Residual diagnostics for detecting the breakdown of the single power-law approximation in photoelectron yield spectroscopy: application to doped silicon
Abstract
Our automated analysis of photoelectron yield spectroscopy (PYS) estimates the threshold Ith and the exponent n of a single power law for every spectrum. When this model fits poorly, however, the analysis cannot tell whether the data or the model is at fault. Here we present residual diagnostics that separate the two causes. The exponent is scanned continuously on a 1/n-power fit with an Akaike information criterion (AIC) based on the mean absolute error (MAE), and the spread of the resulting Akaike weights (P × Δn) quantifies the uncertainty of the estimate. The normalized MAE (NMAE) and the RMSE-to-MAE ratio (RMR) assess the data quality, the Durbin-Watson (DW) statistic assesses the model adequacy, and the three checks are reported in parallel. With criteria set from an Au reference, the diagnostics were applied to 60 continuous measurements in air of four HF-treated Si samples. For heavily doped p-type Si, DW fell below its criterion, whereas the means of NMAE and RMR remained within their criteria. Prompted by this flag, we fitted the spectrum with a two-component model with fixed exponents (n = 1 and 2.5); the AIC decreased by 56, DW increased from 0.86 to 1.99, and the two components set in at 4.70 and 5.28 eV. For heavily doped n-type Si, the change during air exposure was consistent with a single component. The diagnostics thus identify the spectra that require a multi-component analysis without assuming an emission mechanism.
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BibTeX
@misc{yagyu2026residual,
title = {{Residual diagnostics for detecting the breakdown of the single power-law approximation in photoelectron yield spectroscopy: application to doped silicon}},
author = {Shinjiro Yagyu and Takahiro Nagata and Yoshiyuki Nakajima},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11331},
eprint = {2610.11331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11331},
}
RIS
TY - UNPB
TI - Residual diagnostics for detecting the breakdown of the single power-law approximation in photoelectron yield spectroscopy: application to doped silicon
AU - Shinjiro Yagyu
AU - Takahiro Nagata
AU - Yoshiyuki Nakajima
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.11331
UR - https://arxiv.org/abs/2610.11331
AB - Our automated analysis of photoelectron yield spectroscopy (PYS) estimates the threshold Ith and the exponent n of a single power law for every spectrum. When this model fits poorly, however, the analysis cannot tell whether the data or the model is at fault. Here we present residual diagnostics that separate the two causes. The exponent is scanned continuously on a 1/n-power fit with an Akaike information criterion (AIC) based on the mean absolute error (MAE), and the spread of the resulting Akaike weights (P × Δn) quantifies the uncertainty of the estimate. The normalized MAE (NMAE) and the RMSE-to-MAE ratio (RMR) assess the data quality, the Durbin-Watson (DW) statistic assesses the model adequacy, and the three checks are reported in parallel. With criteria set from an Au reference, the diagnostics were applied to 60 continuous measurements in air of four HF-treated Si samples. For heavily doped p-type Si, DW fell below its criterion, whereas the means of NMAE and RMR remained within their criteria. Prompted by this flag, we fitted the spectrum with a two-component model with fixed exponents (n = 1 and 2.5); the AIC decreased by 56, DW increased from 0.86 to 1.99, and the two components set in at 4.70 and 5.28 eV. For heavily doped n-type Si, the change during air exposure was consistent with a single component. The diagnostics thus identify the spectra that require a multi-component analysis without assuming an emission mechanism.
ER -