Recovery of SIMS depth profiles with account for nonstationary effects

•Hoffmann's MRI-model was used for determination of nonstationary depth resolution function.•We proposed the description of the nonstationary depth profiling by Fredholm integral equation.•The way of solving an inverse problem of nonstationary depth profiling was described.•The proposed algorithm was tested on a SiGe multilayered structure.•Obtained results were compared with conventional deconvolution and x-ray reflectometry data. In this work we consider a method of accounting for the nonstationary effects in recovery of SIMS depth profiles. The depth resolution function (DRF) is described by Hofmann's nonstationary MRI (mixing-roughness-information depth) model using the depth-dependent parameters. The effects in question include the nonstationary atomic mixing and development of surface roughness. A mathematical description of the nonstationary depth profiling process by the Fredholm integral equation of the first kind is proposed. The inverse problem is solved using an algorithm based on the Tikhonov regularization method. The proposed nonstationary recovery method is tested on both model and real structures. The development of surface roughness in SIMS depth profiling of the real structure was observed. Grazing incidence x-ray reflectometry (XRR) technique was used to verify the results of SIMS profiles restoration for periodic structure containing thin Ge layers in the Si matrix. The advantages of the proposed recovery algorithm to allow for the nonstationary effects are shown.