Linearity tests for secondary electron multipliers used in isotope ratio mass spectrometry

Abstract

Methods are described for testing the linearity in the count-rate response of discrete dynode secondary electron multipliers (SEM), widely used to detect the smallest ion currents in various fields of mass spectrometry. The results consistently reveal small degrees of nonlinearity and demonstrate the need to test and characterize the response of SEMs to achieve accurate measurements. Recommendations and mathematical algorithms are given to improve the measurement results of secondary electron multipliers used in isotope ratio mass spectrometry. Analyses of a certified uranium reference material (CRM U500, 234U/ 235U/ 236U/ 238U ≈ 0.01/1/0.0015/1) using a SEM in ion-counting mode yielded deviations from linearity ranging up to 1.5% in the measured 234U/ 235U and 236U/ 235U ratios. Because the dead time of the ion-counting electronics was determined independently, the observed deviations could be distinguished from the dead-time effect, indicating that nonlinearity was inherent to the SEM. It is shown that the deviations have a similar dependence on count rate for four SEMs produced by ETP and two SEMs produced by MasCom: for count rates below ∼2 × 10 4 counts per second no deviations were found, and consequently, no correction is required. Beyond that rate, the output response of the SEM starts to increase linearly with the logarithm of the applied count rate, with slopes ranging between 0.2% and 0.9% per decade of count rate for the SEMs investigated in this work. Based on the observed deviations, an appropriate correction algorithm, called restricted logarithmic rate effect (RLR), was developed and tested by further measurements of Certified Reference Materials U030A, U050, U200, U500, and U900. A comparison with the uncorrected data and the overall logarithmic corrected data shows the excellent performance of the RLR correction for achieving accurate isotope ratio results. For the proper reporting of ion-counting measurements, the uncertainty in quantifying the nonlinearity component should be included in the total uncertainty budget. The RLR correction is associated with an increase in the uncertainty budget by a factor of 1.1–1.5, even for count rates beyond 10 5 counts per second. Furthermore, the deviations from linearity show a small dependence on the high voltage applied to the SEM. Surface charge effects at the final dynode stages of the SEM are inferred to be responsible for the observed nonlinearity. These effects occur within different manufactured varieties of discrete dynode electron multipliers. These observations indicate that linearity checks are required when a SEM is used for high-accuracy isotope ratio measurements of small quantities of analyte.