Correlation between microstructure deflections and film/substrate curvature under generalized stress fields

TL;DR

This paper develops an analytical theory linking macroscopic curvature of stressed film/substrate systems with microscopic deflections, extending to nonlinear stress fields and validated by simulations, with applications to silicon carbide growth.

Contribution

It introduces a generalized analytical model connecting microscopic deflections to macroscopic curvature under complex stress fields, validated through finite element simulations.

Findings

Wafer curvature techniques may not accurately determine stress in heteroepitaxial silicon carbide due to substrate defects.

The developed theory extends stress-deflection relations to nonlinear stress fields.

Finite element simulations support the analytical model's validity.

Abstract

In this article we develop an analytical theory that correlates the macroscopic curvature of stressed film/substrate systems with the microscopic in-plane and out-of-plane deflections of planar rotators. Extending this stress-deflection relations in the case of nonlinear stress fields and validating the results with the aid of finite element simulations. We use this theory to study the heteroepitaxial growth of cubic silicon carbide on silicon (100) and discover that due, to defects generated on the silicon substrate during the carbonization process, wafer curvature techniques may not allow the determination of the stress field in the grown films either quantitatively or qualitatively.