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Modified Stoney’s equation with anisotropic substrates undergoing large deformations

Injeti, Sai Sharan and Vyas, Nihit and Annabattula, Ratna Kumar (2021) Modified Stoney’s equation with anisotropic substrates undergoing large deformations. Mechanics Research Communications, 113 . Art. No. 103685. ISSN 0093-6413.

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Thin film deposition is a key fabrication step in several opto-mechanical and electronics applications. For instance, thin film coatings can act as reflective interfaces, protective coatings or they can be used to modify the thermal behavior of the film-substrate system. For effective design, it is important to understand the deformation of the system in response to residual stresses during thin film deposition. The widely used Stoney’s equation to measure this deformation assumes isotropic elasticity of the substrate together with infinitesimal strains and rotations. In this work we relax both constraints, where we study the deformation of commonly used substrates made of single crystal Si(001) and Si(111) wafers that undergo large rotations. We derive relations between normalized substrate curvature and thin film mismatch strain and validate our analysis with numerical results. The methodology presented can be used for more accurate understanding of a broad range of film-substrate systems in semiconductors.

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Additional Information:© 2021 Elsevier Ltd. Received 10 February 2021, Revised 22 February 2021, Accepted 23 February 2021, Available online 26 February 2021. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Subject Keywords:Stoney’s equation; Thin film; Anisotropic substrate; Large deformation
Record Number:CaltechAUTHORS:20210301-104905215
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Official Citation:Sai Sharan Injeti, Nihit Vyas, Ratna Kumar Annabattula, Modified Stoney’s equation with anisotropic substrates undergoing large deformations, Mechanics Research Communications, Volume 113, 2021, 103685, ISSN 0093-6413, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108246
Deposited By: Tony Diaz
Deposited On:01 Mar 2021 19:09
Last Modified:12 Mar 2021 18:44

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