Angle resolved x-ray photoelectron spectroscopy assessment of the structure and composition of nanofilms—including uncertainties—through the multilayer model

The multilayer model (MLM) for assessing the structural and composition parameters of multilayered nanofilms from angle-resolved x-ray photoelectric spectroscopy is described in detail. It is compared with regularized back-transform (RBT) approaches such as the maximum entropy method (MEM) with Tikhonov-type regularizations. The advantages of MLM over MEM, such as the possibility of assessing confidence ranges, modeling structures beyond conformal multilayered nanofilms, and modeling abrupt interfaces, are discussed and exemplified. In contrast with MLM, the RBT methods have shortcomings such as the violation of the conservation of information and the inability to adequately address the dependence of the effective attenuation length on the material. Examples of the application of MLM to conformal films and systems with protrusions are shown. The covariance matrix method (CMM) is described and applied to assess uncertainties in structural parameters and composition under the MLM. The CMM constitutes the canonical method for assessing confidence ranges and adequately accounts for the covariance among structural (e.g., layer thicknesses) and composition parameters.