Quantitative calibration and germanium SIMS depth profiling in Ge$_x$Si$_{1-x}$/Si heterostructures

Methods for minimizing nonlinear matrix effects in the quantitative determination of germanium concentrations in Ge$_x$Si$_{1-x}$ layers by secondary ion mass spectrometry are discussed. The analysis conditions with positive GeCs$^+$, SiCs$^+$ and negative Ge$^-$, Si$^-$ secondary ions produced during sputtering by cesium ions are used in the TOF.SIMS-5 setup with a time-of-flight mass analyzer. In contrast to published works for TOF.SIMS setups, the linear dependence of the ion-concentration ratio Ge$^-$/Si$^-$ on $x/(1-x)$ is shown. Two new linear calibrations for the germanium concentration as a function of the cluster Ge$_2^-$ secondary ion yield are proposed. The calibration factors are determined for all linear calibrations at various energies of sputtered cesium ions and Bi$^+$ and probe Bi$^+_3$ ions. It is shown for the first time that the best depth resolution among the possible conditions of quantitative germanium depth profiling in Ge$_x$Si$_{1-x}$/Si multilayer heterostructures is provided by the calibration mode using elemental Ge$^-$ и Si$^-$ negative secondary ions.