Comprehensive modelling of secondary-ion energy spectra measured with a magnetic sector field instrument: I. Concept and basic features

•Simple approach described to model secondary ion energy spectra.•Only three parameters required to characterise the magnetic mass spectrometer.•Width of resolution function may be derived from shift of leading edge of spectrum.•Alternatively, integral yields can be used.•Resolution and width of spectrum add in quadrature.

In order to correlate measured secondary-ion energy spectra with theoretically predicted energy distributions of sputtered atoms, one needs to know the properties of the employed mass spectrometer. Here the resolution function and the transmission of a frequently employed magnetic sector-field instrument (IMS-nf series) are described using a simple concept. Modelling of energy spectra is greatly facilitated by the recently provided evidence that the ionisation probability of secondary ions is independent of their emission velocity. Hence the ejected ions may be described by Thompson-type energy distributions which are fully defined by the surface binding energy, Es, of sputtered atoms. On passage through the mass spectrometer the energy distributions are modified in response to the energy dependent transmission of the ion optical system, the aberrations of the lenses and the non-negligible size of the resolution defining apertures, notably the circular contrast aperture (CA) on the entrance side of the spherical energy analyser (aperture diameter d) and the energy slit on the exit side (slit width s). The diameter d determines a characteristic energy Ec up to which secondary ions with emission angles up to 90° to the surface normal are fed through the CA. At higher energies the transmission theoretically decreases as 1/E. Resolution functions are derived by convolving a rectangular box of unit height and width ω with a Gaussian featuring a standard deviation σ. The shape, width and height of the modelled energy spectra depend in a characteristic manner on ω, σ, Ec and Es. Owing to the very low characteristic energies (Ec ≤ 0.1 eV) associated with small CAs (d ≤ 50 μm), the resulting energy spectra contain very little useful information on the physics of the emission process. The peak position and the width of energy distributions are reproduced best using contrast apertures large enough to achieve Ec > 2Es, in combination with a slit width corresponding to ω < Es/4. Inspecting calculated spectra on absolute scales, variations of ω are seen to shift the low-energy edge towards lower (‘negative’) energies by ω/2. With Es as an input parameter, the true origin of the energy scale may be assessed with an accuracy of about ±0.05 eV. In measured spectra, the full widths at half maximum of the original distribution and the resolution function add up roughly in quadrature. Evidence in favour of the described concept is presented in the companion paper.

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