Comparison of regularization methods for the inversion of ARXPS data

Paynter, R.W.; Rondeau, Maxime

doi:10.1016/j.elspec.2010.12.025

Cited by 11 publications

(12 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dependence on the initial model is discussed further in the succeeding texts. The ‘slopes’ and ‘curves’ functions attempt to regularize the calculated depth profile by limiting the total slope or curvature in the produced depth profiles and have been shown to provide excellent results for ARXPS depth profiling . ‘Ent‐model’ calculates the informational entropy between the produced depth profile and a prior; this method is probably the most commonly used for ARXPS.…”

Section: Resultsmentioning

confidence: 99%

“…Regularization functions are employed to reduce the dependence of depth profile extraction on the collected noise. However, even with a regularization function, some noise dependence may still exist, especially as noise levels increase . To ensure that the results are consistent for any noisy data, the previously mentioned calculations for each regularization function were repeated for 50 times with different simulated 10% random noise; average results were shown in Figs 1 through 4.…”

Section: Resultsmentioning

confidence: 99%

“…Methods used in this work were based on the regularization methods previously applied to ARXPS. An excellent exposition of these methods can be found elsewhere . The problem of data processing is based in the science of uncertainties and probability theory; there are a variety of algorithms with various advantages and disadvantages that can be used to achieve better resolution of the data.…”

Section: Methodsmentioning

confidence: 99%

“…An α that is too small will result in overfitting the data (fitting the noise), while a large α will result in a poor fit to the experimental data. While this parameter can be optimized analytically, it is often easier to perform the regularization routine using various values for α and selecting the result that provides the simultaneously optimized values for S and C . Here, this is accomplished by minimizing a parameter d :

d = \sqrt{{italicS}^{2} + {italicC}^{2}}

…”

Section: Methodsmentioning

confidence: 99%

“…The N matrix corresponding to the value of α minimizing d as per Eqn was kept as the final result; no further optimization of α was performed. Following Paynter and Rondeau, various regularization functions, S , listed in Table , were tested using simulated data and will be discussed in the Results section in the succeeding texts.…”

Section: Methodsmentioning

confidence: 99%

See 4 more Smart Citations

Nondestructive compositional depth profiling using variable‐kinetic energy hard X‐ray photoelectron spectroscopy and maximum entropy regularization

Krajewski

Opila

Pallem

et al. 2014

Surface & Interface Analysis

View full text Add to dashboard Cite

We discuss the calculation of nondestructive compositional depth profiles from regularization of variable kinetic energy hard X-ray photoelectron spectroscopy (VKE-XPS) data, adapting techniques developed for angle-resolved XPS. Simulated TiO 2 /Si film structures are analyzed to demonstrate the applicability of regularization techniques to the VKE-XPS data and to determine the optimum choice of regularization function and the number of data points. We find that using a maximum entropy-like method, when the initial model/prior thickness is similar to the simulated film thickness, provides the best results for cases where prior knowledge of the sample exists. For the simple structures analyzed, we find that only five kinetic energy spectra are necessary to provide a good fit to the data, although in general, the number of spectra will depend on the sample structure and noisiness of the data. The maximum entropy-like algorithm is then applied to two physical films of TiO 2 deposited on Si. Results suggest interfacial intermixing. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

d = \sqrt{{italicS}^{2} + {italicC}^{2}}

…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Nondestructive compositional depth profiling using variable‐kinetic energy hard X‐ray photoelectron spectroscopy and maximum entropy regularization

Krajewski

Opila

Pallem

et al. 2014

Surface & Interface Analysis

View full text Add to dashboard Cite

show abstract

Surface analysis insight note: Straightforward concentration depth profiling by angle‐resolved X‐ray photoelectron spectroscopy using a Tikhonov regularization algorithm

Murdoch

McCulloch

2023

Surface & Interface Analysis

View full text Add to dashboard Cite

Angle‐resolved X‐ray photoelectron spectroscopy (ARXPS) is a technique used for depth‐dependent analysis in the near‐surface region of samples. Calculation of a concentration depth profile using ARXPS requires an inverse Laplace transform, which adds considerable complexity to the analysis. In this insight note, the Tikhonov regularization algorithm for depth profile reconstruction from ARXPS data is examined. The steps required to produce a concentration depth profile are provided. The discussion includes strategies that deal with elastic scattering, electron attenuation, choice of regularization terms and optimization of the regularization parameters. The method is implemented in a Microsoft Excel spreadsheet that allows users to calculate a depth profile for data collected at up to five angles for five different peak components.

show abstract

Regularization methods for the extraction of depth profiles from simulated ARXPS data derived from overlayer/substrate models

Paynter

2012

Journal of Electron Spectroscopy and Related Phenomena

View full text Add to dashboard Cite

Comparison of regularization methods for the inversion of ARXPS data

Cited by 11 publications

References 22 publications

Nondestructive compositional depth profiling using variable‐kinetic energy hard X‐ray photoelectron spectroscopy and maximum entropy regularization

Nondestructive compositional depth profiling using variable‐kinetic energy hard X‐ray photoelectron spectroscopy and maximum entropy regularization

Surface analysis insight note: Straightforward concentration depth profiling by angle‐resolved X‐ray photoelectron spectroscopy using a Tikhonov regularization algorithm

Regularization methods for the extraction of depth profiles from simulated ARXPS data derived from overlayer/substrate models

Contact Info

Product

Resources

About