*nl*where

_{j}*n*is the principal quantum number,

*l*is the angular momentum quantum number and

*j*=

*l*+

*s*(where

*s*is the spin angular momentum number and can be ±½). All orbital levels except the s levels (

*l*= 0) give rise to a doublet with the two possible states having different binding energies. This is known as spin-orbit splitting (or

*j*-

*j*coupling)[1]. The peaks will also have specific area ratios based on the degeneracy of each spin state, i.e. the number of different spin combinations that can give rise to the total

*j*(see Table 1). For example, for the 2

*p*spectra, where

*n*is 2 and

*l*is 1,

*j*will be 1/2 and 3/2. The area ratio for the two spin orbit peaks (2

*p*

_{1/2}:2p

_{3/2}) will be 1:2 (corresponding to 2 electrons in the 2

*p*

_{1/2}level and 4 electrons in the 2

*p*

_{3/2}level). These ratios must be taken into account when analyzing spectra of the

*p*,

*d*and

*f*core levels. An example of this splitting for the Sc 2

*p*peak for Sc

_{2}O

_{3}is shown in Figure 1. Spin-orbit splitting values (eV) can be found in a variety of databases[2,3]. These values will be needed when fitting spectra where the chemical shifts are larger than the spin-orbit splitting. For example, the As 3

*d*spectrum for an oxidized GaAs surface in Figure 2 shows that all spin-orbit doublets must be fit in order to properly identify the species present. The 3

*d*

_{5/2}and 3

*d*

_{3/2}doublet for each chemical specie is constrained to have 3:2 peak area ratios, equal FWHM, and a peak separation of 0.69 eV.

Figure 1. An example of spin-orbit splitting in the Sc 2

*p*spectrum of Sc_{2}O_{3}.Figure 2. The As 3

*d*spectrum of a sample of oxidized GaAs. Each chemical specie is fit with the 3

*d*

_{5/2}and 3

*d*

_{3/2}doublet that is constrained to have a 3:2 peak area ratio, equal FWHM for the two peaks of the doublet, and a peak separation of 0.69 eV.

References:

[1] D. Briggs, XPS: Basic Principles, Spectral Features and Qualitative Analysis, in: D. Briggs, J.T. Grant (Eds.), Surface Analysis by Auger and X-ray Photoelectron Spectroscopy, IM Publications, Chichester, 2003, pp. 31-56.

[2] J.F. Moulder, W.F. Stickle, P.E. Sobol, K.D. Bomben, Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Corp, Eden Prairie, MN, 1992.

[3] C.D. Wagner, A.V. Naumkin, A. Kraut-Vass, J.W. Allison, C.J. Powell, J.R. Jr. Rumble, NIST Standard Reference Database 20, Version 3.4 (Web Version) (http:/srdata.nist.gov/xps/) 2003.