The ‘infinite velocity method’: a means of concentration calibration in secondary ion mass spectrometry?

Abstract

The so-called infinite velocity (iv) method, recently suggested by P. van der Heide as a means of quantifying, without standards, the signals measured by secondary ion mass spectrometry (SIMS), has been analysed critically. The iv method is essentially based upon two assumptions. (1) Secondary ion energy spectra can be described as a product of the isotopic concentration of the analysed species, the flux of sputtered neutrals, the instrument transmission, the detector efficiency, and the ionization probability, an ansatz that had already been used repeatedly in earlier work. (2) The ionization probability increases exponentially with decreasing inverse ion velocity, and in the limit of infinite velocity, all sputtered atoms are fully ionized. Hence, the matrix effect in SIMS is removed. Secondary ion yields at infinite velocity can be derived by extrapolation of measured energy spectra after eliminating the energy dependence of the sputtered atom flux and the instrument transmission, both considered to be the same for all elements and isotopes. It is shown that, if the energy-dependent neutral flux and the instrument transmission were in fact universal correction functions, concentration calibration could be achieved by extrapolation of ion yield ratios, without even knowing the analytical form of these functions. Literature results as well as (re)analysed data of van der Heide provide clear evidence that the matrix effect is not removed at infinite velocity. Many of the previously ignored problems originate from the fact that the formalism used for data processing has never been outlined in a quantitatively correct manner. As a result, the importance of normalization factors associated with the use of the unknown input functions remained unnoticed (e.g. the surface binding energy and the shape of the energy and angular distributions). Element-specific differences in these parameters give rise to corresponding errors in concentration calibration. The frequently derived non-exponential inverse-velocity dependence of the ‘corrected’ ion yields can be reproduced if one considers rather small deviations from the arbitrary assumptions made in the data processing. It is concluded that, even if all errors in the basic formalism are removed, the iv method does not provide reliable data, neither on elemental concentrations nor on ionization or neutralization phenomena, the reason being that (1) none of the parameters and functions required for extracting ion fractions from measured energy spectra is known with the required accuracy, and (2) the matrix effect cannot be removed by extrapolation procedures.