Energy spectra of sputtered ions: assessment of the instrumental ...

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H. Gnaser 80 magnetic sector features a homogeneous magnetic field with inclined field boundaries. The mass resolution was M/ΔM ~ 300. The detection of secondary ions was done by a discrete-dynode electron multiplier, and count rates were limited to
Energy spectra of sputtered ions A ¼ R e jC e ja 2 (2) Calculated energy resolution ΔE (eV) FWHM Cs + energy spectrum (eV) 10 2 CA1 CA2 CA3 CA4 10 1 10 10 2 10 3 Exit slit width (µm) CA1 CA2 CA3 CA4 10 1 10 10 2 10 3 10 2 (a) Exit slit width (µm) (b) The radius of the electrostatic sector is R e = 85 mm, the constant C e = 3.5, and a is the angle to which the beam is constrained in the radial direction (a ~ 0.012). [21] With these numbers, a value of A ~40mm is obtained. Eqn (1) may then be used to estimate the theoretically predicted values of ΔE for the different S 1 and S 2 ; Fig. 3(b) shows such an evaluation which produces a qualitative agreement with the experimental data. The discrepancies that are found might be due to the presence of the other optical elements (the magnetic sector and severa lenses), which follow the energy analyzer and possible uncertainties associated with the specific values of C e and a. It was noted in the context of Fig. 1 that for wide exit slits, the energy spectra exhibit a box-type shape, at least in the lowenergy and the central parts. This feature is illustrated in Fig. 4, which depicts the distributions obtained for all four CAs and S 2 = 1400 mm. In a recent publication, [18] it was proposed that a box-shaped resolution function R(E) might be an appropriate description for the bandwidth in electric and magnetic sector-field instruments such as the one used in the present work. Specifically, the following normalized resolution function was applied RE ð Þ ¼ 1 4ΔE 1 þ erf E þ 0:5ΔE E pffiffiffi 1 erf 2 s 0:5ΔE pffiffiffi 2 s Eqn (3) constitutes the convolution of a rectangular box with a Gaussian of standard deviation s. [18] Such a box-type function R(E) is plotted in Fig. 4 (dashed line), using ΔE = 37.6 eV and s = 1.3 eV. Clearly, the function describes the experimental spectra quite well in the low-energy and the central parts. As suggested by Wittmaack, [18] the resolution function given in Eqn (3) could be used to compute energy spectra via a convolution using R(E). Their comparison with the corresponding experimental distributions would then constitute a test as to the validity of the resolution function. This approach was tested for several measured energy spectra. Figure 5 displays normalized Cs + distributions (3) Figure 3. (a) The measured FWHM of the Cs + spectra as a function of the exit slit width for the four CAs. (b) The energy resolution ΔE calculated according to Eqn (1), with an aberration of A =40mm. of the CAs. In addition, optical aberrations may possibly contribute to the values of the FWHM for small slit sizes. Theoretically, the relative energy resolution E/ΔE of an electrostatic sector analyzer such as the one in the present SIMS instrument depends on the energy dispersion D E , the widths of the entrance and exits slits, S 1 and S 2 ,theanalyzer’s magnification M, and some possible contributions due to optical aberration effects A [6] : E ΔE ¼ D E MS 1 þ S 2 þ A (1) Cs + intensity (normalized) 10 -1 1 10 -2 10 -3 S 2 = 1400 μm CA1 CA2 CA3 CA4 Box-type In the present case, S 1 is determined by the diameter of the CAs and M is unity because of the symmetry of the entrance and exit positions of the sector field. For an electrostatic sector, the contribution due to aberration in the radial plane is given by [19,20] -20 0 20 40 60 Emission energy (eV) Figure 4. Normalized Cs + energy spectra for the four different CAs and the exit slit S 2 = 1400 mm (solid symbols). The dashed line is the resolution function given in Eqn (3). 81 Surf. Interface Anal. 2013, 45, 79–82 Copyright © 2012 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/sia
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