/10.1017/S0305004100019952

5.     Sondheimer E.H. The mean free path of electrons in metals. Advances in Physics. 1952. Vol.1. No.1. P.1-42. https://doi.org/10.1080/00018735200101151

6.     Mayadas A.F., Shatzkes M., Janak J.F. Electrical resistivity model for polycrystalline films: the case of specular reflection at external surfaces. Applied Physics Letters. 1969. Vol.14. No.11. P.345-347. https://doi.org/10.1063/1.1652680

7.     Mayadas A.F., Shatzkes M. Electrical-Resistivity Model for Polycrystalline Films: the Case of Arbitrary Reflection at External Surfaces. Phys. Rev. B. 1970. Vol.1. No.4. P.1382- 1389. https://doi.org/10.1103/PhysRevB.1.1382

8.     Larson D.C. Size-Dependent Electrical Conduction in Thin Metal Films and Wires.In Physics of Thin Films: Advances in Research and Development, Ed. by Francombe M.H., Hoffman R.W. New York and London, Academic Press. 1971. Vol.6. P.81-149. https://doi.org/10.1016/B978-0-12-533006-0.50009-8

9.     Andreev V.G., Vdovin V.A., Pronin S.M., Khorin I.A. Measurements of the optical coefficients of nanometer-thick metallic films at frequency of 10 GHz. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2017. No.11. Available at: http://jre.cplire.ru/jre/nov17/17/text.pdf (In Russian)

10. Camacho J.M., Oliva A.I. Surface and grain boundary contributions in the electrical resistivity of metallic nanofilms. Thin Solid Films. 2006. Vol.515. P.1881-1885. https://doi.org/10.1016/j.tsf.2006.07.024

11. Sambles J.R, Elsom K.C., Jarvis D.J. The electrical resistivity of gold films. Phil. Trans. R. Soc. Lond., Ser. A. 1982. Vol.304. No.1486. P.365-396. https://doi.org/10.1098/rsta.1982.0016

12. Schneider M.A., Wenderoth M., Heinrich A.J., Rosentreter M.A., Ulbrich R.G. Current transport through single grain boundaries: A scanning tunneling potentiometry study. Applied Physics Letters. 1996. Vol.69. No.9. P.1327- 1329. https://doi.org/10.1063/1.117583

13. Babichev A.P., Babushkina N.A., Bratkovskii A.M. et al. Fizicheskie velichiny: Spravochnik. [Physical Quantities: a Handbook], Ed. by Grigor’ev I.S., Meylikhov E.Z. Moscow, Energoatomizdat Publ. 1991. 1232 p. (In Russian)

14. Klages S., Schöck M., Sürgers C., Löhneysen H. v. Electronic Transport in Ultrathin Gold Films on Si(111). Journal of Low Temperature Physics. 2004. Vol.137. No.3/4. P.509- 522. https://doi.org/10.1023/B:JOLT.0000049068.94956.26

15. Lucas M.S.P. The effects of surface layers on the conductivity of gold films. Thin Solid Films. 1968. Vol.2. No.4. P.337-352. https://doi.org/10.1016/0040-6090(68)90039-4

16. Galchenkov L.A., Pyataikin I.I. Enhancement of conduction electron reflection specularity in gold films coated with Langmuir-Blodgett nanolayers. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2019. No.11. https://doi.org/10.30898/1684-1719.2019.11.6

17.   Durkan C., Welland M. E. Size effects in the electrical resistivity of polycrystalline nanowires. Phys. Rev. B. 2000. Vol.61. No.20. P.14215- 14218. https://doi.org/10.1103/PhysRevB.61.14215

18. Khorin I., Orlikovsky N., Rogozhin A., Tatarintsev A., Pronin S., Andreev V., Vdovin V. Optical coefficients of nanometer-thick copper and gold films in microwave frequency range. Proc. of SPIE. 2016. Vol.10224. P.1022407-1- 1022407-7. https://doi.org/10.1117/12.2266504

For citation:

Pyataikin I.I. Influence of the grain size effect on the coefficients of reflection, transmission, and absorption of microwaves by the polycrystalline metal films. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No.10. https://doi.org/10.30898/1684-1719.2020.10.5 (In Russian)