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...