Kinetic Model for Dependence of Thin Film Stress on Growth Rate, Temperature, and Microstructure
Abstract
During deposition, many thin films go through a range of stress states, changing from compressive to tensile and back again. In addition, the stress depends strongly on the processing and material parameters. We have developed a simple analytical model to describe the stress evolution in terms of a kinetic competition between different mechanisms of stress generation and relaxation at the triple junction where the surface and grain boundary intersect. The model describes how the steady state stress scales with the dimensionless parameter D/LR where D is the diffusivity, R is the growth rate, and L is the grain size. It also explains the transition from tensile to compressive stress as the microstructure evolves from isolated islands to a continuous film. We compare calculations from the model with measurements of the stress dependence on grain size and growth rate in the steady state regime and of the evolution of stress with thickness for different temperatures.
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Kinetic models suggest stress in thin films is formed between tensile and compressive states; compressive stress forms when atoms are inserted at boundaries, while tensile stress is generated through grain boundary formation.
“The kinetic models also suggest that the stress in thin films is formed between the tensile and compressive states. The latter is formed when atoms are inserted at the boundaries, while tensile stress is generated through grain boundary formation [152].”
From Metal Oxide Thin Films for Advanced Photonic Applications (2026) · cites this paper as [152]
Thermal stress arises from mismatch between thermal expansion coefficients of the deposited film and the substrate, while intrinsic stress is determined by deposition kinetics.
“The thermal stress may arise from the mismatch between the thermal expansion coefficients (CTE) of the deposited film and the substrate, while the intrinsic one is determined by the kinetics of the deposition [152,153].”
From Metal Oxide Thin Films for Advanced Photonic Applications (2026) · cites this paper as [152]
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- Authors
- Chason, E., Shin, J. W., Hearne, S. J., & Freund, L. B.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Venue
- Journal of Applied Physics
- Publisher
- AIP Publishing
- Published
- 2012-04-15
- Volume
- 111
- Issue
- 8
- ISSN
- 0021-8979 (ISSN-L)
- 1089-7550
- OpenAlex
- W2076138392
- Cited by
- 134
- References
- 29
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 7 · 2023: 11 · 2022: 9 · 2021: 11 · 2020: 14 · 2019: 21 · 2018: 9 · 2017: 2 · 2016: 9 · 2015: 4 · 2014: 17 · 2013: 4 · 2012: 1
- FWCI
- 10.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Physics (publishedVersion)
- Funders
- U.S. Department of Energy
- National Nuclear Security Administration
- Lawrence Livermore National Laboratory
- Sandia National Laboratories
- Topics
- Physical Sciences › Engineering › Mechanics of Materials › Metal and Thin Film Mechanics
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Thin Films
- Physical Sciences › Materials Science › Materials Chemistry › Advanced Materials and Semiconductor Technologies
- Keywords
- film stress, stress evolution, kinetic model, stress relaxation, triple junctions, grain boundaries, surface diffusion, growth rate (crystal and thin-film growth), grain size, microstructure evolution, deposition temperature, analytical model
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