Corrigendum: Characterization of the effluent of a He/O2 micro-scaled atmospheric pressure plasma jet by quantitative molecular beam mass spectrometry (2010 New J. Phys. 12 013021)

In this corrigendum, we report and correct an error in the calibration procedure of the molecular beam mass spectrometry ( MBMS ) diagnostics used for measurement of atomic oxygen densities in the ef ﬂ uent of a micro-scaled atmospheric pressure plasma jet ( μ – APPJ ) in He / O 2 gas mixture ( Ellerweg et al 2010 New J. Phys. 12 013021 ) . The difference in the tuning of the used electron impact ionization mass spectrometer at low electron energy used for O atom detection ( E el  =  18 eV ) and for the measurement of the calibration gases CH 4 and Ne ( E el  =  70 eV ) has resulted in the underestimation of the O atom densities by a factor of 2.9. The O 3 signal and the signal of its calibration gas ( Ar ) have been both measured at 70 eV electron energy and O 3 density stays, therefore, unaffected. Updated ﬁ gures with rescaled O densities corrected according to new MBMS measurements with updated mass spectrometry setup, as well as a detailed description of the calibration procedure, are provided here. The corrected O densities provide much better agreement with the of the two-photon absorption induced ﬂ uorescence ( )


Introduction
Absolute densities of reactive species are very important information for understanding plasma-chemical processes in low-and atmospheric plasmas and the radical interaction with surfaces or liquids, allowing for example the quantitative estimation of reaction yields. Additionally, absolute densities are essential for validation of plasma simulation models. One of the available diagnostics is the molecular beam mass spectrometry (MBMS), which can provide absolute densities of ground state species at a plasma-facing surface based only on their mass and ionization threshold, without a necessity of existence of accessible optical transitions for absorption measurements or problems with non-radiative quenching in fluorescence measurements. Still, a careful comparison of the signal measured for the species of interest with a signal measured for a calibration species with known density has to be performed to obtain absolute density information. In this corrigendum, we discuss first the calibration procedure, pointing out the source of error we had in our previous work [1]. After that, we present the updated figures with corrected O atom densities, which were scaled up from the original values to the new density values as obtained in the new MBMS measurement campaign.

Calibration procedure
The gas mixture at one atmosphere is sampled through a sampling orifice (diameter typically at or below 100 μm) into a differentially pumped system with several pumping stages, where a molecular beam (MB) is formed. Even reactive species are preserved in the MB, because they are transported downwards without any collisions with walls and a collision-less flow regime is established a few diameters behind the sampling orifice. The species in the MB are ionized in electron impact collisions in the ionizer of the mass spectrometer and the formed ions are extracted, filtered according to their mass and energy, and detected with secondary electron Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. multiplier detectors. The measured signal of the species i at the detector S i detector (in counts/second) is proportional to the unknown density in the gas mixture n i mixture according to the formula [2, 3]: ionizer F i sampling is the factor taking into account the reduction of the species i density in the expansion and transport in the MB into the ionizer after its sampling through the sampling orifice, s ( ) E i el is the ionization cross section at the used electron energy, I emission is the electron emission current through the ionizer, Lionizer the effective ionizer length, β extraction the ion extraction efficiency from the ionizer, and T(m i ) the mass-dependent transmission function of the quadrupole and energy filter. The transport of neutral species from the sampling orifice to the detector is illustrated in figure 1.
Most of the mentioned factors cannot be measured directly and the calibration of the measured signal is performed with the measurement of selected stable calibration species with known density n . cal mixture By dividing formula (1) for species i with the same formula for calibration species, we obtain: where the same I emission has been used for both measurements and where we have assumed that β extraction and Lionizer are the same for both i and calibration species. Expression (2) simplifies further for non-collisional sampling (species mean free path>diameter of the sampling orifice, e.g. in case of low-pressure plasma analysis), because the reduction of the species density on the way into the ionizer is only a function of system geometry: with r is the sampling orifice radius and x the effective distance between the sampling orifice and the ionizer. The situation is more complex during the collisional sampling, which is the case during atmospheric plasma analysis. A supersonic free jet is formed behind the sampling orifice. The pressure drop in front of and at the sampling orifice, large density gradients behind it, and the presence of the second orifice/skimmer, all lead to a variety of Figure 1. Simplified scheme of the species transport from the gas mixture into the ionizer, their ionization there and finally their transport through the mass spectrometer into the detector in the measuring procedure in the MBMS. f i ionizer is the ion flux of species i from the ionizer into the rest of the mass spectrometer. Only two pumping stages are shown and a beam chopper, used for background signal subtraction, is omitted in the scheme for simplicity. composition distortions [4]. Typically, light and small species radially diffuse much faster from the axis of the MB and the composition of the MB shifts towards heavier/larger species. These sampling effects are taken into account by using the same gas mixture during the calibration measurements as in the plasma analysis (the same collisional partners in the supersonic expansion with calibration species) and similar i and calibration species (similar mass and degree of freedom). The F i sampling and F cal sampling factors can be considered the same under these conditions.
The neutral species in the ionizer are ionized in an electron impact ionization process. The ion yield depends on the electron energy dependent ionization cross section, the electron density in the ionizer (proportional to the electron emission current), the spatial overlap of the electron cloud with the MB represented by Lionizer , and ion extraction efficiency β extraction . β extraction takes into account the probability that an ion leaves the ionizer in the direction of the ionizer exit hole into the following part of the mass spectrometer. As already mentioned before, both Lionizer and β extraction can be assumed constant under ideal conditions and they cancel in the calibration procedure. We explain below that this assumption is not valid for the case where the electron energy changes from a low energy region around 18-25 eV to a high energy region around 70 eV.
The final transport of the ions through the mass spectrometer to the detector is described by massdependent transmission efficiency T(m i ), which mainly takes into account the discrimination of the heavier ions due to the longer transit time through the quadrupole mass filter (higher loss probability) at the same transport energy. This transmission function can be obtained by measuring under identical conditions calibration species with a variety of masses with known ionizer densities. The typical scaling of the T(m i ) is with (m i ) −z , where z1 [5].

Source of error in our previous calibration
Measurements with an updated setup ('new MBMS' here) on the COST reference microplasma jet [6] (a jet with the same geometry, electrode material (stainless steel) and operation parameters as the original μ-APPJ) have revealed a discrepancy between new and previously determined O atom densities, whereas the same ozone densities have been obtained. The only difference in the O atom calibration procedure performed in the original work and in the new measurements has been identified as a source of this discrepancy. This difference is the use of 70 eV electron energy during the measurement of calibration signal for CH 4 and Ne calibration species in the original work, whereas the O atoms have been detected at 18 eV electron energy to avoid dissociative ionization of O 2 or O 3 molecules (threshold ionization mass spectrometry). The new measurements were using Ne as calibration gas with the same mass spectrometer settings (tuning) during O atoms (at 18 eV) and Ne calibration gas (25 eV) measurements.
The effect of higher electron energy should not have, in the ideal case, any effect, because the ionization cross section at 70 eV electron energy has been used, providing the same s ( ) E S cal el cal detector ratio in the formula (1), independent of electron energy. However, higher electron energy influences the real distribution of electrons in the ionizer, influencing the effective ionizer length. The ions are also generated in the ionizer at slightly different locations and their extraction efficiency changes as well. These electron energy dependent changes in the ionizer demonstrated themselves in the slightly different tuning of the device which we used at 18-25 eV and 70 eV to obtain maximal ion signal (tuning procedure performed both at low and high electron energy). The Ne signal measured under experimental conditions and with electron energy of 25 eV has not been, unfortunately, recorded during the original measurements and the measured data cannot be, therefore, directly checked and recalibrated. We performed a test comparing the s ( ) E S cal el cal detector ratio for Ne under low and high electron energies (25 and 70 eV) and otherwise the same conditions and mass spectrometer settings. The obtained difference was a factor 1.6, corroborating our conclusions about the source of the error. This factor is not 2.9 because the measurements have been performed in different MBMS setup (updated geometry with different position of the MB in the ionizer) and different mass spectrometry tuning.
Updated figures from the original work