In this article, we propose a new model to explain how heteroepitaxial layers grown on a twist-bonded thin layer may have a significantly reduced number of threading dislocations even if the strain in the epitaxial layers is relaxed. We first point out the deficiency in the existing compliant substrate theory by showing that all the synthesized "compliant substrates" fail to behave as "ideal" free-standing templates assumed by the current theory. Our new model is constructed on the based of stress field interactions between the heteroepitaxial layer and the embedded twist boundary. In the new model, the reduction in threading dislocation density originates from the extension of the dislocation half loops due to the effect of misfit dislocation pinning by the twist boundary. When the average size of the dislocation half loops increases substantially from micrometers to millimeters or even to the size of the wafer, the density of threading dislocations drops significantly. This model does not require any "macroscopic" motion between the bonded thin layer and the handle wafer as the current theory does, which makes it more agreeable with the experimental results.
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