Quantitative x-ray photoelectron spectroscopy: Quadrupole effects, shake-up, Shirley background, and relative sensitivity factors from a database of true x-ray photoelectron spectra

An analysis is provided of the x-ray photoelectron spectroscopy (XPS) intensities measured in the National Physical Laboratory (NPL) XPS database for 46 solid elements. This present analysis does not change our previous conclusions concerning the excellent correlation between experimental intensities, following deconvolving the spectra with angle-averaged reflection electron energy loss data, and the theoretical intensities involving the dipole approximation using Scofield’s cross sections. Here, more recent calculations for cross sections by Trzhaskovskaya et al. involving quadrupole terms are evaluated and it is shown that their cross sections diverge from the experimental database results by up to a factor of 5. The quadrupole angular terms lead to small corrections that are close to our measurement limit but do appear to be supported in the present analysis. Measurements of the extent of shake-up for the 46 elements broadly agree with the calculations of Yarzhemsky et al. but not in detail. The predicted constancy in the shake-up contribution by Yarzhemsky et al. implies that the use of the Shirley background will lead to a peak area that is a constant fraction of the true peak area including the shake-up intensities. However, the measured variability of the shake-up contribution makes the Shirley background invalid for quantification except for situations where the sensitivity factors are from reference samples similar to those being analyzed.

Figure 1

Values of $\gamma$ and $\delta$ for the different elements and core levels for Mg x rays plotted by interpolating the data of Trzhaskovskaya et al.[20, 21] given at $1000\mathrm{eV}$ and $1500\mathrm{eV}$, to the $\mathrm{Mg}\mathrm{K}\alpha$ energy, (a) $\gamma$, and (b) $\delta$. Similar open and filled symbols refer to the lower and higher binding energy components of a spin-orbit split pair, respectively.

Figure 2

Spectroscopic factors for the different elements, plotted from the data of Yarzhemsky et al.[35]

Figure 3

Ratio of the experiment and theory, for each peak in XPS for the $1s$ $(+)$, $2p$ $(•)$, $3p$ $(▿)$, $3d$ $(\circ )$, $4p$ $(*)$, $4d$ $(◻)$, $4f$ $(\times )$, $5p$ $(◇)$, and $5d$ $(\star )$ electrons using the angle-averaged REELS background subtraction for Mg with the element-specific transport correction factor included.[5]

Figure 4

Data from the quadrupole theory from Trzhaskovskaya et al.,[20, 21] (a) ratio of the cross section to that of Scofield,[26] (b) the angular term $[1+(\gamma ∕3+\delta )∕(3^{0.5}{D}_1\left)\right]$, and (c) the product of the parameters in (a) and (b), as a function of $Z$. For convenience, in the plot in (b), the simple $Z$ dependence of $\omega$ $(\omega =0.05\sqrt{Z})$ is used with 1% accuracy in the ordinate. Similar open and filled symbols refer to the lower and higher binding energy components of a spin-orbit split pair, respectively.

Figure 5

Correlation plot for the ratio of experiment to theory using the Scofield cross section and the quadrupole term $[1+(\gamma ∕3+\delta )∕(3^{0.5}{D}_1\left)\right]$.

Figure 6

The ratio of peak, $P_{\mathrm{R}}$, area to total peak area $(P_{\mathrm{R}}+B_{\mathrm{R}})$ including shake-up as a function of $Z$ for $(◻)$ Mg x rays, $(엯)$ Al x rays and $(•)$ the calculations of $f$ by Yarzhemsky et al.[35]

Figure 7

X-ray photoelectron spectra showing the angle-averaged REELS background and the Shirley backgrounds for the same elements and regions as Figs. 5 to 8 in Ref. 5, (a) $2s$ and $2p$ peaks for Al using Mg x rays, (b) $3s$, $3p$, and $3d$ peaks for Cu using Al x rays, (c) $4s$, $4p$, and $4d$ peaks in Mo using Al x rays, (d) $4f$, $5s$, $5p$, and $5d$ peaks in Ta using Al x rays. The angle-averaged REELS background is the lowest curve except for the $\mathrm{Mo}4s$ peak and the region around $1430\mathrm{eV}$ for Ta. The peaks for each element are listed above in order of their kinetic energy.

Figure 8

Intensities, $P_{\mathrm{S}}$, from the XPS database of spectra using Mg x rays measured with the Shirley background. Intensities for the $p$, $d$, and $f$ levels are all for the sum of the two components of the doublet peaks.

Figure 9

Intensities, $I^{\infty }$, for the data in Fig. 8 calculated as described in Refs. 3, 5.

Figure 10

Ratio of the experimental peak intensities, $P_{\mathrm{S}}$, to that calculated, $I^{\infty }$, (a) for all peaks with the doublet peaks summed, (b) for the main peaks and with only the lower binding energy peak of any doublet peak. In (b) the straight line is Eq. (9).

Figure 11

Aluminium $2s$ and $2p$ data for clean Al using $\mathrm{Al}\mathrm{K}\alpha$ x rays, (a) ratio for $2s∕2p$ intensities $(◻)$ experimental data[43] using $4.1°$ analyzer acceptance angle, $(∎)$ experimental data[43] using $1.4°$ acceptance angle, (—-) calculations for dipole theory with $\beta$ from Yeh and Lindau,[39] (- - -) calculations for quadrupole theory using Trzhaskovskaya et al.’s data[20] for $\gamma$ and $\delta$, (b) calculations for the peak intensities as in (a), ignoring instrumental and emission angle effects. The geometry is unusual with x-rays incident at right angles (i.e., normally) on the rear of the sample and the measurements are as a function of the angle of emission so that the abscissa is $180°\text{−}\theta °$.

Figure 12

Value of $\theta °$ for the maximum $\mathrm{Si}2p$ peak intensity, using the quadrupole theory, as a function of the photon energy, ignoring instrumental and emission angle effects.