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A statistical model of secondary ion emission and attenuation clarifies disparities in quasi‐simultaneous arrival coefficients measured with secondary ion mass spectrometry
Author(s) -
Jones Clive,
Fike David A.
Publication year - 2020
Publication title -
rapid communications in mass spectrometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.528
H-Index - 136
eISSN - 1097-0231
pISSN - 0951-4198
DOI - 10.1002/rcm.8958
Subject(s) - ion , electron multiplier , poisson distribution , negative binomial distribution , attenuation , chemistry , secondary electrons , secondary ion mass spectrometry , atomic physics , computational physics , physics , statistics , electron , mathematics , nuclear physics , optics , organic chemistry
Rationale Secondary ion mass spectrometry data collected using electron multiplier detectors are subject to a correction for the quasi‐simultaneous arrival (QSA) effect. Published Poisson statistical models indicate that the QSA coefficients, β , should have an invariant value of 0.5, whereas, with one exception, published experimental determinations vary between 0.6 and 1.0, with a mean value of 0.75. Methods We developed a more complex model, combining both ion emission and attenuation, that predicts the observed range in measured β and elucidates the mechanism of secondary ion formation. For a given aperture setting, any secondary ion has an equal probability of successful transit to the electron multiplier. Binomial statistics can model pass–fail aperture attenuation but require probability distributions of the quasi‐simultaneously emitted (QSE) ion tally, per primary ion, as input. Assuming (a) that each primary ion impact results in 0, 1, 2,… secondary ion emissions, randomly, with an average K s and (b) that there is finite probability (P2) of a further emission process dependent on K s , the required QSE probability distributions were generated via a combined Poisson–binomial statistical model. Results The value of β was output as a function of K s and P2. For values of P2 > 0 and any value of K s , β always exceeds 0.5. As P2 → 0, β → 0.5; for values of increasing P2 > 0.5 and decreasing K s < 0.5, β → >1. Conclusions Were the emission of one ion not to influence the probability of the formation of a second (i.e. model output for P2 = 0), β should always be 0.5. Yet measurements have never reported this value. Consequently, assuming that published β values are correct, emissions of QSE secondary ions do not occur independently, and it may be inferred that there are linked mechanisms of secondary ion formation as shown here.