The Effect of Scattering of Phonons, Surface and Grain Boundary on electrical Properties for Tungsten Nanometallic

Authors

Ammar R. Alzobaie Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. https://orcid.org/0009-0003-8341-673X
May A. Mohammed Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0003-3883-402X
Haider F. Abdul Amir University of Algoma, Canada. https://orcid.org/0009-0003-5974-1444

DOI:

https://doi.org/10.30526/38.4.4118

Keywords:

Tungsten, Mayadas, Nanometals, Scattering, Resistivity

Abstract

In the context of increasing the use of nanometals in electrical and electronic applications and improving their unique electrical properties, this research explains the effect of the mechanisms of scattering of phonons at room-temperature (293K) in addition to the scattering and reflection of electrons at the surface and at grain boundary on the electrical resistivity of Tungsten metal at different thicknesses. The electrical resistivity of Tungsten was obtained by solving the Boltzmann transport equation which the electron scattering coefficient at the surface (p) is calculated by the Fuch-Sondheimer model, and the grain boundary reflection coefficient (R) by the Mayadas-Shatzkes model were calculated as (p=0.89) and (R=0.18) for Tungsten metal based on the mean of the free path of the electrons. The results showed that there is a linear relationship between the mechanisms of scattering and resistivity, and an inverse relation between electrical resistivity (ρ) and the thickness of the nanometal (d) and extending to a large range of thicknesses. Moreover, the defects of the crystal lattice and the roughness of the surface have an evident impact on the electrical properties of Tungsten metal. In addition, we obtained an excellent consistency between experimental data and theoretical results of electrical resistivity. These results provide important predictions for the use of nano-Tungsten as an interconnection between micro integrated electronic circuits and in various electrical devices

Author Biographies

Ammar R. Alzobaie , Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq.

Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq.
May A. Mohammed , Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq.

Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq.
Haider F. Abdul Amir , University of Algoma, Canada.

University of Algoma, Canada.

References

1. Rossnagel SM, Kuan TS. Alteration of Cu conductivity in the size effect regime. J Vac Sci Technol B . 1 January 2004; 22 (1): 240–247. https://doi.org/10.1116/1.1642639

2. Plombon JJ, Andideh E, Dubin VM, Maiz J. Influence of phonon, geometry, impurity, and grain size on copper line resistivity. Appl Phys Lett. 11 September 2006; 89 (11): 113-124. https://doi.org/10.1063/1.2355435

3. Maîtrejean S, Gers R, Mourier T, Toffoli A, Passemard G. Experimental measurements of electron scattering parameters in Cu narrow lines. Microelectron Eng. 2006;83(11–12): 2396-2401. https://doi.org/10.1016/j.mee.2006.10.044

4. Kapur P, Chandra G, McVittie JP, Saraswat KC. Technology and reliability constrained future copper interconnects. II. Performance implications. IEEE Trans. Electron Devices. 2002;49(4):598–604. https://doi.org/10.1109/16.992867

5. Kapur P, McVittie JP, Saraswat KC. Technology and reliability constrained future copper interconnects. I. Resistance modeling. IEEE Trans. Electron Devices. 2002;49(4):590–597. https://doi.org/10.1109/16.992867

6. Fuchs K. The conductivity of thin metallic films according to the electron theory of metals. In: Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press; 1938;34(1):100–108. https://doi.org/10.1017/S0305004100019952

7. Sondheimer EH. The mean free path of electrons in metals. Adv Phys. 2001;50(6):499–537. https://doi.org/10.1080/00018730110102187

8. Zhang XG, Butler WH. Conductivity of metallic films and multilayers. Phys Rev B. 1995;51(15):10085. https://doi.org/10.1103/PhysRevB.51.10085

9. Mayadas AF, Shatzkes M, Janak JF. Electrical resistivity model for polycrystalline films: the case of specular reflection at external surfaces. Appl Phys Lett. 1969;14(11):345–347.https://doi.org/10.1063/1.1652680

10. Meteab FA, Mohammed MAS. The Effect of Phonons-Surface and Grain-Boundary Scattering on Electrical Properties of Metallic Ag. 2023;6(4):182–187. https://doi.org/10.30526/36.4.3234

11. Mayadas AF, Shatzkes M. Electrical-resistivity model for polycrystalline films: The case of arbitrary reflection at external surfaces. Phys Rev B. 1970;1(4):1382–1389. https://doi.org/10.1103/PhysRevB.1.1382

12. Tešanović Z, Jarić M V, Maekawa S. Quantum transport and surface scattering. Phys Rev Lett. 1986;57(21):2760. https://doi.org/10.1103/PhysRevLett.57.2760

13. Trivedi N, Ashcroft NW. Quantum size effects in transport properties of metallic films. Phys Rev B. 1988;38(17):12298. https://doi.org/10.1103/PhysRevB.38.12298

14. Meyerovich AE, Ponomarev I V. Surface roughness and size effects in quantized films. Phys Rev B. 2002;65(15):155413. https://doi.org/10.1103/PhysRevB.65.155413

15. Moors K, Sorée B, Magnus W. Modeling surface roughness scattering in metallic nanowires. J Appl Phys. 2015;118(12). https://doi.org/10.1063/1.4931573

16. Hegde G, Povolotskyi M, Kubis T, Boykin T, Klimeck G. An environment-dependent semi-empirical tight binding model suitable for electron transport in bulk metals, metal alloys, metallic interfaces, and metallic nanostructures. I. Model and validation. J Appl Phys. 2014;115(12). https://doi.org/10.1063/1.4868977

17. Jones SLT, Sanchez-Soares A, Plombon JJ, Kaushik AP, Nagle RE, Clarke JS, et al. Electron transport properties of sub-3-nm diameter copper nanowires. Phys Rev B. 2015;92(11):115413. https://doi.org/10.1103/PhysRevB.92.115413

18. Munoz RC, Arenas C. Size effects and charge transport in metals: Quantum theory of the resistivity of nanometric metallic structures arising from electron scattering by grain boundaries and by rough surfaces. Appl Phys Rev. 2017;4(1). https://doi.org/10.1063/1.4974032

19. Lanzillo NA. Ab Initio evaluation of electron transport properties of Pt, Rh, Ir, and Pd nanowires for advanced interconnect applications. J Appl Phys. 2017;121(17). https://doi.org/10.1063/1.4983072

20. Choi D, Wang B, Chung S, Liu X, Darbal A, Wise A, et al. Phase, grain structure, stress, and resistivity of sputter-deposited tungsten films. J Vac Sci Technol A. 2011;29(5). https://doi.org/10.1116/1.3622619

21. Choi D, Kim CS, Naveh D, Chung S, Warren AP, Nuhfer NT, et al. Electron mean free path of tungsten and the electrical resistivity of epitaxial (110) tungsten films. Phys Rev B—Condensed Matter Mater Phys. 2012;86(4):45432. ‏https://doi.org/10.1103/PhysRevB.86.045432

22. Choi D, Moneck M, Liu X, Oh SJ, Kagan CR, Coffey KR, et al. Crystallographic anisotropy of the resistivity size effect in single crystal tungsten nanowires. Sci Rep. 2013;3(1):2591. https://doi.org/10.1038/srep02591

23. Choi D, Liu X, Schelling PK, Coffey KR, Barmak K. Failure of semiclassical models to describe resistivity of nanometric, polycrystalline tungsten films. J Appl Phys. 2014;115(10). https://doi.org/10.1063/1.4868093

24. Choi D. The electron scattering at grain boundaries in tungsten films. Microelectron Eng. 2014;122:5–8. https://doi.org/10.1016/j.mee.2014.03.012

25. Hau-Riege CS. An introduction to Cu electromigration. Microelectron Reliab. 2004;44(2):195–205. ‏ https://doi.org/10.1016/j.microrel.2003.10.020

26. Choi D, Barmak K. On the potential of tungsten as next-generation semiconductor interconnects. Electron Mater Lett. 2017;13:449–456. https://doi.org/10.1007/s13391-017-1610-5

27. Xu DE, Chow J, Mayer M, Jung JP, Yoon JH. Sn-Ag-Cu to Cu joint current aging test and evolution of resistance and microstructure. Electron Mater Lett. 2015;11:1078–1084. https://doi.org/10.1007/s13391-015-5201-z

28. Sharma A, Xu DE, Chow J, Mayer M, Sohn HR, Jung JP. Electromigration of composite Sn-Ag-Cu solder bumps. Electron Mater Lett. 2015;11:1072–1077. https://doi.org/10.1007/s13391-015-4454-x

29. Choi D, Barmak K. On the potential of tungsten as next-generation semiconductor interconnects. Electron Mater Lett. 2017;13:449–456. https://doi.org/10.1007/s13391-017-1610-5

30. Sun T, Yao B, Warren AP, Barmak K, Toney MF, Peale RE, et al. Surface and grain-boundary scattering in nanometric Cu films. Phys Rev B—Condensed Matter Mater Phys. 2010;81(15):155454. https://doi.org/10.1103/PhysRevB.81.155454

31. Sondheimer EH. The influence of a transverse magnetic field on the conductivity of thin metallic films. Phys Rev. 1950;80(3):401. https://doi.org/10.1103/PhysRev.80.401‏

32. Sun T, Yao B, Warren AP, Barmak K, Toney MF, Peale RE, et al. Dominant role of grain boundary scattering in the resistivity of nanometric Cu films. Phys Rev B—Condensed Matter Mater Phys. 2009;79(4):41402. https://doi.org/10.1103/PhysRevB.79.041402.

33. Almajedi RF, Mohammed MAS. The effect of scattering of phonons, size and grain boundary on electrical properties for (Co and Ni) nano metals. In: J Physics: Conference Series. IOP Publishing; 2024. p. 12009. https://doi.org/10.1088/1742-6596/2857/1/012009.

34. Alderbas FAM, Najeeb MAS. The effect of phonons-surface and grain-boundary scattering on electrical properties of metallic Al, Cu. In: AIP Conference Proceedings. AIP Publishing; 2023. https://doi.org/10.1063/5.0172558

35. Renucci P, Gaudart L, Petrakian JP, Roux D. Electron transport properties of magnesium thin films. Thin Solid Films. 1985;130(1–2):75–86. https://doi.org/10.1016/0040-6090(85)90297-4.

36. Harbbi KH. Effect of the Synthesis Time on Structural Properties of Copper Oxide. Ibn AL-Haitham J Pure Appl Sci. 2023;36(2):181–190. https://doi.org/doi.org/10.30526/36.2.3024.

37. Wadi KM, Jasim KA, Shaban AH, Kamil MK, Nsaif FK. The effects of sustainable manufacturing pressure on the structural properties of the pb2ba2ca2cu3o9+ σ compound. J Green Eng. 2020;10(9):6052–6062. https://doi.org/10.1088/1757-899X/1258/1/012008.

38. Al-Saadi TM. Investigating the Structural and Magnetic Properties of Nickel Oxide Nanoparticles Prepared by Precipitation Method. Ibn Al-Haitham J Pure Appl Sci. 2022;35(4):94–103. https://doi.org/10.30526/35.4.2872.

39. Lim JW, Mimura K, Isshiki M. Thickness dependence of resistivity for Cu films deposited by ion beam deposition. Appl Surf Sci. 2003;217(1–4):95–99. https://doi.org/10.1016/S0169-4332(03)00522-1.

40. Meteab FA, Mohammed MAS. The Effect of Phonons-Surface and Grain-Boundary Scattering on Electrical Properties of Metallic Ag. Ibn Al-Haitham J Pure Appl Sci. 2023;6(4):182–187. https://doi.org/10.30526/36.4.3234.

41. Ahmed ZW, Khadim AI, ALsarraf AHR. The effect of doping with some rare earth oxides on electrical features of ZnO varistor. Energy Procedia. 2019;157:909–917. https://doi.org/10.1016/j.egypro.2018.11.257.