On the interplay between relaxation, defect formation, and atomic Sn distribution in Ge_(1−x)Sn_(x) unraveled with atom probe tomography

Ge_(1−x)Sn_(x) has received a lot of interest for opto-electronic applications and for strain engineering in advanced complementary-metal-oxide-semiconductor technology, because it enables engineering of the band gap and inducing strain in the alloy. To target a reliable technology for mass application in microelectronic devices, the physical problem to be addressed is to unravel the complex relationship between strain relaxation (as induced by the growth of large layer thicknesses or a thermal anneal) and defect formation, and/or stable Sn-cluster formation. In this paper, we study the onset of Sn-cluster formation and its link to strain relaxation using Atom Probe Tomography (APT). To this end, we also propose a modification of the core-linkage [Stephenson et al., Microsc. Microanal. 13, 448 (2007)] cluster analysis method, to overcome the challenges of limited detection efficiency and lateral resolution of APT, and the quantitative assessment for very small clusters (<40 atoms) embedded in a random distribution of Sn-atoms. We concluded that the main relaxation mechanism for these layers is defect generation (misfit dislocations, threading dislocations, etc.), irrespective of the cause (thickness of layer or thermal anneal) of relaxation and is independent of the cluster formation. The low thermodynamic solubility limit of Sn in Ge seems to be the driving force for Sn-cluster formation. Finally, we also discuss the spatial distribution of Sn in clusters and relate them to the theoretically predicted stable Sn clusters [Ventura et al., Phys. Rev. B 79, 155202 (2009)]