We analyzed the X-ray photoelectron spectra (XPS) of carbon 1s states in graphene and oxygen-intercalated graphene grown on SiC(0001) using Bayesian spectroscopy. To realize highly accurate spectral decomposition of the XPS spectra, we proposed a framework for discovering physical constraints from the absence of prior quantified physical knowledge, in which we designed the prior probabilities based on the found constraints and the physically required conditions. This suppresses the exchange of peak components during replica exchange Monte Carlo iterations and makes possible to decompose XPS in the case where a reliable structure model or a presumable number of components is not known. As a result, we have successfully decomposed XPS of one monolayer (1ML), two monolayers (2ML), and quasi-freestanding 2ML (qfs-2ML) graphene samples deposited on SiC substrates with the meV order precision of the binding energy, in which the posterior probability distributions of the binding energies were obtained distinguishably between the different components of buffer layer even though they are observed as hump and shoulder structures because of their overlapping.
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