Nonlinear calibration curves in secondary ion mass spectrometry for quantitative analysis of gesi heterostructures with nanoclusters

For the first time in the practice of secondary ion mass spectrometry, we obtained a nonlinear calibration curve for the ratio of the cluster and elementary secondary ions of germanium Ge$_{2}$/Ge without secondary ions of silicon, which enables the quantification of germanium in Ge$_{x}$Si$_{1-x}$ heterostructures in the entire range of 0 $< x\le$ 1. We developed a method for quantitative lateral analysis based on the plotting of a lateral map of $x$. An algorithm to identify and analyze the lateral heterogeneity of $x$ in Ge$_{x}$Si$_{1-x}$ heterostructures with 3D clusters by comparing the results of depth profiling analysis, obtained using linear and nonlinear calibration curves, is developed, and concentration $x$ in the self-assembled nanoislands is determined.