Author: Liu Ning ｜ RealMeter Instruments (Shanghai)
The ion-current intensity reported by a quadrupole residual gas analyzer (RGA) is not the gas content; converting between the two requires relative sensitivity factors (RSF). RSF varies from instrument to instrument and drifts with operating conditions, making it the most uncertain link in the RGA quantification chain. This paper consolidates three rounds of experiments. Round one used a mixture of He, N₂, Ar, Kr and Xe at approximately 20% each (xenon enriched in ¹³²Xe; hereafter the “132 mixture”) admitted through a calibrated leak; two batches of sample spectra with paired backgrounds were used to back-calculate the measured RSF of an Inficon Transpector 2 H200M and to verify the gas composition. Round two used the same mixture admitted through calibrated leaks in three experiments — repeated opening/closing of one leak, switching between two leaks, and power-cycling the ion-source filament — to examine the influence of measurement conditions on quantitative results. Round three specifically examined sampling geometry: the same pair of leaks connected to a near-source port versus a near-pump port (Experiment 4), and a single leak switched between the upper and lower inlet ports through a tee-and-valve manifold (Experiment 5). The results show that, under fixed operating conditions, Ar-referenced RSF values with isotope-abundance correction are reproducible: in round one, the two independently back-calculated batches differ by no more than 2.5% (Ar channel largest); in round two, the cross-experiment deviation within one round is about 6% (maximum 6.1%). After correction with the measured RSF, the compositions of both batches agree with the certified values within ±0.17%. The leak-rate difference between the two leaks changes only the absolute signal magnitude (about 1%–4%), not the compositional ratios. Power-cycling the filament leaves the background structure essentially unchanged (net-signal deviation within 5% overall), accompanied by a small sensitivity drift of about 2%–4%. Round three produced results of an entirely different magnitude: the same gas flow, admitted at different inlet positions, yields net signals differing by a factor of 1.22–1.74 (heavy gases saturating at roughly 1.5–1.75); the ratio increases monotonically with mean thermal speed and saturates with mass. The Ar-referenced RSF likewise changes with the connection geometry (He differs by about 18% between upper/lower ports; Kr by about 10% in the opposite direction) — sampling geometry is a systematic effect more than an order of magnitude larger than the leak-rate and filament perturbations, and is the first condition that must be fixed in quantitative measurement. The RSF of He is markedly higher than that of the other gases and is doubly sensitive to both the peak-evaluation convention and the inlet position; its absolute quantification must be calibrated in situ every time.
Keywords: residual gas analysis; quadrupole mass spectrometry; relative sensitivity factor; isotope-abundance correction; calibrated leak standards; ion-source filament; sampling geometry; inlet-position effect
In vacuum processing, semiconductor equipment, and specialty-gas delivery, the residual gas analyzer is the routine tool for answering “what gases are in the chamber right now, and in what proportions.” It ionizes the gas, separates ions by mass-to-charge ratio, and produces an m/z–intensity spectrum. A common engineering misuse is to read the height of a peak directly as the abundance of that gas — which is physically incorrect.
There are three layers of reasons. First, different gases differ in ionization efficiency and in transmission through the quadrupole; at the same partial pressure their signals can differ severalfold. Second, the vacuum chamber itself has a background (residual water vapor, air ingress, etc.), so the measured signal is a superposition of sample and background. Third, the isotopes of one element split into several peaks, and taking only the main peak discards the contribution of the others.
Correcting these three layers one by one is what leads from a spectrum back to composition. The first and third corrections converge into a single parameter — the relative sensitivity factor (RSF). But RSF is not a universal constant: it is determined jointly by the ion-source condition, quadrupole transmission, and detector gain of the specific instrument, and a vendor’s generic sensitivity table often differs from reality by a factor of several. It is worth noting that the mainstream vendor RSF tables trace their early origins to ionization-gauge (not mass-spectrometer) data from decades ago, reused across models ever since; the deviation between table values and the response of a specific instrument may be structural. This is consistent with recent literature: an intercomparison of 11 identical-model RGAs at Daresbury Laboratory found that sensitivity coefficients are not transferable between individual instruments [7]; Marshall et al. further demonstrated systematically the non-transferability of sensitivity coefficients and the necessity of in-situ calibration [9].
A more complete picture is that a reproducible quantitative RGA measurement depends on five variables — gas species, individual instrument, operating parameters, date, and installation geometry. The first four determine the instrument response; the fifth (geometry) enters, to first order, as an independent multiplicative factor — geometry does not change the definition of RSF, but it changes the definition of the measured partial pressure itself. The three rounds of experiments in this paper constitute a step-by-step test of this framework: round one calibrates the instrument response, round two tests robustness along the parameter and operating-condition dimensions, and round three directly measures the geometry effect.
Experiment numbering used throughout: Study 1 is the composition verification and RSF back-calculation; Study 2 comprises Experiment 1 (single-leak repetition), Experiment 2 (two-leak switching), and Experiment 3 (filament power-cycling); Study 3 comprises Experiment 4 (two leaks at different ports) and Experiment 5 (single leak switched by tee). The text below consistently uses “Study n / Experiment n.”
The working principle of a quadrupole mass spectrometer can be summarized as follows: gas molecules are ionized by electron bombardment, ions of different m/z pass sequentially through the quadrupole field, and the detector records the ion current at each m/z. The horizontal axis of the spectrum is therefore m/z (in amu) and the vertical axis is ion current (denoted Y, in amperes). Y is the “amount of signal detected,” not a partial pressure. Converting Y to partial pressure requires multiplying by the RSF of that gas on this specific instrument:
true partial pressure = Y_net × RSF
A larger RSF means the gas gives a weaker signal at equal partial pressure (low ionization efficiency or high transmission loss), requiring a larger coefficient to restore; a smaller RSF means the opposite.
All measurements in this work were performed under molecular-flow conditions (mixture admitted through calibrated leaks, chamber in high vacuum). One addition is needed (expanded in Study 3): the formula above presupposes that “the measured partial pressure is uniquely defined.” Under molecular flow, a number-density gradient exists along the “source (inlet) → sink (pump port)” path, and an RGA connected at different positions does not measure the same partial pressure. The complete expression is: Y_net = geometry factor × instrument response × true gas supply — the geometry factor is a property of the installation, the instrument response is a property of the individual instrument, and the two are calibrated separately.
The background is the spectrum measured with the sample gas closed off, under otherwise identical vacuum conditions. Sample and background spectra superpose linearly, so:
Y_net(m/z) = Y_sample(m/z) − Y_background(m/z)
In practice, integration windows are used instead of point-by-point subtraction: an m/z interval is defined around each gas’s main peak, and the background area is subtracted from the sample area within that interval. The windows used in this work are: He 3.6–4.6, N₂ 27.6–28.6, Ar 39.6–40.6, Kr 78.0–86.6 (the whole isotope cluster), Xe 128.0–136.6 (the whole isotope cluster).
The necessity of background subtraction is directly visible in our data: in Study 1 the N₂ background is 6.50×10⁻⁷ A, the same order as the sample signal of 1.10×10⁻⁶ A — without subtraction the N₂ result would be systematically inflated; the Kr and Xe backgrounds are only at the 10⁻⁹ level, so subtraction changes little. Background therefore affects different gases unequally and must be handled gas by gas.
The same peak can be quantified by “peak height” (maximum intensity within the window) or “peak area” (integral over the window). The two differ by a factor of about 3, and that factor is gas-dependent (measured area/height ratios, first batch: He 3.15, Ar 3.48) — the root cause is that peak width varies with m/z under quadrupole mass resolution. Switching conventions therefore changes the relative weighting between gases (for the same dataset evaluated by height instead of area, the weight of He relative to Ar rises by about 10%). The three rounds of this work used two conventions: Study 1 used area integration (summing the whole isotope clusters), while Studies 2 and 3 used peak height (maximum within ±0.2 amu of the target mass). Calibration and application must use the same convention; cross-convention comparison requires prior conversion.
In addition, no interference from doubly charged ions or fragment peaks was observed at the five monitored peaks (m/z 4, 28, 40, 84, 132). Strong peaks do exist at m/z 14, 20, 42, 66 in the source spectra (order 10⁻⁸ A); their positions coincide with N₂²⁺, Ar²⁺, Kr²⁺, Xe²⁺ respectively and do not overlap the monitored peaks, so they do not affect the evaluation.
When the monitored peak is only one isotope of an element, that peak represents only part of the element total. A correction by the “monitored-peak abundance” a is then required, writing the effective partial-pressure ratio as the product of composition ratio C and abundance a, C × a.
This step cannot be omitted in this work. Taking Kr as an example, ⁸⁴Kr accounts for about 57% of natural krypton; without correction, the Kr RSF would be overestimated from about 1.15 to about 2.0 — an error exceeding 70%. Likewise, in the 132 mixture used here the xenon is enriched in ¹³²Xe, whose abundance is given by the gas-supplier specification (certified value 94.421%) and is a precondition known before blending. Under this precondition, the m/z 132 peak is necessarily far higher than natural-abundance expectations — an inevitable consequence of the known composition; the data processing simply applies the given abundance directly, with no further interpretation needed.
The abundance values used in the three rounds are listed in Table 1:
Table 1. Monitored-peak abundances
| Monitored peak | Abundance a | Source |
|---|---|---|
| Xe-132 | 94.42% | Enriched; gas-supplier specification (certified 94.421%) |
| Kr-84 | 56.99% | Natural abundance [2] (value used for correction; supplier’s certified value 56.564%; the two differ by 0.43 percentage points, ~0.75% relative, counted as a Kr-channel uncertainty component) |
| Ar-40 | 99.96% | Natural abundance [2] |
| He-4 | ≈100% | Natural abundance [2] |
| N₂-28 | 99.27% | Natural abundance of ¹⁴N¹⁴N [2] |
Note: the Kr-84 abundance correction uniformly uses the natural abundance 56.99%; the supplier’s certified value (56.564%) and our measured value (56.02%, see §3.3) are both close to but different from it. Their differences (<0.75%) are treated as a Kr-channel uncertainty component and do not change the direction of any conclusion.
Let S(i) (≡ Y_net(i)) be the net signal of gas i, C(i) its composition ratio, and a(i) the monitored-peak abundance. Under the assumption that “the effective partial-pressure ratio of each component equals its composition ratio” (this assumption comes from the nominally equal mixture composition, see §3.1):
response per unit pressure R(i) = S(i) / [ C(i) × a(i) ]
RSF(i) = R(reference gas) / R(i)
The three rounds of this work used N₂ and Ar respectively as reference gases (the reference gas has RSF ≡ 1). It must be emphasized that the choice of benchmark does not change any quantitative conclusion. With Ar as benchmark, for example:
RSF_Ar(g) = Y_net(Ar) / Y_net(g)
Y_net(g) × RSF_Ar(g) = Y_net(Ar) (a constant)
That is, after switching benchmark, the corrected values of the five gases remain equal to each other, and the composition calculation is completely unchanged. Section 3.6 verifies this with measured data.
It must be made explicit that the RSF back-calculated by the above procedure is an “apparent RSF.” The components of the mixture have equal molar ratios, but the molecular-flow conductance of a calibrated leak scales as ∝ C_i/√m_i, and the steady-state partial pressure in the chamber is further affected by the pump’s different effective speeds for different gases — the back-calculated result therefore absorbs, beyond instrument sensitivity, the leak conductance (∝1/√m) and differential-pumping factors. Its validity condition is “the calibration chain is identical to the application chain” (same leak type, same chamber, same pump operating point). Apparent RSF and the vendor sensitivity table (a pure instrument quantity) are not the same physical quantity, and their ratio cannot be attributed entirely to instrument deviation; but as an engineering calibration quantity, the apparent RSF is self-consistent and adequate. Throughout this paper, “measured RSF” means apparent RSF.
The test object is the 132 mixture (“132” is named after the monitored peak of the enriched xenon isotope ¹³²Xe), with nominal composition He : N₂ : Ar : Kr : Xe = 1 : 1 : 1 : 1 : 1. The actual fractions given by the gas supplier are: Batch 1 — He 19.96%, N₂ 20.07%, Ar 19.95%, Kr 19.93%, Xe 20.09%; Batch 2 — He 20.00%, N₂ 19.96%, Ar 19.97%, Kr 19.97%, Xe 20.10%. Both batches sum to 100%.
Measurements used an Inficon Transpector 2 H200M [1], with the mixture admitted through a calibrated leak. The data consist of four xlsx files [3]: sample spectra of the two batches and their paired background spectra, all covering m/z 0.6–150 at 0.2 amu steps. Sample spectra are at the 10⁻⁷ A level; background spectra range from 10⁻⁹ to 10⁻⁷ A depending on the channel (N₂ highest).
The ion-source emission current in this round was 2000 μA, identical for both batches; other ion-source parameters are the same as in Study 2 (see §4.1). The emission current differs between Study 1 and Studies 2/3 (2000 μA vs 1000 μA); care is required when comparing absolute RSF values across studies (see the end of §4.5 and Appendix IV).
Processing with the integration-window method of §2.2 gives the net signals of the two batches (Table 2, in A):
Table 2. Study 1 net signals (area-integration convention)
| Gas | m/z window | Batch 1 sample | Batch 1 background | Y_net (Batch 1) | Y_net (Batch 2) |
|---|---|---|---|---|---|
| He | 3.6–4.6 | 1.696×10⁻⁷ | 9.782×10⁻¹¹ | 1.695×10⁻⁷ | 1.619×10⁻⁷ |
| N₂ | 27.6–28.6 | 1.103×10⁻⁶ | 6.501×10⁻⁷ | 4.526×10⁻⁷ | 4.298×10⁻⁷ |
| Ar | 39.6–40.6 | 4.677×10⁻⁷ | 8.593×10⁻⁹ | 4.591×10⁻⁷ | 4.482×10⁻⁷ |
| Kr | 78.0–86.6 | 4.066×10⁻⁷ | 2.255×10⁻⁹ | 4.043×10⁻⁷ | 3.907×10⁻⁷ |
| Xe | 128.0–136.6 | 4.209×10⁻⁷ | 1.658×10⁻⁹ | 4.193×10⁻⁷ | 4.074×10⁻⁷ |
The net signals of the two batches are consistent in magnitude (2%–5% apart). Without correction, the five gases’ signal fractions are clearly not 20% each — He is only about 9%, while N₂, Ar, Kr, Xe lie between 21% and 24% — a direct manifestation of differing ionization efficiencies, and the very reason RSF must be introduced (Figure 2).
Before back-calculating the RSF, a test can be performed that relies on no RSF assumption at all. The RSF values of the isotopes of one element are approximately equal, so normalizing the intensities of all isotope peaks of the same element should approximately reproduce that element’s internal isotope abundances. This test uses only signal ratios among isotopes and involves no cross-element conversion; its absolute accuracy is limited by quadrupole mass discrimination (about ±1% in this work).
The measured results for the Kr cluster are listed in Table 3 (I_peak is the maximum within a ±0.2 amu window):
Table 3. Kr isotope-cluster fractions
| Kr isotope | m/z | Batch 1 I_peak (A) | Batch 1 fraction | Batch 2 fraction | Certified atom% | Deviation (Batch 1) |
|---|---|---|---|---|---|---|
| Kr-78 | 78 | 5.267×10⁻¹⁰ | 0.417% | 0.413% | 0.335% | +0.082% |
| Kr-80 | 80 | 3.274×10⁻⁹ | 2.591% | 2.594% | 2.209% | +0.382% |
| Kr-82 | 82 | 1.575×10⁻⁸ | 12.463% | 12.626% | 11.302% | +1.161% |
| Kr-83 | 83 | 1.550×10⁻⁸ | 12.269% | 12.261% | 11.869% | +0.400% |
| Kr-84 | 84 | 7.080×10⁻⁸ | 56.024% | 56.025% | 56.564% | −0.540% |
| Kr-86 | 86 | 2.052×10⁻⁸ | 16.236% | 16.080% | 17.721% | −1.485% |
The measured results for the Xe cluster are listed in Table 4:
Table 4. Xe isotope-cluster fractions
| Xe isotope | m/z | Batch 1 I_peak (A) | Batch 1 fraction | Batch 2 fraction | Certified atom% | Deviation (Batch 1) |
|---|---|---|---|---|---|---|
| Xe-124 | 124 | 0 | 0.000% | 0.001% | 0.001% | −0.001% |
| Xe-126 | 126 | 0 | 0.000% | 0.000% | 0.002% | −0.002% |
| Xe-128 | 128 | 4.775×10⁻¹² | 0.004% | 0.004% | 0.362% | −0.358% |
| Xe-129 | 129 | 1.006×10⁻¹¹ | 0.008% | 0.009% | 0.007% | +0.001% |
| Xe-130 | 130 | 1.383×10⁻¹⁰ | 0.109% | 0.114% | 0.010% | +0.099% |
| Xe-131 | 131 | 4.804×10⁻⁹ | 3.780% | 3.749% | 2.886% | +0.894% |
| Xe-132 | 132 | 1.192×10⁻⁷ | 93.835% | 93.831% | 94.421% | −0.586% |
| Xe-134 | 134 | 2.875×10⁻⁹ | 2.262% | 2.289% | 2.306% | −0.044% |
| Xe-136 | 136 | 2.315×10⁻¹² | 0.002% | 0.002% | 0.004% | −0.002% |
There are two main conclusions. First, the measured fraction of Kr-84 within Kr is 56.024% (Batch 1) and 56.025% (Batch 2), versus the certified 56.564% — a deviation of 0.54%, below 0.6%; batch-to-batch repeatability of the main-peak fraction is better than 0.01%. Second, the measured fraction of Xe-132 within Xe is 93.835% and 93.831%, versus the certified 94.421% — a deviation of about −0.6%. Low-abundance isotopes (Xe-124/126/136) are below the RGA detection limit and recorded as 0%; Xe-128 measures 0.004% versus the certified 0.362%, reflecting the quadrupole’s insufficient sensitivity to weak low-abundance peaks rather than any gas-source problem.
After normalization with “main peak = 100%,” the cross-isotope ratios are likewise stable across batches (Table 5):
Table 5. Isotope ratios relative to the main peak (= 100%)
| Ratio | Certified abundance | Batch 1 measured | Batch 2 measured |
|---|---|---|---|
| ⁸²Kr / ⁸⁴Kr | 19.98 | 22.25 | 22.54 |
| ⁸³Kr / ⁸⁴Kr | 20.98 | 21.90 | 21.88 |
| ⁸⁶Kr / ⁸⁴Kr | 31.33 | 28.98 | 28.70 |
| ¹²⁹Xe / ¹³²Xe | 0.01 | 0.01 | 0.01 |
| ¹³¹Xe / ¹³²Xe | 3.06 | 4.03 | 4.00 |
| ¹³⁴Xe / ¹³²Xe | 2.44 | 2.41 | 2.44 |
¹³⁴Xe/¹³²Xe falls at 2.41 and 2.44 in the two batches (certified 2.44), in good agreement; ⁸²Kr/⁸⁴Kr and ⁸⁶Kr/⁸⁴Kr deviate from the certified values by −7.5% to +11.4%, a common magnitude for quadrupole mass discrimination.
The isotope distributions of the two batches are consistent, indicating that the gas source executed the same recipe in blending, with no compositional discrepancy between batches.
With N₂ as benchmark (RSF_N₂ ≡ 1), back-calculation from the net signals of §3.2 per the §2.5 formulas is compared with the vendor sensitivity table in Table 6:
Table 6. Measured apparent RSF (N₂ benchmark) versus vendor sensitivity table
| Gas | Vendor table | Batch 1 back-calculated | Batch 2 back-calculated | Two-batch mean (recommended) | Measured / vendor |
|---|---|---|---|---|---|
| He | 0.14 | 2.671 | 2.654 | 2.663 | 19.0× |
| N₂ | 1.00 | 1.000 | 1.000 | 1.000 | 1.0× |
| Ar | 1.20 | 0.986 | 0.959 | 0.972 | 0.8× |
| Kr | 0.50 | 1.119 | 1.100 | 1.110 | 2.2× |
| Xe | 0.27 | 1.080 | 1.055 | 1.067 | 4.0× |
The RSF values back-calculated independently from the two batches differ by no more than 2.5% (Ar channel largest, about 2.8% by table values / about 2.2% by recomputation) — good repeatability under identical operating conditions. Compared with the vendor table, the differences range from 0.8× (Ar) to 19.0× (He). As stated in §2.5, these ratios contain both instrument response and transport/pumping factors (for example, about 2.6× of the He 19.0× comes from the molecular-flow conductance of the calibrated leak, √(28/4)), and cannot be attributed entirely to instrument deviation; but in any case, the vendor’s generic sensitivity table cannot be applied directly to quantification on this H200M — in-situ back-calculation with one’s own instrument and samples is mandatory (Figure 3). This conclusion is consistent with recent literature [7][9].
Substituting the two-batch mean RSF and computing fraction = Y_net(g) × RSF(g) ÷ Σ[Y_net(g) × RSF(g)] × 100%, the comparison with the supplier’s certified fractions is shown in Table 7:
Table 7. Corrected versus certified compositions
| Gas | Batch 1 corrected | Batch 1 certified | Deviation | Batch 2 corrected | Batch 2 certified | Deviation |
|---|---|---|---|---|---|---|
| He | 20.09% | 19.96% | +0.13% | 19.91% | 20.00% | −0.09% |
| N₂ | 20.15% | 20.07% | +0.08% | 19.85% | 19.96% | −0.11% |
| Ar | 19.87% | 19.95% | −0.08% | 20.13% | 19.97% | +0.16% |
| Kr | 19.97% | 19.93% | +0.04% | 20.03% | 19.97% | +0.06% |
| Xe | 19.92% | 20.09% | −0.17% | 20.08% | 20.10% | −0.02% |
All deviations in both batches fall within ±0.17%; the two largest are Xe (Batch 1, −0.17%) and Ar (Batch 2, +0.16%). Corrected with the measured RSF, the RGA-measured compositions agree with the certified values. The nature of this test must be stated: the RSF was back-calculated from the two-batch mean signal, so a small back-calculated deviation is largely inevitable by construction — it verifies the self-consistency of the computational chain, and does not constitute an independent verification of accuracy. Independent verification requires applying the RSF from a single batch to the other batch, or re-measuring with an independent certified gas; this is included in the follow-up plan. A separate caution concerns the N₂ channel — the m/z 28 signal in the background is of the same order as the sample (background ≈ 1.4× the net signal, versus <2% for other channels), so the residual after subtraction contributes roughly two orders of magnitude more to the net signal than in other channels; this channel is structurally more uncertain and should be independently verified with a reference gas.
To test whether the conclusions depend on the benchmark choice, the back-calculation was repeated with Ar-40 as benchmark (RSF_Ar ≡ 1), Table 8:
Table 8. Ar-benchmark back-calculation (Study 1)
| Gas | Y_net (Batch 1) | Y_net (Batch 2) | RSF_Ar (Batch 1) | RSF_Ar (Batch 2) | Two-batch mean |
|---|---|---|---|---|---|
| He | 1.695×10⁻⁷ | 1.619×10⁻⁷ | 2.7088 | 2.7685 | 2.7387 |
| N₂ | 4.526×10⁻⁷ | 4.298×10⁻⁷ | 1.0142 | 1.0430 | 1.0286 |
| Ar | 4.591×10⁻⁷ | 4.482×10⁻⁷ | 1.0000 | 1.0000 | 1.0000 |
| Kr | 4.043×10⁻⁷ | 3.907×10⁻⁷ | 1.1353 | 1.1472 | 1.1413 |
| Xe | 4.193×10⁻⁷ | 4.074×10⁻⁷ | 1.0949 | 1.1004 | 1.0976 |
The conversion between the two benchmarks is RSF_Ar(g) = RSF_N₂(g) ÷ RSF_N₂(Ar). Taking He as example: 2.6626 ÷ 0.9724 = 2.7382, consistent with the two-batch mean of 2.7387 in the table. Per the derivation in §2.5, after switching benchmark the corrected values of the gases remain equal to each other and the corrected fractions are unchanged.
Study 1 established three facts: the measured apparent RSF of this H200M differs from the vendor table by 0.8×–19.0× (including transport/pumping factors), so generic values cannot be applied; after correction with the measured RSF, the compositions of both batches are self-consistent with the certified values (within ±0.17%); the isotope distributions are highly consistent between batches, supporting the conclusion that the gas source shows no blending discrepancy.
Study 1 answered “what the RSF is.” But if measurement conditions themselves can change the RSF, then a calibration holds only under the conditions at the time of calibration. Study 2 likewise used calibrated leaks as the gas source, and examined exactly this, through repeated opening/closing and switching of leaks and through filament power-cycling. It must be stated in advance: the two leaks in Study 2 were connected at the same chamber position — a control baseline that is crucial when Study 3 judges the position effect.
The three experiments used the same mixture (He, N₂, Ar, Kr, Xe at about 20% each), admitted through calibrated leaks into the RGA, with full m/z 0.6–150 spectra collected [4]. They differ in the leak object and filament state (Table 9):
Table 9. Design of the three Study 2 experiments
| Item | Exp. 1 (single-leak repetition) | Exp. 2 (two-leak switching, same port) | Exp. 3 (filament cycling) |
|---|---|---|---|
| Leak object | 011002 × 3 runs | 011002, 011027 × 3 runs each | 011002, 011027 × 3 runs each |
| Inlet position | same position | same position (key control condition) | same position |
| Filament state | normal measurement procedure | kept on throughout | switched off and on before each run |
| Background data | collected separately | collected with filament on | collected separately before each run |
| Monitored peaks | He 4 / N₂ 28 / Ar 40 / Kr 84 / Xe 132 | same | same |
| Focus | single-leak repeatability | leak-to-leak consistency | filament cycling effects |
The two leaks have similar nominal leak rates; per the measured data in §4.3, their signals differ by about 1.3%–4.0%, so they can be regarded as a pair of “approximately equal-rate” leaks. The instrument operating parameters of the three experiments are completely identical (Table 10), which is the prerequisite for cross-comparison:
Table 10. Ion-source operating parameters (uniform across Studies 2/3)
| Parameter | Set value | Meaning |
|---|---|---|
| Emission Current | 1000 μA | filament emission current |
| Electron Energy | 102 eV | ionizing electron energy |
| Focus | 27 V | ion focusing voltage |
| Ion Energy | 10000 meV | ion injection energy (10 eV) |
| Sensitivity Mass Factor | 1 | mass sensitivity factor |
| Sensitivity | 7.9588×10⁻⁵ | instrument sensitivity (signal-to-pressure coefficient; units per the instrument manual [1]) |
The data-processing chain is uniformly four steps: peak evaluation (maximum within ±0.2 amu of the target mass) → background subtraction → isotope-abundance correction → RSF calculation normalized to Ar.
The mixture was admitted through calibrated leak 011002, which was opened and closed repeatedly for three measurement runs; backgrounds were collected separately. Net signals are listed in Table 11 (in A):
Table 11. Experiment 1 net signals (011002, three repetitions)
| Gas | Run 1 | Run 2 | Run 3 |
|---|---|---|---|
| He (4) | 1.591×10⁻⁸ | 1.541×10⁻⁸ | 1.542×10⁻⁸ |
| N₂ (28) | 1.017×10⁻⁷ | 9.690×10⁻⁸ | 9.320×10⁻⁸ |
| Ar (40) | 1.019×10⁻⁷ | 1.003×10⁻⁷ | 9.838×10⁻⁸ |
| Kr (84) | 5.055×10⁻⁸ | 4.939×10⁻⁸ | 4.841×10⁻⁸ |
| Xe (132) | 8.626×10⁻⁸ | 8.415×10⁻⁸ | 8.272×10⁻⁸ |
The RSF values derived from the net signals (Ar = 1): He 6.41–6.51, N₂ 1.00–1.05, Kr 1.15–1.16, Xe 1.12–1.13; the three-run deviation is within ±1.5% for He/Kr/Xe and about ±3% for N₂. The data also show a consistent “first run high, then slowly declining” trend (about 3%–5% for most gases, up to 8.4% for N₂), consistent with the conclusion that single-leak repeated measurement is stable and usable for calibration. There are two candidate origins of this trend: first, after gas admission the chamber-line system needs an equilibration time on the order of the time constant τ = V/S_eff; second, after the filament is switched on the ion source undergoes a thermal-stabilization process (both attributions are speculative; the trend itself is reliable). It is recommended to wait no less than five response time constants before acquisition, or to uniformly take data from the stabilized segment (see Recommendation 3).
With the ion-source filament kept on throughout, the two calibrated leaks 011002 and 011027 (slightly different leak rates) were switched at the same inlet position, three runs each; backgrounds were collected with the filament on. The net signals of the six runs are listed in Table 12 (in A):
Table 12. Experiment 2 net signals (two leaks, same port)
| Gas | 011002 run 1 | 011002 run 2 | 011002 run 3 | 011027 run 1 | 011027 run 2 | 011027 run 3 |
|---|---|---|---|---|---|---|
| He (4) | 1.672×10⁻⁸ | 1.603×10⁻⁸ | 1.572×10⁻⁸ | 1.653×10⁻⁸ | 1.570×10⁻⁸ | 1.561×10⁻⁸ |
| N₂ (28) | 1.141×10⁻⁷ | 1.034×10⁻⁷ | 1.008×10⁻⁷ | 1.056×10⁻⁷ | 1.006×10⁻⁷ | 9.985×10⁻⁸ |
| Ar (40) | 1.105×10⁻⁷ | 1.059×10⁻⁷ | 1.055×10⁻⁷ | 1.063×10⁻⁷ | 1.043×10⁻⁷ | 1.048×10⁻⁷ |
| Kr (84) | 5.387×10⁻⁸ | 5.115×10⁻⁸ | 5.079×10⁻⁸ | 5.182×10⁻⁸ | 5.027×10⁻⁸ | 5.030×10⁻⁸ |
| Xe (132) | 9.281×10⁻⁸ | 8.695×10⁻⁸ | 8.579×10⁻⁸ | 8.796×10⁻⁸ | 8.503×10⁻⁸ | 8.503×10⁻⁸ |
The leak-to-leak ratios of the three-run means are: He 1.013, N₂ 1.040, Ar 1.021, Kr 1.022, Xe 1.029. The ratios of the five gases are very close to each other, indicating that the signal of 011002 is overall about 1%–4% higher, the difference arising from the leak rate rather than any species-selective permeation. The RSF values calibrated independently for the two leaks agree (He ≈ 6.6, Kr 1.18, Xe 1.15) with deviation below 1%. All six runs likewise show the “first high, then slowly declining” trend.
This set of ratios (1.013–1.040) plays the role of a criterion in Study 3: it calibrates the difference band of “the same pair of leaks at the same position” — a leak-rate difference changes only the height of the ratio, not its shape (the five gases are equally high). If, in Experiment 4, the ratios of the two leaks moved to different ports vary systematically with gas species, the part beyond this band can only be attributed to position (see §5.1).
Experiment 3 used the same mixture and the same two leaks as Experiment 2, but before each measurement the ion-source filament was switched off and back on, and a background was collected separately before each measurement. Net signals are listed in Table 13 (in A):
Table 13. Experiment 3 net signals (filament switched off and back on)
| Gas | 011002 run 1 | 011002 run 2 | 011002 run 3 | 011027 run 1 | 011027 run 2 | 011027 run 3 |
|---|---|---|---|---|---|---|
| He (4) | 1.651×10⁻⁸ | 1.604×10⁻⁸ | 1.592×10⁻⁸ | 1.684×10⁻⁸ | 1.604×10⁻⁸ | 1.577×10⁻⁸ |
| N₂ (28) | 1.082×10⁻⁷ | 1.060×10⁻⁷ | 1.050×10⁻⁷ | 1.087×10⁻⁷ | 1.060×10⁻⁷ | 1.063×10⁻⁷ |
| Ar (40) | 1.123×10⁻⁷ | 1.083×10⁻⁷ | 1.075×10⁻⁷ | 1.132×10⁻⁷ | 1.098×10⁻⁷ | 1.088×10⁻⁷ |
| Kr (84) | 5.362×10⁻⁸ | 5.118×10⁻⁸ | 5.100×10⁻⁸ | 5.407×10⁻⁸ | 5.196×10⁻⁸ | 5.153×10⁻⁸ |
| Xe (132) | 8.965×10⁻⁸ | 8.621×10⁻⁸ | 8.514×10⁻⁸ | 9.117×10⁻⁸ | 8.752×10⁻⁸ | 8.685×10⁻⁸ |
The backgrounds before and after filament cycling are compared in Table 14 (in A):
Table 14. Background comparison across filament cycling
| Gas | Exp. 2 background (filament on) | Exp. 3 background (after cycling, 6-run mean) | Change |
|---|---|---|---|
| He | 5.1×10⁻¹¹ | 4.2×10⁻¹¹ | order of magnitude unchanged |
| N₂ | 1.61×10⁻⁷ | 1.67×10⁻⁷ | +4%, order unchanged |
| Ar | 1.9×10⁻⁹ | 1.9×10⁻⁹ | unchanged |
| Kr | 1.2×10⁻¹⁰ | 8.9×10⁻¹¹ | slightly lower, absolute amount tiny |
| Xe | 2.0×10⁻¹⁰ | 1.8×10⁻¹⁰ | slightly lower, absolute amount tiny |
The background structure is not changed by cycling the filament: orders of magnitude are fully preserved; only Kr and Xe are slightly lower (absolute amounts at the 10⁻¹¹–10⁻¹⁰ level, no impact on results), while the N₂ channel rises by 4% under the influence of residual air.
Net-signal and RSF comparison (Table 15): broken down by leak, the net-signal ratios (Exp. 3 / Exp. 2) for the 011002 branch are 0.98–1.02, and for the 011027 branch 1.02–1.05; the combined overall deviation is within 5%.
Table 15. Filament-cycling effects on net signals and RSF
| Gas | Net-signal ratio (Exp.3/Exp.2, 011002) | Net-signal ratio (011027) | RSF · Exp. 2 | RSF · Exp. 3 |
|---|---|---|---|---|
| He | 1.00 | 1.02 | 6.60–6.65 | 6.77–6.83 |
| N₂ | 1.00 | 1.05 | 1.01–1.03 | 1.03 |
| Ar | 1.02 | 1.05 | 1.00 (benchmark) | 1.00 (benchmark) |
| Kr | 1.00 | 1.03 | 1.18 | 1.20 |
| Xe | 0.98–0.99 | 1.03 | 1.15–1.16 | 1.19–1.20 |
The RSF shifts up overall by about 2%–4% (He 6.6 → 6.8), the same order as normal inter-experiment drift. The engineering implication is clear: filament switching does not compromise data usability, but after switching one should wait for signal stabilization before measuring, and collect a separate background before each measurement as in Experiment 3.
Comparing the RSF of the three experiments on the same benchmark (Ar = 1), Table 16:
Table 16. Cross-experiment RSF of Study 2 (Ar = 1)
| Gas (monitored peak) | Exp. 1 RSF | Exp. 2 RSF | Exp. 3 RSF | Max deviation |
|---|---|---|---|---|
| He (m/z 4) | 6.44 | 6.65 | 6.78 | +5.3% |
| N₂ (m/z 28) | 1.03 | 1.01 | 1.03 | −1.9% |
| Ar (m/z 40) | 1.00 | 1.00 | 1.00 | benchmark |
| Kr (m/z 84) | 1.155 | 1.178 | 1.199 | +3.8% |
| Xe (m/z 132) | 1.126 | 1.154 | 1.195 | +6.1% |
The maximum cross-experiment deviation is about 6% (Xe 6.1%, He 5.3%); the other gases are within 4%. The ordering of relative sensitivities is preserved in all experiments: He far above the other gases, Kr and Xe close, N₂ and Ar close. For the purposes of this study, the RSF is reproducible across the three experiments and can serve as the quantitative correction parameter of this instrument under similar operating conditions. But note the boundary of this conclusion: all three experiments were performed at the same inlet position and the same emission current (1000 μA) — “RSF is reproducible” holds when conditions are fixed; Study 3 will show that once the position changes, the RSF changes far beyond the 6% seen here.
Cross-study RSF comparison (must be stated explicitly): the He RSF (Ar benchmark) back-calculated in Study 1 at 2000 μA emission current with the area-integration convention is 2.74, whereas in Studies 2/3 at 1000 μA with the peak-height convention it is 6.4–6.8 — a factor of about 2.4; the cross-study differences for N₂/Kr/Xe are only 2%–6%. The convention difference explains only about 10% of this; the main discrepancy is associated with the systematic change of emission current and ion-source state, to which the He channel is abnormally sensitive (possibly involving ion-source saturation or space-charge effects; the exact cause is listed as an open issue). Therefore: RSF values are valid only when parameters are fixed; cross-emission-current and cross-convention comparisons are invalid; absolute RSF values from different studies of this paper are not used interchangeably.
Study 2 yields three conclusions: single-leak three-run RSF deviations are small (within ±1.5% for He/Kr/Xe, about ±3% for N₂); with two leaks switched at the same port, the five-gas signal ratios are 1.013–1.040, the difference arising purely from leak rate, with no species-selective permeation observed; after filament power-cycling the background orders of magnitude are unchanged, net-signal deviations are within 5% overall, and the RSF shifts up by only about 2%–4% — ion-source switching has little effect on quantitative results.
The first two rounds were all performed at the same inlet position, and their conclusion was “leak rate and filament cause perturbations of only a few percent.” Study 3 examines a variable never isolated before: the inlet position. The chamber has two inlet ports — an upper port near the RGA ion source (near-source) and a lower port near the turbomolecular pump (near-pump). Two progressive experiments:
The net signals of the two leaks over three runs are shown in Figure 7. Taking the three-run means, the net-signal ratios of the near-source port (Leak 2) to the near-pump port (Leak 1) are listed in Table 17:
Table 17. Experiment 4 net-signal ratios (near-source / near-pump, three-run means)
| Gas | He | N₂ | Ar | Kr | Xe |
|---|---|---|---|---|---|
| Ratio (Leak 2 / Leak 1) | 1.22 | 1.59 | 1.50 | 1.57 | 1.58 |
Criterion first (§4.3): if the difference were merely a leak-rate difference, the five-gas ratios should lie entirely within the same-port band (1.013–1.040) and be essentially equal in height. The measured ratios are 1.22–1.59, span 0.37, and vary systematically with gas species (Figure 8) — more than an order of magnitude beyond the same-port band, attributable only to inlet position. Within-run repeatability (maximum deviation from the three-run mean) does not exceed about 10%, far smaller than the 22%–59% inter-port difference. Taking Ar as example: about 7.3 near-pump vs about 11.0 near-source (×10⁻⁸ A).
Experiment 4 still has an alternative explanation: the leak-rate difference of the two leaks might happen to “look like” a position effect. Experiment 5 excludes this alternative with a single leak. Net signals of three runs at each port are shown in Figure 9; run-by-run ratios and means are listed in Table 18:
Table 18. Experiment 5 net-signal ratios (upper / lower port, three-run means)
| Gas | He | N₂ | Ar | Kr | Xe |
|---|---|---|---|---|---|
| Upper/lower net-signal ratio | 1.34 | 1.51 | 1.57 | 1.74 | 1.69 |
The run-by-run ratios deviate from their means by no more than about 5%; what must be recorded honestly is that the run-by-run ratios of all five gases show a consistent slow monotonic decline (e.g., Xe 1.744→1.682→1.653), consistent with the ongoing equilibration of the chamber-line system, and this does not affect the mean-value conclusions.
The two experiments agree in magnitude and shape (Figure 10): the Experiment 5 ratios are systematically 4%–11% higher for He/Ar/Kr/Xe (arising from the different background levels of the two rounds), while the N₂ channel does not follow this pattern owing to background interference (Experiment 5 is instead about 5% lower) — the position effect holds in both directions of “changing the leak” and “not changing the leak.” The same gas flow, merely admitted at a different position, yields net signals differing by a factor of 1.22–1.74; the ~3% difference between the Kr and Xe ratios (1.74 vs 1.69; 1.57 vs 1.58 in Experiment 4) is smaller than the within-run repeatability (range ~5%), so the two are indistinguishable within uncertainty and are not interpreted as a true ordering. For comparison with Study 2: leak-rate difference about 1%–4% (Experiment 2), filament switching within 5% overall (Experiment 3) — the position effect is more than an order of magnitude larger than the perturbations introduced by leak-rate differences and filament cycling in this system.
The ratio rises monotonically with the mean thermal speed v̄ = √(8kT/πm) (∝ 1/√m) and tends toward saturation (Figure 11; n = 5, the correlation serves only as a trend indicator, not a quantitative law); versus mass itself it clearly saturates — Kr and Xe differ in mass by 56%, yet their ratios differ by only 0.00–0.05. At 25 °C the mean thermal speeds span about a factor of 6 (He 1256 m/s → Xe 220 m/s). The empirical line in the figure, “ratio ≈ 1.7 − 0.9/√m,” is drawn only as a visual guide; its coefficients carry no physical meaning. Superficially “the heavier the gas, the stronger the position effect”; in essence it is the transport properties that vary with the gas.
Working hypothesis for the mechanism (to be tested): under molecular flow, the steady-state molecular density in the ionization region is determined by the competition between “molecules reaching the ionization region” and “molecules being pumped away.” With near-pump admission, most molecules are pumped away before reaching the ionization region; with near-source admission, molecules first traverse the ionization region and are ionized with higher probability — this explains the ~1.5× magnitude difference. The lower He ratio (1.22–1.34 instead of ~1.6) is likewise self-consistent in direction: turbomolecular pumps have a low compression ratio for He and significant backflow, so the pump port acts as a partial reflector rather than an ideal absorber, and backflow smears out the density gradient; heavy gases are nearly ideally absorbed at the pump port and the effect saturates. This hypothesis is compatible with all observations, but it is not the only explanation (alternative mechanisms, such as differences in the ionization-region transit probability or residence time for He, are not excluded); the discriminating test is a pump-port throttling experiment — prediction: after throttling, the He ratio should rise toward ~1.6 while the heavy gases barely move (test plan in [10]).
The apparent RSF with Ar benchmark and isotope-abundance correction is listed in Table 19:
Table 19. Apparent RSF under different connections (Ar = 1)
| Connection | He | N₂ | Kr | Xe |
|---|---|---|---|---|
| Exp. 4 · lower port (near-pump, Leak 1) | 5.27 | 1.10 | 1.19 | 1.14 |
| Exp. 4 · upper port (near-source, Leak 2) | 6.48 | 1.04 | 1.13 | 1.10 |
| Exp. 5 · upper port (near-source) | 6.71 | 1.02 | 1.19 | 1.15 |
| Exp. 5 · lower port (near-pump) | 5.68 | 0.98 | 1.31 | 1.24 |
He differs by about 18% between upper/lower ports (6.71 vs 5.68), and Kr by about 10% in the opposite direction (1.19 vs 1.31) — the position effect is not a mere overall gain; it changes the relative weighting among gases. Since the RSF in this paper is an apparent quantity (§2.5), the connection dependence here includes both instrument response and pumping-path changes, which are not separated under the current experimental design. This adds a second layer of constraint beyond Conclusion 7’s “the He channel must be calibrated in situ every time”: He is sensitive to the evaluation convention (§2.3, ~10%) and deviates most strongly with inlet position (ratio 1.22–1.34, far from the heavy-gas saturation value of ~1.6–1.7); the two sensitivities share one origin — He’s transport and pumping behavior sits at the edge of the system. Engineering implication: applying a vendor table or historical RSF to convert compositions introduces a systematic error that varies with the connection; in every quantitative round the RSF must be measured in situ against a reference gas, and the calibration connection must be identical to the application connection.
Study 3 shows that inlet position changes the net signal by a factor of 1.22–1.74 and changes the apparent RSF itself (He ~18%) — more than an order of magnitude larger than leak-rate differences and filament perturbations. Metrology-grade work has long guarded against this: in the Daresbury 11-RGA intercomparison, the gas-inlet line was deliberately arranged at right angles to the instruments to avoid beam effects [7]; this paper provides a direct quantification of the position effect and its gas-dependent pattern. The complete geometry framework (configuration–position–orientation, three layers; condensable-vapor amplification; publication discipline) is given in [10].
The vendor sensitivity table cannot be applied directly to this H200M. The measured apparent RSF differs from the vendor table by 0.8×–19.0× (He 19.0×, Xe 4.0×, Kr 2.2×, Ar 0.8×); these differences contain both instrument response and transport/pumping factors, but in any case demonstrate that generic tables cannot be applied directly — in-situ calibration with one’s own instrument and certified gases is mandatory. The early origins of mainstream table values trace to ionization-gauge rather than mass-spectrometer data from decades ago, suggesting that such deviations may be structural.
The Ar-referenced back-calculation procedure with isotope-abundance correction is stable and reliable under fixed operating conditions. In Study 1 with N₂ as benchmark, independently back-calculated RSF values of the two batches differ by no more than 2.5%; in Study 2 the cross-experiment deviation is about 6% (maximum 6.1%). Across operating conditions (emission current 2000 vs 1000 μA), the He-channel RSF drifts by a factor of about 2.4, and cross-condition comparison is invalid.
Compositions corrected with the measured RSF are self-consistent with the certified values. All gases in both batches deviate within ±0.17%, so the 132 mixture can be regarded as satisfying 1:1:1:1:1; the largest deviations are Xe (−0.17%) and Ar (+0.16%). This test is a self-consistency check; independent verification of accuracy is included in the follow-up plan. The N₂ channel, owing to its high background share, is structurally more uncertain than the other channels and should be independently verified with a reference gas.
Isotope abundances provide a verification independent of RSF. The measured fraction of Kr-84 in Kr is 56.02% versus the certified 56.564%, and Xe-132 in Xe is 93.83% versus 94.421%; both deviations are below 0.6%, and batch-to-batch repeatability is better than 0.01%. These results support the conclusion that the gas source shows no blending discrepancy; the absolute accuracy of the self-check is limited by quadrupole mass discrimination (about ±1%).
A leak-rate difference does not change the compositional ratios. With the two leaks at the same port, the five-gas signal ratios are 1.013–1.040, highly uniform across gases, with no species-selective permeation observed; the independently calibrated RSF values of the two leaks agree within 1%. (This conclusion holds only “at the same inlet position” — see Conclusion 8.)
Filament power-cycling has little effect on quantification. After switching the filament off and on, background orders of magnitude are unchanged, net-signal deviations are within 5% overall (0–2% for the 011002 branch, 2–5% for 011027), and the RSF shifts up by only about 2%–4%; but the first measurement after switching runs slightly high, so one should wait for signal stabilization before measuring.
The He channel must be treated separately. Its apparent RSF is markedly higher than that of the other gases (about 6.4–6.8 at 1000 μA with peak height; about 2.7 at 2000 μA with area integration — the two are not directly comparable); it is sensitive to the evaluation convention (~10%), deviates most with inlet position (ratio 1.22–1.34, far from the heavy-gas saturation of ~1.6–1.7), and is abnormally sensitive to emission-current changes (a factor of ~2.4). Convention sensitivity and position sensitivity share one origin — He’s transport and pumping behavior sits at the edge of the system. Absolute quantification of He must be calibrated in situ every time.
Inlet position is the largest systematic factor. Merely switching the same gas flow between the upper/lower inlet ports changes the net signal by a factor of 1.22–1.74 (heavy gases saturating at about 1.5–1.75); the ratio rises monotonically with mean thermal speed and saturates with mass; the apparent RSF changes with the connection (He ~18%, Kr ~10% in the opposite direction). The position effect is more than an order of magnitude larger than leak-rate and filament perturbations, and is the first condition to fix in quantitative measurement; its mechanism (competition in pump-port absorption completeness) is a working hypothesis, with the pump-port throttling experiment as the discriminating test.
The measurement chain is five-element, but decomposable to first order. Gas × instrument × parameters × date determine the instrument response, and installation geometry enters as an independent multiplicative factor; the upper/lower-port ratio measured in this study is the ratio of two geometry factors (a relative measurement — an absolute definition of the geometry factor requires normalization to a chosen reference configuration). The separability of “geometry × instrument function” is a first-order working hypothesis — Study 3 demonstrates the existence and magnitude of the geometry effect, but does not directly test its cross-terms with instrument parameters (requiring a factorial experiment over emission current × position, included in the follow-up plan); when geometry pushes the head pressure into the nonlinear regime or condensable vapors are involved, cross-terms are expected to appear and the whole system must be re-validated. The calibration position must equal the application position; geometry is published together with the data.
In-situ calibration is not optional — it is the only correct form. Vendor tables are not transferable (Study 1 + literature [7][9]), and both operating conditions and position rewrite the RSF (Studies 2/3) — the only reliable approach is in-situ inversion anchored to traceable calibrated leak standards / reference gases, under fixed geometry and fixed parameters, with periodic re-calibration.
For routine production-line monitoring, prefer the direct Kr/Xe intensity ratio. This indicator needs no RSF and bypasses isotope correction; it is the most stable quantity in this work’s data.
For precise quantification, use the measured RSF and re-calibrate periodically. The recommended procedure is Ar-referenced with isotope correction, re-calibrated every 1–3 months with the same cylinder of 132 certified gas to monitor RSF drift; as a first-pass daily check, whether the background-subtracted uncorrected fractions remain within their established intervals can serve as the screening criterion.
Allow sufficient equilibration time before formal quantification. All three experiments show a consistent “first high, then slowly declining” trend (about 3%–5% for most gases, up to 8% for N₂), probably originating from the gas-inlet system’s response time constant (τ = V/S_eff) and the filament thermal-stabilization process; it is recommended to wait no less than 5τ before acquisition, or to uniformly take the stabilized segment.
Collect a separate background for every measurement, especially for the N₂ channel. The N₂ background is of the same order as the sample signal, and the uncertainty of background subtraction is amplified; independent verification of the N₂ component with a reference gas is recommended.
Watch low-level anomalous peaks at the spectrum tail. In Study 1 data, weak peaks with net signals of about 1.2×10⁻¹¹ A and 5.5×10⁻¹² A exist near m/z 119 and m/z 147, about 3–4 orders of magnitude below the main peaks of the five gases, with no substantive impact on this quantification; but their positions belong to neither the five gases nor their isotopes, and their evolution should be tracked in long-term trend monitoring.
Record and fix the ion-source parameters. Per the prevailing requirements for quadrupole sensitivity calibration (ISO 14291 [5], ISO/TS 20175 [8]), calibration results must state the emission current, electron energy, and mass-resolution settings; these parameters should be recorded together with every acquisition, ensuring that calibration and routine measurement run under identical conditions.
Admit calibration gas near the ion source; calibration position = application position. Study 3 shows that near-source/near-pump readings differ by a factor of 1.22–1.74; once chosen, the calibration port should be fixed in the operating procedure and must not be changed for maintenance convenience — any “port change” maintenance is equivalent to switching to an uncalibrated instrument.
Publish geometry together with the data. Any quantitative data should state the sampling configuration (parallel/series) and the relative orientation of inlet and pump ports; the leak outlet must not face the RGA ion source directly (direct line-of-sight beaming can superimpose significant bias, see [10]).
Extended experimental plan. Cross-configuration (parallel/series) comparison, the pump-port throttling test (the discriminating experiment for the §5.3 hypothesis), and a factorial experiment over emission current × position (testing the separability hypothesis) are included in the follow-up plan and can be performed on the existing tee setup; the cause of the He channel’s abnormal sensitivity to emission current (ion-source saturation?) is listed as an open issue.
I. Data sources. Study 1 used four xlsx files (sample spectra of the two mixture batches and their paired backgrounds) [3]. Study 2 used 23 xlsx files in total [4]: Experiment 1 — 4 (1 background + 3 samples); Experiment 2 — 7 (1 background + 6 samples); Experiment 3 — 12 (6 backgrounds + 6 samples, background collected separately before each measurement). Study 3 used 36 xlsx files in total: Experiment 4 — 12 (6 samples + 6 background segments); Experiment 5 — 24 (3 runs per port × 2 scans = 12 samples; 6 background segments × 2 scans = 12). All files cover m/z 0.6–150 at 0.2 amu steps. Raw data are available from the author on request.
Differences in evaluation conventions. Study 1 integrated the whole isotope clusters of Kr and Xe by area, whose values already represent the element totals without further abundance multiplication; Studies 2 and 3 used main-peak height multiplied by the monitored-peak abundance. The two conventions are physically equivalent (both point to “the element’s response per unit pressure”) but differ numerically by a peak-shape-dependent systematic factor (measured area/height ratios: He 3.15, Ar 3.48).
Reference benchmark. Study 1 used N₂ as the reference benchmark; Studies 2 and 3 used Ar; the benchmark choice does not change quantitative conclusions (see §2.5), and the conversion relation was verified with measured data in §3.6.
Limitations. The conclusions of this paper are limited to this specific H200M and its operating conditions during the experiments; RSF drifts with ion-source aging, vacuum level, and detector gain, and must be re-calibrated before cross-instrument or cross-period use. Study 1 differs from Studies 2/3 in emission current (2000 vs 1000 μA), so absolute RSF values are not comparable across studies (He channel differs by a factor of ~2.4; cause under investigation). The dates of the experimental rounds were not systematically recorded; “date-dimension robustness” was not directly tested in this work, and the date is handled as a calibration-validity management item. Study 3’s geometric conclusions are limited to this chamber’s two-port layout; the pattern “ratio rises monotonically with mean thermal speed” is transferable, but the saturation value (about 1.5–1.75) depends on the specific chamber geometry and pump operating point and is not transferable. The molecular-flow premise is based on leak-admission high-vacuum operation; chamber pressure readings were not logged item by item. The behavior of condensable vapors in series configurations is a physical inference from flow conservation and prior adsorption experiments; the corresponding experiment has not been performed (see the boundary statement in [10]).
V. Complete statement of the measurement chain. A reproducible, comparable quantitative measurement must simultaneously fix five variables: gas species, individual instrument, operating parameters, date, and installation geometry. To first order, the measurement chain decomposes into “geometry factor × four-element instrument response,” the two being calibrated and carried separately; this separability is a working hypothesis, not directly tested by a cross-term factorial experiment. The three rounds of this study correspond respectively to: instrument-response calibration (Study 1), parameter/operating-condition robustness (Study 2), and geometry-factor-ratio measurement (Study 3).
[1] INFICON Inc. Transpector 2 Residual Gas Analyzer User’s Manual [M]. East Syracuse, NY: INFICON, 2020.
[2] IUPAC. Isotopic Compositions of the Elements 2013 (IUPAC Technical Report) [R]. Pure and Applied Chemistry, 2016, 88(3): 293–306.
[3] Project experimental data. RGA spectra of two batches of the 132 mixture with paired backgrounds (m/z 0.6–150, 0.2 amu steps) [DS]. 2026.
[4] Project experimental data. RGA experimental data of calibrated leaks 011002 / 011027 (Experiments 1–5, m/z 0.6–150, 0.2 amu steps) [DS]. 2026.
[5] ISO 14291:2012, Vacuum gauges — Definitions and specifications for quadrupole mass spectrometers [S]. Geneva: ISO, 2012.
[6] Stanford Research Systems. Partial Pressure Analysis with RGAs (Application Note) [R/OL]. Sunnyvale, CA: SRS.
[7] Lieszkovszky L, Filippelli A R, Tilford C R. Metrological characteristics of a group of quadrupole partial pressure analyzers [J]. Journal of Vacuum Science & Technology A, 1990, 8(5): 3838–3854. DOI: 10.1116/1.576458.
[8] ISO/TS 20175:2018. Vacuum technology — Vacuum gauges — Characterization of quadrupole mass spectrometers for partial pressure measurement [S]. 2018.
[9] Marshall A, Malyshev O, Luff R, et al. Comparison of residual gas analyser sensitivity coefficients in high to ultra-high vacuum [J]. Vacuum, 2025, 241: 114668.
[10] RealMeter Instruments (Shanghai). RGA Sampling Geometry Technical White Paper — How Installation Changes Your Measurement (RMI-TN-2026-01) [R]. 2026. (Company technical report, available from the author on request)
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