Factor analysis applied to the study of valence band resonant photoemission spectra in transition‐metal compounds

Abstract

We have applied factor analysis to the study of the valence band resonant photoemission spectra of a TiO 2 thin film. Classical analysis of the photoemission spectra as a function of the photon energy through the Ti 2p → 3d absorption edge does not give a clear understanding of the resonant process, because the resonance phenomenon is present along the valence band and the only differences on the resonance are related to the distribution of cationic d-states. However, factor analysis of the spectra allows a more quantitative analysis of the resonance phenomena. Analysis of the RPES spectra is not always an easy task. The most common analysis involves a plot of the intensities of the main structures in the valence band as a function of the photon energy to obtain constant initial state (CIS) curves. However, the CIS curves obtained by this method do not always give a clear understanding of the resonance process. In general, the different features in the valence band are of mixed cationic-anionic character due to hybridization. This mixed character leads to the fact that all the features show a similar CIS spectrum except for the difference in enhancement, which is proportional to the contribution of the cationic d-states to the different features analysed. The main purpose of this paper is to apply factor analysis to analyse the valence band resonant photoemission spectra in transition-metal compounds. To this end, and as an example, we present an analysis of the 2p ! 3d valence band resonant photoemission spectra of a TiO 2 thin film and show how factor analysis gives a satisfactory explanation of the resonant photoemission in TiO 2 , allowing experimental cross-sections of the Ti 3d states in the corresponding energy range to be determined. For comparison, we have included a classical analysis to show the mixed character of the different resonant profiles (i.e. CIS spectra) at several binding energies within the valence band.Factor analysis is a multivariative statistical method that has been used as a standard method of data handling in analytical chemistry, 2 mainly in the analysis of Auger Factor analysis applied to photoemission 245 and core-level photoelectron spectra. 3 -7 Studies using factor analysis of the valence band structure are very scarce. To our knowledge, factor analysis has been applied only to the study of the electronic structure of SnO 8 and TiN. 9Factor analysis allows the determination of the number of principal components, which can be combined linearly to represent a sequence of experimental spectra, as well as their concentrations as a function of photon energy. This property supports the use of factor analysis for resonant photoemission spectra. Rutile (TiO 2 ) has been studied already by resonant photoemission at the 3p ! 3d edge 10 -12 and at the 2p ! 3d edge 13 -15 using the classical method. It is worth noting that, as observed by Prince et al., 13 resonance effects at the L 2,3 edge give much higher intensity than for the M 2,3 edge, so we have chosen the 2p ! 3d edge for facto...

X‐ray photoelectron spectroscopy‐based valence band spectra of passive films on titanium

“…The major peak at VB energy region is located between 3 and 10 eV relative to E F . This peak is sometimes deconvoluted into three 21–23 and five 24–26 component peaks without physical meaning attached to the modelled components, although the VB spectrum consists of two distinct maxima separated in binding energy by approximately 2.5 eV based on physical orbitals in most of previous studies 27–33 . Therefore, the major peak between 3‐ and 10‐eV peak was deconvoluted into two peaks.…”

“…The VB spectrum in the 3-10 eV range mostly reflected the presence of O 2p (approximately 5.5 eV) and O 2p-Ti 3d hybridized states (approximately 7.5 eV) in the oxide layer, but the Ti 3d partial density of states spreads all VB. [21][22][23]30,35 The oxygen VB is composed of a variety of orbitals: t 1g , t 2u , 3t 1u , 1t 2g , 2t 1u , 2e g , and 2a 1g . Among these, the 1t 2g and 2e g orbitals are π and σ bonding to the Ti 3d states, with 12% and 21% charge density at each Ti site, respectively.…”

“…The Ti 3d contribution to the 8‐eV peak must be higher than that to the 5.7‐eV peak, because the 8.0‐eV peak resonated stronger than the 5.7‐eV peak. The VB spectrum in the 3–10 eV range mostly reflected the presence of O 2p (approximately 5.5 eV) and O 2p‐Ti 3d hybridized states (approximately 7.5 eV) in the oxide layer, but the Ti 3d partial density of states spreads all VB 21–23,30,35 . The oxygen VB is composed of a variety of orbitals: t 1g , t 2u , 3t 1u , 1t 2g , 2t 1u , 2e g , and 2a 1g .…”

“…This peak is sometimes deconvoluted into three [21][22][23] and five [24][25][26] component peaks without physical meaning attached to the modelled components, although the VB spectrum consists of two distinct maxima separated in binding energy by approximately 2.5 eV based on physical orbitals in most of previous studies. [27][28][29][30][31][32][33] Therefore, the major peak between 3-and 10-eV peak was deconvoluted into two peaks. In other words, VB region spectra were deconvoluted into four peak components: Peak A at approximately 1 eV, continuous beyond 0 eV (E F ), broad Peak B at approximately 5 eV, Peak C at approximately 8 eV, and Peak D in the 11-14 eV window.…”