ANALYSIS OF EXISTING MODELS OF STRESS IN THIN FILMS AND COATINGS

О. В. Шорінов

Abstract


The analysis of existing models of stress in thin films and coatings was carried out. While reaching critical value, stress can lead to defects, cracks, delamination of coating from substrate, etc. The task of prediction and controlling of the direction and magnitude of the stress of coating-substrate system is relevant nowadays regardless of coating and thin films deposition methods. Different types of coatings and thin films are widely used in almost all industries: optics, mechanical engineering, measuring technology, medicine, micro- and nanoelectronics, etc. Development and investigation of new promising methods for the formation of nanostructures, such as nanowires in a plasma environment, requires a sufficient theoretical basis for the origin and growing of stresses. Depending on the mechanism, the causes of stress in thin films and coatings can be: chemical reactions, phase transformations, inclusions and impurities, particle bombardment (the cause of internal stress during coating growing); temperature changes (the cause of thermal stress due to different values of coefficients of thermal expansion of coating and substrate materials); deformation of coating-substrate system, etc. Models of stress development in coatings and thin films can be divided into the following groups: stress that occur at the coating-substrate interface, internal coating stress, and stress at the coating-environment interface. The study presents methods of stress measuring in thin films and coatings. Based on the results of the current research, it can be concluded that the existing models of stress in the process of growth of coatings and films, as well as stress arising under the action of external forces, describe only the causes of the stress and unfortunately do not give an understanding of their complex effect on stress-strain state of coating-substrate system and need further development and improvement. Stress relaxation is also important to obtain new structures and certain properties of coatings. The development of stress management tools can be considered as one of the ways to increase the lifetime of products with coatings and thin films.


Keywords


stress-strain state, stress, nanotechnology, thin films and coatings, destruction of coatings

References


Mechanical behavior of metallic thin films on polymeric substrates and the effect of ion beam assistance on crack propagation / M. George, C. Coupeau,, J. Colin, J. Grilhé // Acta Materialia. – 2005. – Vol. 53. – iss. 2. – P. 411-417. DOI: https://doi.org/10.1016/j.actamat.2004.09.036

The influence of a brittle Cr interlayer on the deformation behavior of thin Cu films on flexible substrates: Experiment and model / V. M. Marxab, F. Tothc, A. Wiesinger, J. Berger, Ch. Kirchlechner, M. J. Cordill, F. D. Fischer, F. G. Rammerstorfer, G. Dehma // Acta Materialia. – 2015. – Vol. 89. – P. 278-289. DOI: https://doi.org/10.1016/j.actamat.2015.01.047

Atomic force microscopy study of the morphological shape of thin film buckling / C. Coupeau // Thin Solid Films. – 2002. – Vol. 406, – iss. 1-2. – P. 190-194. DOI: https://doi.org/10.1016/S0040-6090(01)01772-2

An experimental study of the influence of imperfections on the buckling of compressed thin films / M.-W. Moon, J.-W. Chung, K.-R. Lee, K. H. Oh, R. Wang, A. G. Evans // Acta Materialia. – 2002. – Vol. 50. – iss. 5. – P. 1219-1227. DOI: https://doi.org/10.1016/S1359-6454(01)00423-2

How soft substrates affect the buckling delamination of thin films through crack front sink-in / R. Boijoux, G. Parry, J.-Y. Faou, C. Coupeau // Applied Physics Letters. – 2017. – Vol. 110. – iss. 14. – P. 141602. DOI: https://doi.org/10.1063/1.4979614

From telephone cords to branched buckles: A phase diagram / J.-Y. Faou, S. Grachev, E. Barthel, G. Parry // Acta Materialia. – 2017. – Vol. 125. – P. 524-531. DOI: https://doi.org/10.1016/j.actamat.2016.12.025

Enhanced Proton Conductivity in Y‐Doped BaZrO3 via Strain Engineering / A. Fluri, A. Marcolongo, V. Roddatis, A. Wokaun, D. Pergolesi, N. Marzari, T. Lippert // Advanced Science. – 2017. – Vol. 4. – iss. 12. – P. 1700467. DOI: https://doi.org/10.1002/advs.201700467

Growth stress induced tunability of dielectric permittivity in thin films / K. V. L. V. Narayanachari, H. Chandrasekar, A. Banerjee, K. B. R. Varma, R. Ranjan, N. Bhat, S. Raghavan // Journal of Applied Physics. – 2016. – Vol. 119. – iss. 1. – P. 014106. DOI: https://doi.org/10.1063/1.4939466

Sander, D. The correlation between mechanical stress and magnetic anisotropy in ultrathin films / D. Sander // Reports on Progress in Physics. – 1999. – Vol. 62. – iss. 5. – P. 809-858.

Sander, D. The role of surface stress in structural transitions, epitaxial growth and magnetism on the nanoscale / D. Sander, Z. Tian, J. Kirschner // Journal of Physics: Condensed Matter. – 2009. – Vol. 21, iss. 13. – P. 134015. DOI: https://doi.org/10.1088/0953-8984/21/13/134015

Lee, M. L. Strained Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors / M. L. Lee, E. A. Fitzgerald // Journal of Applied Physics. – 2005. – Vol. 95. – iss. 1. – P. 011101. DOI: https://doi.org/10.1063/1.1819976

Vertical Graphene Growth on SiO Microparticles for Stable Lithium Ion Battery Anodes / L. Shi, C. Pang, S. Chen, M. Wang, K. Wang, Z. Tan, P. Gao, J. Ren, Y. Huang, H. Peng, Z. Liu // Nano Letters. – 2017. – Vol. 17. – iss. 6. – P. 3681-3687. DOI: https://doi.org/10.1021/acs.nanolett.7b00906

Growing vertical graphene sheets on natural graphite for fast charging lithium-ion batteries / Y. Mu, M. Han, J. Li, J. Liang, J. Yu // Carbon. – 2021. – Vol. 173. – P. 477-484. DOI: https://doi.org/10.1016/j.carbon.2020.11.027

Vertically-oriented graphene nanowalls: Growth and application in Li-ion batteries / Q. Yang, J. Wu, S. Li, L. Zhang, J. Fu, F. Huang, Q. Cheng // Diamond and Related Materials. – 2019. – Vol. 91. – P. 54-63. DOI: https://doi.org/10.1016/j.diamond.2018.11.007

Zhang, Z. Vertically Aligned Graphene Nanosheet Arrays: Synthesis, Properties and Applications in Electrochemical Energy Conversion and Storage / Z. Zhang, C.-S. Lee, W. Zhang // Advanced Energy Materials. – 2017. – Vol. 7. – iss. 23. – P. 1700678. DOI: https://doi.org/10.1002/aenm.201700678

Facile growth of vertically-aligned graphene nanosheets via thermal CVD: The experimental and theoretical investigations / H. Wang, E. Gao, P.Liu, D. Zhou, D. Geng, X. Xue, L. Wang, K. Jiang, Z. Xu, G. Yu // Carbon. – 2017. – Vol. 121. – P. 1-9. DOI: https://doi.org/10.1016/j.carbon.2017.05.074

Study of CuO Nanowire Growth on Different Copper Surfaces / G. Fritz-Popovski, F. Sosada-Ludwikowska, A. Köck, J. Keckes, G. A. Maier // Scientific Reports. – 2019. – Vol. 9. – P. 1-13. DOI: https://doi.org/10.1038/s41598-018-37172-8

Cu2O/CuO heterojunction catalysts through atmospheric pressure plasma induced defect passivation / Avishek Dey, Gauthaman Chandrabose, A. Lois, O. Damptey, E. S. Erakulan, R. Thapa, S. Zhuk, G. K. Dalapati, S. Ramakrishna, N. St. J. Braithwaite, A. Shirzadi, S. Krishnamurthy / Applied Surface Science. – 2021. – Vol. 541. – P. 148571. DOI: https://doi.org/10.1016/j.apsusc.2020.148571

Macroscale synthesis of CuO nanowires on FTO plane substrate / Y. Mabuchi, R. N. Mohamed, X. Li, J. Liang, N. Kishi, T. Soga // Modern Physics Letters B. – 2019. – Vol. 33. – iss. 11. – P. 1950138. DOI: https://doi.org/10.1142/S0217984919501380

Adsorption of H2, CO2, CH4, CO, N2 and H2O in activated Carbon and Zeolite for Hydrogen production / F. V. S. Lopes, C. A. Grande, A. M. Ribeiro, J. M. Loureiro, O. Evaggelos, V. Nikolakis, A. E. Rodrigues // Separation Science and Technology. – 2009. – Vol. 44. – P. 1045-1073. DOI: https://doi.org/10.1080/01496390902729130

Adsorption of CO2, CH4, and N2 in Activated Carbon Honeycomb Monolith / R. P. Ribeiro, T. P. Sauer, F. V. Lopes, R. F. Moreira, C. A. Grande, A. E. Rodrigues // Journal of Chemical & Engineering Data. – 2008. – Vol. 53. – P. 2311-2317. DOI: https://doi.org/10.1021/je800161m

Baranov, O. Towards a highly-controllable synthesis of copper oxide nanowires in radio-frequency reactive plasma: fast saturation at the targeted size / O. Baranov, G. Filipič, U. Cvelbar // Plasma Sources Science and Technology. – 2019. – № 28. – P. 084002. DOI: https://doi.org/10.1088/1361-6595/aae12e

Баранов, О. О. Теоретична модель формування одновимірних наноструктур оксиду міді в умовах плазмового середовища [Текст] / О. О. Баранов // Відкриті інформаційні та комп'ютерні інтегровані технології : Нац. аерокосм. ун-т ім. М. Є. Жуковського «Харк. авіац. ін-т». – Харків, 2020. – № 88. – С. 141 – 161. DOI: https://doi.org/10.32620/oikit.2020.88.11

Teixeira, V. Residual stress and cracking in thin PVD coatings / V. Teixeira // Vacuum. – 2002. – Vol. 64. – iss. 3-4. – P. 393-399. DOI: https://doi.org/10.1016/S0042-207X(01)00327-X

Thornton, J.A. Stress-related effects in thin films / J.A. Thornton, D. Hoffman // Thin Solid Films. ‒ 1989. ‒ Vol. 171. – iss. 1. ‒ P. 5-31. DOI: https://doi.org/10.1016/0040-6090(89)90030-8

Hunt, R. A model of deadherence due to stresses in an elastic film / R. Hunt, B. Gale // Journal of Physics D: Applied Physics. ‒ 1972. ‒ Vol. 5. – iss. 2. ‒ P. 359-372. DOI: https://doi.org/10.1088/0022-3727/5/2/318

Finegan, J., Hoffman, R. AEC Technical Report No. 18 / J. Finegan, R. Hoffman. – Case Institute of Technology, Cleveland, 1961 – 34 p.

Rottmayer, R. E. Solid state physics program. Growth effects thin nickel films: Technical Report No. 79 / R. E. Rottmayer. – Case Western Reserve Univ., Cleveland, Ohio., 1972. – 78 p.

Koch, R. Microstructural changes in vapour-deposited silver, copper and gold films investigated by internal stress measurements / R. Koch, R. Abermann // Thin Solid Films. ‒ 1986. ‒ Vol. 140. – iss. 2. ‒ P. 217-226. DOI: https://doi.org/10.1016/0040-6090(86)90265-8

Chaudhari, P. Grain growth and stress relief in thin films / P Chaudhari // Journal of Vacuum Science and Technology. ‒ 1972. ‒ Vol. 9. – iss. 1. ‒ P. 520-522. DOI: https://doi.org/10.1116/1.1316674

Doerner, M. F., Nix, W.D. Stresses and deformation processes in thin films on substrates / M. F. Doerner, W. D. Nix // Critical Reviews in Solid State and Material Sciences. ‒ 1988. ‒ Vol. 14. – iss. 3. ‒ P. 225-268. DOI: https://doi.org/10.1080/10408438808243734

D’Heurle, F. M. Aluminum films deposited by rf sputtering / F. M. D’Heurle // Metall. Trans. – 1970. – Vol. 1. – iss. 3. – P. 725-732. DOI: https://doi.org/10.1007/BF02811600

Windischmann, H. An intrinsic stress scaling law for polycrystalline thin films prepared by ion beam sputtering / H. Windischmann // J. Appl. Phys. – 1987. – Vol. 62. – iss. 5. – P. 1800-1807. DOI: https://doi.org/10.1063/1.339560

Abermann, R., Koch, R. In situ study of thin film growth by internal stress measurement under ultrahigh vacuum conditions: Silver and copper under the influence of oxygen / R. Abermann, R. Koch // Thin Solid Films. ‒ 1986. ‒ Vol. 142. – iss 1. ‒ P. 65-76.

Sigmund, P. Sputtering by ion bombardment theoretical concepts. In: Behrisch R. (eds) Sputtering by Particle Bombardment I. Topics in Applied Physics. – Springer, Berlin, Heidelberg. - 1981. – Vol. 47.– P. 9-71. DOI: https://doi.org/10.1007/3540105212_7

Effect of ion bombardment during deposition on the x‐ray microstructure of thin silver films / T. C. Huang, G. Lim, F. Parmigiani, E. Kay // Journal of Vacuum Science & Technology A. ‒ 1985. ‒ Vol. 3. – iss. 6. ‒ P. 2161-2166. DOI: https://doi.org/10.1116/1.573271

Kay, E. Effect of energetic neutralized noble gas ions on the structure of ion beam sputtered thin metal films / E. Kay, F. Parmigiani, W. Parrish // Journal of Vacuum Science & Technology A. ‒ 1987. ‒ Vol. 5. – iss. 1. ‒ P. 44-51. DOI: https://doi.org/10.1116/1.574135

Windischmann, H. Intrinsic stress in sputter-deposited thin films // Crit. Rev. Solid State Mater. Sci. – 1992. – Vol. 17. – iss. 6. – P. 547-596. DOI: https://doi.org/10.1080/10408439208244586

On the origin of stress in magnetron sputtered TiN layers / J.-D. Kamminga, Th. H. de Keijser, R. Delhez, E. J Mittemeijer // J. Appl. Phys. – 2000. – Vol. 88. – iss. 11. – P. 6332-6345. DOI: https://doi.org/10.1063/1.1319973

Abadias, G. Diffraction stress analysis in fiber-textured TiN films grown by io-beam sputtering: Application to (001) and mixed (001)+(111) texture / G. Abadias, Y. Y. Tse // J. App. Phys. – 2004. – Vol. 95. – iss. 5. – P. 2414-2428. DOI: https://doi.org/10.1063/1.1646444

Stress field in sputtered thin films: Ion irradiation as a tool to induce relaxation and investigate the origin of growth stress / A. Debelle, G. Abadias, A. Michel, C. Jaouen // J. Appl. Phys. – 2004. – Vol. 84. – iss. 24. – P. 5034-5036. DOI: https://doi.org/10.1063/1.1763637

Doerner, M. F. Stresses and deformation processes in thin films on substrates / M. F. Doerner, W. D. Nix // Crit. Rev. Solid State Mater. Sci. – 1988. – Vol. 14. – iss. 3. – P. 225- 268. DOI: https://doi.org/10.1080/10408438808243734

White, G. E. In situ study of film stresses in metal silicides using absorption-edge-contour mapping / G. E. White, H. Chen // J. Appl. Phys. – 1990. – Vol. 68. –iss. 7. – P. 3317-3321. DOI: https://doi.org/10.1063/1.346384

Buaud, P. P. In situ strain measurements during the formation of platinum silicide films / P. P. Buaud, F. M. d’Heurle, E. A. Irene, B. K. Patnaik, N. R. Parikh // J. Vac. Sci. Technol. B. – 1991. – Vol. 9. – iss. 5. – P. 2536-2541. DOI: https://doi.org/10.1116/1.585688

Gergaud, P. Chenevier Stresses arising from a solid state reactions between palladium films and Si(001) investigated by in situ combined x-ray diffraction and curvature measurements / P. Gergaud, O. Thomas // J. Appl. Phys. – 2003. – Vol. 94. – iss. 3. – P. 1584-1591. DOI: https://doi.org/10.1063/1.1590059

Abermann, R. Internal stress of vapour-deposited aluminium films: Effect of O2 and water vapour present during film deposition / R. Abermann // Thin Solid Films. – 1990. – Vol. 186. – iss. 2. – P. 233-240. DOI: https://doi.org/10.1016/0040-6090(90)90145-4

Murakami, M. Deformation in thin films by thermal strain / M. Murakami // J. Vac. Sci. Techchnol. – 1991. – Vol. 9. – iss. 4. – P. 2469-2476. DOI: https://doi.org/10.1116/1.577258

Time dependence of stress and hillock distributions during electromigration in thin metal film interconnections / L. Klinger, E. Glickman, A. Katsman, L. Levin // Mater. Sci. Eng. B. – 1994. – Vol. 23. – iss. 1. – Р. 15–18. DOI: https://doi.org/10.1016/0921-5107(94)90271-2

The influence of sputter-deposition parameters on piezoelectric and mechanical properties of AlN thin films / A. Ababneh, U. Schmid, J. Hernando, J. L. Sanchez-Rajas, H. Seidel // Mater. Sci. Eng. B. – 2010. – Vol. 172. – iss. 3. – P. 253-258. DOI: https://doi.org/10.1016/j.mseb.2010.05.026

Dutta, S. Ferroelectric and piezoelectric properties of (111) oriented lanthanum modified lead zirconate titanate film / S. Dutta, A. A. Jeyaseelan, S. Sruthi // Thin Solid Films. – 2014. – Vol. 562. – P. 190-194. DOI: https://doi.org/10.1016/j.tsf.2014.04.072

Enhancement of piezoelectric response of diluted Ta doped AlN / H. Liu, F. Zeng, G. Tang, F. Pan // Appl. Surf. Sci. – 2013. – Vol. 270. – P. 225-230. DOI: https://doi.org/10.1016/j.apsusc.2013.01.005

Electrostriction: nonlinear electromechanical coupling in solid dielectrics / R. E. Newnham, V. Sundar, R. Yimnirun, J. Su, Q. M. Zhang // J. Phys. Chem. B. – 1997. – Vol. 101. – iss. 48. – P. 10141-10150. DOI: https://doi.org/10.1021/jp971522c

Direct and inverse measurement of thin film magnetostriction / J.-Ph. Jay, F. Le Berre, S. P. Pogossian, M. V. Indenbom // J. Magn. Mag. Mater. – 2010. – Vol. 322. – iss. 15. – P. 2203-2214. DOI: https://doi.org/10.1016/j.jmmm.2010.02.011

Magnetostriction measurement in thin films using laser Doppler vibrometry / R. Varghese, R. Viswan, K. Joshi, S. Seifikar, Y. Zhou, J. Schwartz, S. Priya // J. Magn. Mag. Mater. – 2014. – Vol. 383. – 179-187. DOI: https://doi.org/10.1016/j.jmmm.2014.03.076

Shintani, A. Temperature dependence of stresses in chemical vapor deposited vitreous films / A. Shintani, S. Sugaki, H. Nakashima // J. Appl. Phys. – 1980. – Vol. 51. – iss. 8. – P. 4197-4205. DOI: https://doi.org/10.1063/1.328277

Lee, C.-C. Modeling and validation of mechanical stress in indium tin oxide layer integrated in highly flexible stacked thin films / C.-C. Lee // Thin Solid Films. – 2013. – Vol. 544. – P. 443-447. DOI: https://doi.org/10.1016/j.tsf.2013.02.084

Mastering the biaxial stress state in nanometric thin films on flexible substrates / D. Faurie, P.-O. Renault, E. Le Bourhis, G. Geandier, P. Goudeau, D. Thiaudiere // Appl. Surf. Sci. – 2014. – Vol. 306. – P. 70-74. DOI: https://doi.org/10.1016/j.apsusc.2014.02.032

Stoney, G. G. The Tension of Metallic Films Deposited by Electrolysis // Proceedings of the Royal Society of London. Series A. ‒ 1909. ‒ Vol. 82. – iss. 553. ‒ P. 172-175.

Janssen, G. Celebrating the 100th anniversary of the Stoney equation for film stress: Developments from polycrystalline steel strips to single crystal silicon wafers / G. Janssen,, M. M. Abdalla, F.van Keulen, B. R. Pujada, B.van Venrooy // Thin Solid Films. ‒ 2009. – Vol. 517. ‒ iss. 6. ‒ P. 1858-1867. DOI: https://doi.org/10.1016/j.tsf.2008.07.014

Shull, A. L. Measurements of stress during vapor deposition of copper and silver thin films and multilayers / A. L. Shull, F. Spaepen // Journal of Applied Physics. ‒ 1996. ‒ Vol. 80. – iss. 11. ‒ P. 6243-6256. DOI: https://doi.org/10.1063/1.363701

Pan, J. Insitu stress measurement of refractory metal silicides during sintering / J. Pan, I. Blech // Journal of Applied Physics. ‒ 1984. ‒ Vol. 55. – iss. 8. ‒ P. 2874-2880. DOI: https://doi.org/10.1063/1.333326

Martinez, R. E. Direct measurement of crystal surface stress / R. E. Martinez, W. M. Augustyniak, J. A. Golovchenko // Physical Review Letters. ‒ 1990. ‒ Vol. 64. – iss. 9. ‒ P. 1035- 1038. DOI: https://doi.org/10.1103/PhysRevLett.64.1035

Moske, M. New UHV dilatometer for precise measurement of internal stresses in thin binary‐alloy films from 20 to 750 K / M. Moske, K. Samwer // Review of Scientific Instruments. ‒ 1988. ‒ Vol. 59. – iss. 9. ‒ P. 2012-2017. DOI: https://doi.org/10.1063/1.1140017

Wilcock, J. A sensitive bending beam apparatus for measuring the stress in evaporated thin films / J. Wilcock, D. Campbell // Thin Solid Films. ‒ 1969. ‒ Vol. 3. – iss. 1. ‒ P. 3-12. DOI: https://doi.org/10.1016/0040-6090(69)90107-2

Yu, Y.-T. Evaluation of residual stresses in thin films by critical buckling observation of circular microstructures and finite element method / Y.-T. Yu, W.-Z. Yuan, D.-Y. Qiao, Q. Liang // Thin Solid Films. ‒ 2008. ‒ Vol. 516. – iss. 12. ‒ P. 4070-4075. DOI: https://doi.org/10.1016/j.tsf.2007.12.153

Blackburn, H. The development of stress and surface temperature during deposition of lithium fluoride films / H. Blackburn, D.Campbell // Philosophical Magazine. ‒ 1963. ‒ Vol. 8. – iss. 89. ‒ P. 823-831. DOI: https://doi.org/10.1080/14786436308213839

Story, H. Stress Annealing in Vacuum Deposited Copper Films / H. Story, R. Hoffman // Proceedings of the Physical Society. Section B. ‒ 1957. ‒ Vol. 70. – iss. 10. ‒ P. 950.

Priest, J. Stress anisotropy in silicon oxide films / J. Priest, H. Caswell, Y. Budo // Journal of Applied Physics. ‒ 1963. ‒ Vol. 34. – iss. 2. ‒ P. 347-351. DOI: https://doi.org/10.1063/1.1702611

Priest, J. R. Apparatus for the Measurement of Stress in Vacuum Evaporated Films / J. R. Priest // Review of Scientific Instruments. ‒ 1961. ‒ Vol. 32. – iss. 12. ‒ P. 1349-1351. DOI: https://doi.org/10.1063/1.1717249

Prevey, P. S. X-ray diffraction residual stress techniques / P. S. Prevéy, D. J. Hornbach. – ASM International, ASM Handbook. ‒ 1986. ‒ Vol. 10. ‒ P. 380-392. DOI: https://doi.org/10.31399/asm.hb.v10.a0006632




DOI: https://doi.org/10.32620/oikit.2021.91.06

Refbacks

  • There are currently no refbacks.