Determining the Complete Residual Stress Tensors in SOS Hetero-Epitaxial Thin Film Systems by the Technique of X-Ray Diffraction

Abstract

This paper investigates residual stress of epitaxial silicon film on SOS thin film systems. The emphasis was to develop a method to obtain accurately the complete residual stress tensors. It was found that using the multiple asymmetric X-ray diffraction method to measure strains in 13 [hkl] directions, the complete residual stress tensors can be determined reliably. The results were verified by both the Raman Backscattering and the substrate curvature methods.

Temperature-dependent residual stresses in a hetero-epitaxial thin film system

“…directions. The previous study of the authors has shown that in the SOS system, the three in-plane film stresses (i.e., σ 11 , σ 12 and σ 22 ) are much larger than the other stress components (i.e., σ 31 , σ 32 and σ 33 ) [12], which indicates that the stress state can be simplified to a plane-stress state. With sufficient numbers of d hkl , the intercept a 0 and variables σ 11 , σ 22 , and σ 33 could be solved using the least-square method from the linear equation set of…”

“…Although the least square algorithm has been well established to solve for the complete stress tensor of a single-crystalline thin film [11,12], the accuracy is influenced by the stress-free lattice constant a 0 . In theory, a 0 changes with temperature owing to the thermal expansion of the lattice.…”

A New Method for Measuring the Residual Stresses in Multi-Layered Thin Film Systems

“…(1), the six strain components are parameters to be calculated using least-square method if a sufficient number (more than six) of ε ΦΨ are obtained. To improve the measurement accuracy, we developed the XRD method to utilize the multiple diffraction peaks pertaining to high Miller index planes [9]. A non-linear regression analysis of the excessive information of the anisotropic elastic strains is then conducted.…”

Production, Characterization and Application of Silicon-on-Sapphire Wafers

“…In order to determine a complete stress tensor in an SOS wafer, the measuring directions are limited by the crystallographic orientations of (hkl) planes that contribute to diffraction. Thus 3-axis sample alignments are required to adjust the measured (hkl) plane in the required direction [39]. This normally adds difficulties to the measurement process.…”