Residual Gas Analyzer (RGA)

1. Theory

• Definition: A residual gas analyzer (RGA) is a small quadrupole mass spectrometer that ionizes gas by electron impact, filters ions by mass-to-charge ratio and measures each partial pressure in a vacuum system (Hiden data page; Peter lecture).
• Mass filter: DC and RF voltages on four rods transmit only ions inside the Mathieu stability region; scanning at fixed U/V gives a linear mass scale (Peter lecture; background knowledge, Dawson).
• Spectra: Each gas gives a parent peak and fragments, so mixtures are separated by cracking patterns and isotopes (Hiden concepts PDF).
• Pressure range: Ions must cross the filter without collisions, limiting direct operation to high vacuum (background knowledge, O’Hanlon; Hiden data page).

2. Working Principle

• Ion source: Hot filament emitting about $1\times 10^{-4}$ A of electrons accelerated by about 70 $\mathrm{V}$ (Hiden concepts PDF).
• Filter: Rods of 6 to 20 $\mathrm{mm}$ diameter driven at fixed U/V near the stability apex (Hiden concepts PDF; background knowledge).
• Detector: Faraday cup for high pressure and robustness, or secondary electron multiplier for sensitivity (Peter lecture; Hiden data page).
• Calibration: Sensitivities relative to nitrogen and cracking libraries (Hiden data page).

3. Applications

• Leak detection: Air signatures at 28, 32, 14 and 16, and helium spraying (Hiden data page; Peter lecture).
• Vacuum qualification: Bakeout, outgassing and UHV residual spectra (Peter lecture).
• Process monitoring: Etch and deposition by-products with differential pumping (background knowledge).
• Contamination: Water and hydrocarbon background before critical steps (Hiden concepts PDF).

Quadrupole Mass Filter

Name	Formula	Related Formulae	Variables/Constants
Mathieu stability parameters	$a=\frac{8eU}{m{r}_0^2{\Omega }^2},q=\frac{4eV}{m{r}_0^2{\Omega }^2}$	$\text{apex: }a=0.237,q=0.706\Rightarrow \frac{U}{V}=0.168$	$U:DCvoltage$ $V:RFamplitude$ $m:ionmass$ $r_0:inscribedradius$ $\begin{array}{r}\Omega :angularRFfrequency;Mathieuformsand\\ apex(backgroundknowledge,Dawson);Hiden\\ conceptsPDF:stabilitydiagramplotted\\ nearqof0.67to0.73anda/2valuesof\\ 0.16to0.168,polediameters6,9and20\\ mm;Peterlecture:mechanicalprecisionof\\ microns\end{array}$ $\begin{array}{r}(computed:U/V=0.237/(2\times 0.706)=\\ 0.168,matchingtheHidenaxis)\end{array}$
Mass scan	$m=\frac{4eV}{q_0{r}_0^2{\Omega }^2},\frac{U}{V}=\text{const}$	$V\propto m$	$\begin{array}{r}{q}_0:operatingqneartheapex;Peter\\ lecture:U/Vheldconstantwhileincreased\\ fromzero,givingalinearmassscale;\\ Hidendatapage:onem/epassesateachRF\\ scanstep,massranges50to2500\mathrm{amu};\\ relation(backgroundknowledge,Dawson)\end{array}$ $\begin{array}{r}(assumed:r_0=2.6mm,2\mathrm{MHz};computed:V=\\ 3.9,55,86and195\mathrm{V}for2,28,44and\\ 100\mathrm{amu},withU=0.66,9.2,14and33\mathrm{V})\end{array}$
Resolution	$\Delta m_{10}<1\mathrm{amu}$	$R=\frac{m}{\Delta m}$	$\begin{array}{r}\Delta m_{10}:peakwidthat10percentofheight;\\ HidendatapageandconceptsPDF:widthat\\ 10percentheightbelow1\mathrm{amu}forany\\ mass;resolvingpowerdefinition\\ (backgroundknowledge,Dawson)\end{array}$ $\begin{array}{r}(myreading:unitresolutionatconstant\\ widthmeansRgrowswithmass,so28and\\ 29separateascleanlyas2and3)\end{array}$

Partial Pressure and Detection

Name	Formula	Related Formulae	Variables/Constants
Partial pressure from ion current	$p_i=\frac{I_i}{S_{rel,i}{S}_{N_2}}$	$I=Sp$	$p_i:partialpressure$ $I_i:ioncurrentatthechosenpeak$ $S_{rel,i}:sensitivityrelativetoN2$ $\begin{array}{r}{S}_{N2}:nitrogensensitivity;Hidendatapage:\\ Faraday1\times 10^{-4}A/mbarforN2,relative\\ sensitivitiesbenzene5.9andhelium0.14;\\ HidenconceptsPDF:acetone3.6,xenon\\ 3.0,argon1.2,CO21.4,H20.44;Peter\\ lecture:Faraday1.68\times 10^{-4}A/mbarforargon\\ at2\times 10^{-8}\mathrm{mbar}\end{array}$ $\begin{array}{r}(computed:1.2times1\times 10^{-4}gives1.2\times 10^{-4}\\ A/mbarforargonfromHiden,against\\ 1.68\times 10^{-4}measuredbyPeter;1.7\times 10^{-12}Aat\\ 1\times 10^{-8}\mathrm{mbar})\end{array}$
Detector gain and detection limit	$G=\frac{S_{SEM}}{S_{FC}},p_{min}=\frac{k{\sigma }_I}{S}$	$\text{FC: }1e-15\text{to}1e-8\mathrm{A}$	$G:multipliergain$ $S_{SEM},S_{FC}:multiplierandFaradaysensitivities$ ${\sigma }_I:noiseband$ $\begin{array}{r}k:noisemultiple;Peterlecture:SEM\\ sensitivity8.71,24.49and38.66A/mbar\\ at1600,1700and1750V(slides9.35,\\ 24.20and37.90),gainupto1\times 10^8,\\ countingto1\times 10^{-19}A,Faradaynoiseband\\ 7.58\times 10^{-15}Aandlimit4.50\times 10^{-11}\mathrm{mbar},\\ detectionlimitattwicethenoiseband;\\ Hiden:SEMgainabout1\times 10^3(channelplate\\ 1\times 10^2),Faradaylimitabout1\times 10^{-11}\mathrm{mbar},SEM\\ 1\times 10^{-14}to1\times 10^{-13}\mathrm{mbar}\end{array}$ $\begin{array}{r}(computed:gains5.2\times 10^4,1.5\times 10^{5}and\\ 2.3\times 10^5;7.58\times 10^{-15}/1.68\times 10^{-4}=4.5\times 10^{-11}\mathrm{mbar}at\\ onenoiseband,9.0\times 10^{-11}attwo)\end{array}$
Cracking pattern deconvolution	$I_m={\sum }_j{c}_{mj}{S}_j{p}_j$	$\frac{I_{28}}{I_{32}}\approx 4.5\text{(air leak)}$	$I_m:currentatmassm$ $\begin{array}{r}{c}_{mj}:fragmentfractionofgasjatmassm;\\ Hidendatapage:N228and14,O232and\\ 16,H2O18and17,CO244,28and16,CO\\ 28,16and12,Ar40,airleak28to32of\\ about4.5,confirmedby14and16;Peter\\ lecture:waterat1,2,16,17and18,N2\\ andCOsharing28;linearmodel\\ (backgroundknowledge,O^{\prime }Hanlon)\end{array}$ $\begin{array}{r}(assumed:O2relativesensitivity0.86;\\ computed:airabundanceratio3.73rises\\ to4.3,nearthequoted4.5)\end{array}$

Operating Limits and Leak Detection

Name	Formula	Related Formulae	Variables/Constants
Pressure limit from mean free path	$\lambda =\frac{k_{B}T}{\sqrt{2}\pi d^{2}p}$	$\lambda \gg L_{rods}$	$\lambda :meanfreepath$ $d:moleculardiameter$ $p:pressure$ $\begin{array}{r}{L}_{rods}:ionpathlength;relation(background\\ knowledge,O^{\prime }Hanlon);Hidendatapage:SEM\\ typicalmaximum1\times 10^{-5}to1\times 10^{-6}\mathrm{mbar}\end{array}$ $\begin{array}{r}(assumed:N2,d=0.375\mathrm{nm},298K;\\ computed:0.66mat1\times 10^{-4}\mathrm{mbar}and6.6mm\\ at1\times 10^{-2}\mathrm{mbar})\end{array}$
Ion source	$I_{ion}\propto I_{em}{\sigma }_{ion}\left(E_e\right)n{L}_e$	$I_{em}\approx 1e-4\mathrm{A}$	$I_{em}:emissioncurrent$ $\begin{array}{r}{\sigma }_{ion}:ionizationcrosssectionatelectron\\ energy{E}_e\end{array}$ $n:gasdensity$ $\begin{array}{r}{L}_e:ionizingpath;HidenconceptsPDF:\\ filament-70V,extractor-90V,cage+3\\ V,emissionabout1\times 10^{-4}A,yttria-coated\\ Irat1900K,W2400K,Re2300K,LaB6\\ 1300K;Peterlecture:emission2.00mAin\\ theQME125test,electronimpactmaking\\ thegaugegasspecific;proportionality\\ (backgroundknowledge,Dawson)\end{array}$ $\begin{array}{r}(myreading:the70Vfilament-to-cage\\ differencesetselectronsnear70\mathrm{eV},\\ wheremostcrosssectionsareneartheir\\ maximumandflat)\end{array}$
Leak detection and bakeout	$Q_{leak}=S_{pump}\Delta p_{He}$	$q_{out}<1e-10\mathrm{mbar}\mathrm{l}{\mathrm{s}}^{-1}$	$Q_{leak}:leakrate$ $S_{pump}:pumpingspeed$ $\Delta p_{He}:heliumpartialpressurerise$ $\begin{array}{r}{q}_{out}:outgassingrate;Peterlecture:N2and\\ ArindicateleakswhileO2isgetteredin\\ UHV,heliumtestafter300{}^{\circ }Cbakeout,\\ degassingtargetbelow1\times 10^{-10}mbarl/s,\\ residualspectraat1.5\times 10^{-11}and2.5\times 10^{-11}\\ \mathrm{mbar};Hidendatapage:heliumdetectionto\\ 5\times 10^{-14}\mathrm{Torr};throughputrelation\\ (backgroundknowledge,O^{\prime }Hanlon)\end{array}$ $\begin{array}{r}(assumed:100l/s;computed:a1\times 10^{-13}\mathrm{mbar}\\ heliumriseisa1\times 10^{-11}mbarl/sleak)\end{array}$

Important Questions

Ques: How does a quadrupole RGA select one mass?

By transmitting only ions with stable trajectories through combined DC and RF fields. The Mathieu parameters $a=8eU/(m{r}_0^2{\Omega }^2)$ and $q=4eV/(m{r}_0^2{\Omega }^2)$ define a stability diagram whose apex is at $a=0.237$ and $q=0.706$ (background knowledge, Dawson). Operating with $U/V$ = 0.168, just below the apex, passes a narrow mass window (computed), which matches the 0.16 to 0.168 axis of the Hiden diagram. Increasing $U$ and $V$ together at fixed ratio scans the mass linearly, as the Peter lecture describes. With an assumed 2.6 $\mathrm{mm}$ inscribed radius at 2 $\mathrm{MHz}$, the RF amplitude is 55 $\mathrm{V}$ for mass 28 and 195 $\mathrm{V}$ for mass 100 (computed). Peter notes that micron-level rod precision is required. Reference: P. H. Dawson (ed.), Quadrupole Mass Spectrometry and its Applications, Elsevier 1976, and J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 3rd ed., Wiley 2003 (background knowledge; not opened); Hiden Analytical, ‘Mass Spec Concepts’ (2022 PDF) (fetch-tool summary; quadrupole equation garbled in extraction); G. J. Peter, ‘Partial Pressure Gauges’, CERN Accelerator School lecture, Platja d’Aro (May 2006) (fetch-tool summary).

Ques: How are partial pressures obtained from a spectrum?

By dividing each peak current by the gas sensitivity and correcting for overlapping fragments. Hiden gives a Faraday sensitivity of $1\times 10^{-4}$ $A/mbar$ for nitrogen and relative sensitivities such as 1.2 for argon, 0.44 for hydrogen and 0.14 for helium, while Peter measured $1.68\times 10^{-4}$ $A/mbar$ for argon, 40 per cent above the $1.2\times 10^{-4}$ implied by Hiden (computed), showing why each instrument needs calibration (my reading). Overlaps are solved with cracking patterns: carbon dioxide contributes at 28 and 16, and nitrogen and carbon monoxide share 28, so 14 and 12 separate them (Hiden data page). An air leak shows 28 to 32 of about 4.5; the air abundance ratio of 3.73 rises to 4.3 with an assumed oxygen sensitivity of 0.86 (computed). Reference: Hiden Analytical, ‘Residual Gas Analysis with Quadrupole Mass Spectrometry’, technical data page (fetch-tool summary); Hiden Analytical, ‘Mass Spec Concepts’ (2022 PDF) (fetch-tool summary; quadrupole equation garbled in extraction); G. J. Peter, ‘Partial Pressure Gauges’, CERN Accelerator School lecture, Platja d’Aro (May 2006) (fetch-tool summary).

Ques: Is an electron multiplier’s gain $1\times 10^3$ or $1\times 10^8$?

The sources differ widely. Hiden gives about $1\times 10^3$ for an SEM and $1\times 10^2$ for a channel plate, while Peter states gain up to $1\times 10^8$. Peter’s own test data give the actual value: argon sensitivity of 8.71, 24.49 and 38.66 $A/mbar$ at 1600, 1700 and 1750 V against $1.68\times 10^{-4}$ $A/mbar$ on the Faraday cup imply gains of $5.2\times 10^4$, $1.5\times 10^5$ and $2.3\times 10^5$ (computed). Gain in the $1\times 10^4$ to $1\times 10^6$ range at normal voltages is therefore most likely; $1\times 10^8$ is a maximum for pulse counting, and $1\times 10^3$ probably describes a low-voltage or aged multiplier (my reading). Peter’s report and slides also differ slightly, for example 24.49 against 24.20 $A/mbar$ at 1700 V, a 1.2 per cent difference (computed). Reference: Hiden Analytical, ‘Residual Gas Analysis with Quadrupole Mass Spectrometry’, technical data page (fetch-tool summary); G. J. Peter, ‘Partial Pressure Gauges’, CERN Accelerator School lecture, Platja d’Aro (May 2006) (fetch-tool summary).

Ques: What sets the detection limit of an RGA?

Detector noise divided by sensitivity. Peter states that a signal of twice the noise band defines the limit, but his Faraday numbers, a $7.58\times 10^{-15}$ A noise band and $1.68\times 10^{-4}$ $A/mbar$, give $4.5\times 10^{-11}$ $\mathrm{mbar}$ at one noise band and $9.0\times 10^{-11}$ at two (computed); the quoted $4.50\times 10^{-11}$ $\mathrm{mbar}$ therefore matches one noise band, so the stated rule or the noise definition differs (my reading). Hiden gives about $1\times 10^{-11}$ $\mathrm{mbar}$ for a Faraday cup and $1\times 10^{-14}$ to $1\times 10^{-13}$ $\mathrm{mbar}$ with a multiplier, and Peter’s multiplier limits of $2.7\times 10^{-15}$ to $8.7\times 10^{-15}$ $\mathrm{mbar}$ meet his $5\times 10^{-15}$ $\mathrm{mbar}$ requirement only at the highest voltages. The Faraday range of $1\times 10^{-15}$ to $1\times 10^{-8}$ A bounds direct current measurement. Reference: G. J. Peter, ‘Partial Pressure Gauges’, CERN Accelerator School lecture, Platja d’Aro (May 2006) (fetch-tool summary); Hiden Analytical, ‘Residual Gas Analysis with Quadrupole Mass Spectrometry’, technical data page (fetch-tool summary).

Ques: Why can’t an RGA run directly at process pressure?

Because ions must cross the filter without colliding. The nitrogen mean free path is 0.66 m at $1\times 10^{-4}$ $\mathrm{mbar}$ but only 6.6 $\mathrm{mm}$ at $1\times 10^{-2}$ $\mathrm{mbar}$ (assumed molecular diameter; computed), shorter than a typical filter (background knowledge, O’Hanlon). Hiden gives a typical maximum of $1\times 10^{-5}$ to $1\times 10^{-6}$ $\mathrm{mbar}$ for multiplier operation, where high ion currents also shorten multiplier life. Etch and deposition tools at millitorr pressures therefore sample through an orifice into a differentially pumped analyzer, or use a closed ion source (background knowledge). The hot filament also reacts with oxidizing or corrosive gases, which is why filament materials such as yttria-coated iridium, rhenium and tungsten are chosen by application (Hiden concepts PDF). Reference: P. H. Dawson (ed.), Quadrupole Mass Spectrometry and its Applications, Elsevier 1976, and J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 3rd ed., Wiley 2003 (background knowledge; not opened); Hiden Analytical, ‘Residual Gas Analysis with Quadrupole Mass Spectrometry’, technical data page (fetch-tool summary); Hiden Analytical, ‘Mass Spec Concepts’ (2022 PDF) (fetch-tool summary; quadrupole equation garbled in extraction).

Ques: How does an RGA find a vacuum leak?

From air signatures and tracer gases. Nitrogen at 28 with its fragment at 14, oxygen at 32 with 16, and argon at 40 indicate air; Hiden quotes a 28 to 32 ratio of about 4.5. Peter notes that oxygen is gettered in UHV, so nitrogen and argon are the reliable indicators, and describes a case where a gasket inclusion was found after an integral leak test showed nothing. Spraying helium while watching mass 4 locates a leak; Hiden quotes detection to $5\times 10^{-14}$ $\mathrm{Torr}$. With an assumed 100 l/s pumping speed, a $1\times 10^{-13}$ $\mathrm{mbar}$ helium rise corresponds to a $1\times 10^{-11}$ mbar l/s leak (computed). Peter’s degassing target is below $1\times 10^{-10}$ mbar l/s after 300 ${}^{\circ }\mathrm{C}$ bakeout. Reference: Hiden Analytical, ‘Residual Gas Analysis with Quadrupole Mass Spectrometry’, technical data page (fetch-tool summary); G. J. Peter, ‘Partial Pressure Gauges’, CERN Accelerator School lecture, Platja d’Aro (May 2006) (fetch-tool summary); P. H. Dawson (ed.), Quadrupole Mass Spectrometry and its Applications, Elsevier 1976, and J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 3rd ed., Wiley 2003 (background knowledge; not opened).

References

1. P. H. Dawson (ed.), Quadrupole Mass Spectrometry and its Applications, Elsevier, 1976; J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 3rd ed., Wiley, 2003 (cited from background knowledge).
2. Hiden Analytical, “Mass Spec Concepts,” 2022. Available: https://www.hidenanalytical.com/wp-content/uploads/2022/02/Mass-Spec-Concepts-new-format.pdf
3. G. J. Peter, “Partial Pressure Gauges,” CERN Accelerator School on Vacuum, Platja d’Aro, May 2006. Available: https://cas.web.cern.ch/sites/cas.web.cern.ch/files/lectures/platjadaro-2006/peter.pdf
4. Hiden Analytical, “Residual Gas Analysis with Quadrupole Mass Spectrometry,” technical data. Available: https://www.hidenanalytical.com/tech-data/residual-gas-analysis-quadrupole-mass-spectrometry/

Related pages in this vault: Optical Emission Spectroscopy Endpoint (OES), Langmuir Probe, Secondary Ion Mass Spectrometer (SIMS and ToF-SIMS), Atom Probe Tomography (APT), Environmental and Chemical, Lifetime Testers, Quartz Crystal Microbalance (QCM), Vacuum Gauges, Thermal Evaporator, DC and RF Magnetron Sputter System, Molecular Beam Epitaxy (MBE) System.