- Email: [email protected]
A gas inlet system for quantitative mass spectrometry
International
Journal of Mass Spectrometry and Zon Processes, 108 (1991) 1-21
1
Elsevier Science Publishers B.V., Amsterdam
A gas inlet system for quantitative J. Hall, S. Lundgren,
mass spectrometry
K.E. Keck and B. Kasemo’
Department of Physics, Chalmers University of Technology, S-412 96 Giiteborg (Sweden)
(Received 28 November 1990; in final form 12 April 1991)
ABSTRACT A gas inlet system for quantitative mass spectrometry is described. The principle is to make the gas pass through the ion source using tubing terminating close to the ion source. With molecular flow conditions in the tubing a directed, reasonably collimated beam is achieved giving rise to a local pressure increase in the ion source. This local pressure increase is due to molecules that have not interacted with the chamber walls, and can easily be obtained for each gas species of interest by taking signal differences or by lock-in techniques if a shutter/chopper is positioned between the gas sample tubing and the ion source. The traditional plagues of quantitative mass spectrometry, namely background gases and wall gas-exchange effects are thus’eliminated. For stable gas species this gas inlet system offers essentially the same advantages as a molecular beam gas inlet, but at much lower cost and complexity and requiring much smaller gas samples for analysis. For example, no differential pumping is required. The properties and performance of the gas sampling system are analysed theoretically and demonstrated by experiments. Good quantitative agreement is obtained between theory and experiment. It is shown theoretically, and verified experimentally, that the ratio, R, between the local pressure rise in the ion source, due to the directed beam, and the average mass spectrometer (MS) chamber pressure varies as R 2 S Ml/2 where S is the pumping speed and M the molecular mass number. As a specific example it is demonstrated how the water vapour content of a gas sample can be correctly measured even in the presence of a high water background in the MS vacuum chamber. It is also shown how the gas inlet device can be used as a simple tool to measure pumping speeds in vacuum systems.
1. INTRODUCTION
Mass spectrometry is inherently an extremely sensitive method of measuring gas composition. In ideal cases it is possible to measure a relative gas concentration (of one gas diluted in another) of 1 x lo*, with a gas sample as small as 10P5cm3 at atmospheric pressure. However, the theoretical sensitivity rarely sets the limit for the measurement accuracy. The accuracy and sensitivity limits are instead usually determined by influences, e.g., from background gases, reactions or degassing in the ion source of the mass spectrometer (MS) analyser, and by temporal variations in pumping speed of the vacuum system. ’ Author
to whom correspondence
0168-1176/91/$03.50
0
should be addressed.
1991 Elsevier Science Publishers
B.V.
2
In the present paper we describe and analyse experimentally and theoretically a simple gas inlet system that greatly suppresses such effects. Basically it offers the same advantages over conventional gas inlet systems as molecular beam gas inlet systems, but at much lower cost and complexity and with much smaller gas consumption. For comparison purposes we first briefly describe some commonly used gas inlet methods in mass spectrometry. Then in Section 2 the principle of the gas inlet system described in this paper is outlined together with a theoretical analysis. A more detailed analysis is given in Appendix A. The third section describes measurements to test the theoretical predictions and also illustrates the performance for measurements of practical interest. These results and possible extensions and improvements are discussed in Section 4. In this section it is also shown how the gas inlet system can be used as a simple tool to measure pumping speeds. 1.1. Simple gas inlet methods
The simplest type of gas inlet system for MS analysis consists of a leak (sometimes differentially pumped) that introduces the gas sample into the MS system at a gas mass flow Q,. The magnitude of Q, and the pumping speed, S, are, if possible, chosen so that the total operating pressure, Q,/S, in the vacuum chamber lies in the region 10-6-10-5Torr, i.e., Q, is typically 10-3-10-4 Torr 1SC’.The pressure in the ion source is then made up of the sum of the system background pressure and the pressure created by Q,.The origin of the background partial pressures is: (a) degassing from the chamber walls and from components in the vacuum system; (b) reactions at hot filaments (ionization gauges, MS filament etc.); (c) back flow and/or gas release in the vacuum pump; and (d) exchange reactions at the walls due to the introduced sample gas. The precision by which a gas sample can be analysed depends to a large extent on how well such background effects can be controlled. The simplest approach to estimate these effects is to record a mass spectrum with the gas inlet closed and then subtract this spectrum from the one measured with an open gas inlet. The differential partial pressures obtained in this way are, however, generally different from the partial pressures of the inlet gas. The reason is that the background gas compositions with the sample gas inlet open and closed are usually different because exchange reactions on the chamber walls and reactions on surfaces in the chamber change the background gas composition (the inlet sample gas components can for example cause release of gas adsorbed on the chamber walls and in ion and cryopumps etc.). For many gases, particularly polar and reactive ones, these errors can be large and the simple background subtraction method then becomes unreliable. Additional measurement errors derive from variations over time in the
3
effective pumping speeds, S’ = Qi/$, of the different gases, i, which determine the corresponding partial pressures. The effective pumping speed is the sum of the pumping speed of the vacuum pump and the chamber walls. Since the latter temporarily may be as large as, or even larger than, the former and may also act as a gas source by release of previously adsorbed gas, large uncertainties may result in the quantitative gas analysis (the chamber walls effectively act as a capacitor for reactive and polar gases). All these effects may to a certain extent be checked and reduced by introducing a known gas mixture, which has a composition as close to the composition of the analysed gas as possible. By an iterative procedure this can give improved but still only approximative control over background effects. The method is tedious, time consuming, and useful only in simple cases. It is thus apparent that the simple gas inlet method discussed above is not generally satisfactory for quantitative MS gas analysis. 1.2. Molecular beam inlet A straightforward, but expensive, method to get around these problems is to use a gas inlet with a molecular beam so that a well collimated beam passes through the ion source [l-4]. The operating principle is the following. The gas is introduced via a nozzle feeding a suitable amount of gas (10-‘-l Torr 1s-‘) into a first vacuum chamber, where a conical aperture (skimmer) skims off most of the gas which is then pumped away. The remaining small gas fraction travels through the skimmer aperture into a second vacuum chamber where it is further collimated by a second aperture. Sometimes a third chamber and collimating aperture are used. In this way a well collimated beam of sample gas of diameter l-2 mm is created. By chopping the beam before it enters the ion source, the relevant background pressures can be readily eliminated. To discuss how this is achieved, we assume that the chopper is in fact a shutter with two positions, open or closed. We also assume for simplicity of notation that the beam contains a single gas species. In the open position the beam passes through the ion source; in the closed position it is stopped by the chopper. In the closed position the situation is then identical to the situation discussed previously, i.e. one has a diffuse leak creating an isotropic pressure, pc,, ( wh ere the subscript cl stands for closed). When the shutter is open the pressure in the MS chamber will be the same as in the closed position everywhere, except along the directed molecular beam where the local pressure, pop, (op for open) will be higher. If measurements are performed with the shutter open and closed and the difference between the two measurements is taken, we obtain the MS signal due to the increased local pressure, Apdir,in the ion source caused by the directed molecular beam. This
4
is exactly the quantity one wants to measure since this difference is proportional to the gas flow, Q,, in the gas inlet system (see eqn. lb below), which in turn, in the case of gas mixtures, gives the sample gas composition. (For a gas mixture the same analysis as above holds for each gas component i-just put a superscript i on p and Q,.) The proportionality -C(Pdir a Q, is not quite trivial. It is, however, correct when the gas flow at the sampling point is viscous and the exit flow is molecular. See also a comment at the end of Section 4.2 and ref. 6. The sensitivity factors in this type of measurement will be different compared with those in the simple gas analysis described previously, due to a mass dependent molecular velocity effect in a molecular beam [4]. The partial densities, or pressures, of the different gas components in the beam will be proportional to the initial sample gas densities multiplied by the square root of the mass of the molecules (provided no supersonic nozzle expansion and seeding effects occur, i.e. we assume a “thermal” beam [4]). This is because the thermal velocity of a molecule is proportional to the inverse square root of the mass of the molecule and the corresponding density in the beam is proportional to the inverse velocity of the molecule (see also Appendix A). To obtain numbers, we consider absolute values of the parameters involved in a realistic case. Let us assume a sample gas-beam flow of 10P6Torr 1s-‘, equivalent to about 3 x 1Ol3molecules s-‘, into the vacuum system, which we assume to be at room temperature. With an effective pumping speed of 100 1s-’ this creates a chamber pressure of z lo-* Torr. If we assume a beam area of 1 mm* and a molecular velocity of 500 m s-‘, we obtain a local beam pressure of 2 x lop6 Torr, from which we see that the local beam pressure can be about 100 times larger than the average chamber pressure created by the beam. Obtaining a corresponding signal increase over the background due to the beam requires that the beam fills up the sensitive region of the ion source entirely, which is seldom realized, but a local pressure increase of z x 10 is realistic with z 100 1SC’ pumping speed. By differential pumping around the MS ion source and/or an increased pumping speed of the analysis chamber, the background pressure in the ion source can be further reduced 2-3 orders of magnitude, with a corresponding improvement of (beam) signal to background ratio. There is essentially only one argument against using a molecular beam as the gas inlet, namely the cost. The gas consumption may also be much too large when only small gas samples are available. The beam forming stage requires two to three pumping stages with diffusion or turbo pumps plus forepumps, valves, pressure meters and maybe alignment mechanisms [l]. Below we describe a much simpler and much cheaper alternative, essentially offering the same advantages as the molecular beam inlet for detection of stable gas components and with a gas consumption 103-lo4 times smaller. The
5
only major limitation in comparison with a molecular beam mass spectrometer is that unstable molecules, e.g. radicals, cannot be detected in the same way as is possible with a molecular beam MS system [3]. 2. A DIRECTED
GAS INLET SYSTEM
2.1. Operating principle
The principle [5] of the gas inlet system, illustrated in Fig. la, is the same as for the molecular beam MS discussed above, but with the important difference that no differential pumping is needed. At the high pressure (gas sampling) end, the sample gas is introduced via a narrow hole (which could also be a permanent leak or a leak valve) into the tubing, which extends almost all the way to the ion source. The narrow hole, acting as a gas leak, controls the amount of gas which is fed into the MS chamber, and brings the flow of gas into the molecular flow regime in the tubing [6]. The angular distribution pattern for gas transmitted through, and exiting from, a tube under these conditions has been subject to both theoretical and experimental work [7]. These results show that the tubing causes considerable collimation of the gas flow at the exit C. With an arrangement where the termination of the tubing is sufficiently close to the ion source, an increased local pressure is therefore created in the effective region, E, (the ionization volume) of the ion source when the shutter/chopper is open. In the same way as described for a molecular beam MS, the local pressure rise in the ion source is obtained by taking the difference between the MS signal recorded with the shutter open and closed. This difference can be obtained electronically as a simple difference signal or by a standard lock-in detection technique if a periodic chopper is used instead of a shutter. The same signal analysis as for the molecular beam MS is applicable, the only difference being that the “beam” leaving the tubing is more divergent. The local pressure increase in the ion source, over the background, may therefore not become quite as large as in the molecular beam case. There may also be some wall collisions (in the ion source) of the beam molecules due to the beam divergence, unless additional collimation is employed. We now derive an expression for the difference, AZii,, between the mass spectrometer signals, I&, and ZJ,,when the shutter is open and closed respectively, to be used for comparison with experimental results described in Section 3. A more extensive theoretical analysis is given in Appendix A. To simplify the analysis we assume that the isotropic partial pressures in the analysis chamber, created by the sample gas flow Qd, are much larger than the system background partial pressures. Incorporation of the system background is fairly straightforward and is done in Section 4. The mass
UHV-chamber
(b) Masd Spectrometer
Orifice -.-
\ 10 mm _____-----_________ \ -___ _____----____--_____--______.
Fig. 1. (a) Principle of the directed-gas inlet system. The sample gas exits from the tube C under molecular flow conditions and is directed through the effective ionization volume, E, of the ion source. The “beam” exiting from C is divergent but strongly peaked in the forward direction for L/r $ 1 (see Fig. 4). A chopper/shutter is used to subtract the beam signal from the isotropic chamber pressure. (b) The experimental set-up used to evaluate the directed-gas inlet system and to measure the R values presented in Table 1 and Fig. 2.
7
spectrometer signals, I’, are proportional to the density (or pressure) of molecules, i, within the effective detection region of the ion source. When the shutter is open, the total partial pressure, p&, in the ion source is the sum of the contribution, Apair, created by molecules, i, which pass directly from the tube exit through the ion source, and the isotropic partial pressure, p:,, in the vacuum chamber due to the sample gas Q$. When the shutter is closed, only molecules which contribute to the isotropic pressure, pi,, are present in the ion source. This contribution is of course the same, independent of whether the shutter is open or closed (providing the shutter is inert with respect to the gas in the beam, and providing pumps are not unsuitably positioned). Thus, the difference in mass spectrometer signals, AZ~ir,with the shutter open and closed is given by A&
= ZAP- Z;, = a’p& - yip;, = JC~L\P;~,
(la)
The sensitivity factors c?, yi and ICY are different because of the mass dependent velocity in the directed beam discussed below and in the Introduction. yi are the normal sensitivity factors for residual gas analysis, ICY are essentially the sensitivities corresponding to the molecular beam mode of operation, and the ai values, which will take absolute values between the values of yi and K~,are defined from the last equality of eqn. la. Since the local “pressure” (or rather density) rise, Ap~ir,is proportional to the directed gas flow Qbwe also have the following equality: AZ& = D’Q;
(lb)
The molecular mass-dependent parameters 8’ relate the difference signals Apai, to the corresponding components, Qi, of the sample gas. The magnitudes of the pi values depend on how large the fraction of molecules i is that passes from the tube exit through the effective detection region of the ion source, on the volume of this effective region, and on the molecular velocity which varies as the square root of the mass. The pi values are easily determined experimentally by calibration for the various sample gases which are let into the system. A theoretical expression for /3’is derived in Appendix A. To estimate semiquantitatively the performance of the gas inlet system let us assume a gas sample flow of Qi = 10e4Torr 1SK’and a pumping speed of S’ = 100 1s-l, producing a background gas pressure ofpi, = 10P6Torr. (In the following we drop for simplicity the superscript i.) For the estimation we assume that the divergence of the gas leaving the inlet tube is such that 10% of the total flow, Q,, (equivalent to about 3 x 10’4moleculess-‘) passes through the effective region of the ion source when the shutter is open. (We show in a separate paper [8] that the cross-section of the effective detection region of the ion source used in this work is of the order of 10 mm’.) If we use 500 m s- ’ for the molecular velocity we get a local pressure increase in the ion
8
source of Apdir = 2 x 10e6Torr due to the directed gas “beam”. In experiments we thus expect to obtain a signal difference, A~dir,which is at least as large, or even larger than, the signal, I,, , when the shutter is closed. As we shall see below this is verified experimentally. In the next section we test experimentally the described gas inlet system and compare the experimental results with the calculations. 3. EXPERIMENTAL
RESULTS
The gas inlet system (Fig. 1) was evaluated experimentally in two different MS systems. The first system was used to test the principle and quantify the performance of the gas inlet system. The results obtained could then be compared with the results of the theoretical analysis presented above and in Appendix A. The second system was used to demonstrate the advantage of the present gas inlet system over conventional inlet systems by measurements of H,O in the inlet gas in the presence of a large HZ0 background. 3.1. Experimental test ofthe principle and quantitative results The vacuum system for the evaluation of the inlet system consists of a stainless steel vacuum chamber and a Balzers QMG 31 I/QMA 150 quadrupole mass spectrometer with a cross beam ion source. The total pressure is measured with an ion gauge. The vacuum chamber is pumped by a turbomolecular pump (Balzers TPU 270). The background pressure in the chamber is in the low 10p9Torr range after bakeout of the system. The gas inlet tube, 300 mm long and 3 mm in diameter, is mounted on a 6 in. flange together with a rotary manipulator, which controls the shutter in front of the ion source (see Fig. lb). The inlet tube is mounted so that its axis goes through the centre of the ion source, perpendicular to the quadrupole axis. The distance, z, between the exit of the inlet tube and the entrance side of the ion source is x 1Omm. The effective width, &, of the ionizing region of the ion source is 4,s z 3.5 mm [8]. The divergence of the sample gas leaving the tube exit, the tube diameter, the distance z and the effective volume of the ion source determine the fraction of the total flow Q, which passes through the ion source. This fraction is estimated theoretically to be about 10% (Appendix A). The performance of the inlet system was quantified by measurements of the ratio, R, between the signal due to the directed inlet sample gas, Al~i,, and the signal with the shutter closed, IC,, due to the isotropic pressure created by the inlet gas. From eqn. la and b we see that R for a given gas is given by
(2)
TABLE 1 Measured ratios R E AZdir/Zclfor different gases Gas Ri
He 1.75
H2 1.30
CH, 2.34
H,O 2.58
N, 2.64
02 3.00
Ar 2.84
COZ 2.93
where A is a constant and S,, is the effective pumping speed for the gas considered. The mass dependence of j3originates from converting the gas flow Q, to gas density (or “local pressure”), which requires dividing Q, by the average molecular velocity in the beam direction. (Note that the mass dependence of R vanishes if one can arrange that Sffvaries as l/M”*). The constant A depends on the size of the effective detection volume in the mass spectrometer ion source and on the geometrical arrangement of the inlet system, i.e., it is an instrumental constant. It can be determined relatively easily experimentally (see below) but is not needed for quantitative MS measurements. (We recall that we have dropped the superscript i. Equation 2 is actually a set of equations, one for each type of gas molecule of interest.) Using the pumping speed values determined as described in Appendix B and given in Table 2, the system performance can now be quantified and the theoretical estimates can be tested by measuring the ratio R of eqn. 2 for various gases. The measured R values are given in Table I. A plot of R divided by the corresponding S,., as a function of the square root of mass number is shown in Fig. 2. The data points are well fitted by a straight line in agreement with eqn. 2. The scattering of data points around the straight line is mainly due to uncertainties in the effective pumping speeds. The slope of the line gives 0.04
I
He/
0
2 2
4
(mass number)
6
8
In
Fig. 2. A plot of the measured R’/& ratio vs. the square root of molecular mass number for the gases given at the data points. (The measured R and S,, values are given in Tables 1 and 2 respectively.) The good straight line tit to the data verities eqn. 2.
10 TABLE 2 Measured and interpolated pumping speeds for different gases Gas &T cs-‘1 aInterpolated
H* 188
He 171”
CH, 122
Hz0 118”
N, 100
02 96
Ar 85
COZ 82”
values.
the instrumental constant A in eqn. 2. we obtain A = 5 x lop3 which is in good agreement with the theoretically estimated value of 4 x lop3 (eqn. 12 in Appendix A). These results are further discussed in Section 4. Note that measurements of R are only made to evaluate the performance, but are not necessary for quantitative gas analysis. The latter only requires measurements of the Aldir value corresponding to the gases of interest and knowledge (by calibration with known gas mixtures) of the sensitivity factors xi (eqn. la). 3.2. Application to measurements of H,O The system used for these measurements [9] was similar to the one described above, but employed a Balzers QMG 112/QMA 120 mass spectrometer with a cross beam ion source. The leak rate of the sample gas was in this case controlled by a quartz tube orifice leak [6] creating a steady state isotropic pressure of pC,= 10V6Torr. The shutter was replaced by a chopper which was electromechanically controlled from the outside of the vacuum chamber and could be used as a closed/open shutter or operated at a frequency of 20Hz when using lock-in detection. The importance of controlling the vacuum chamber background effects during gas analysis is illustrated by the following example. Air with low humidity was let into the vacuum chamber with the directed-gas inlet system. Figure 3 shows the H,O signal as a function of time, recorded with the shutter successively positioned in the “closed” and “open” positions. While feeding a constant flow of gas with constant H,O concentration through the directed-gas inlet system, the H,O background pressure in the vacuum chamber was increased at times A-J, by introducing humid air through a separate leak valve. The MS signal, representing the H,O concentration in the sample gas, is obtained as the difference between the curves marked “open” and “closed”. Note that the difference between the curves displayed in the inset of Fig. 3 (representing the sample gas) stays constant in spite of the increase of the background H,O pressure. With a conventional gas inlet, the lower (isotropic) pressure curve marked “closed” would always have been recorded, creating a severe error in the sample gas analysis.
11
H2Osignal
10
-
20
open
---
-_-
30
Ii -, I----
closed
I
j I I
G
10
20
30
40
t(mW
Fig. 3. Measurement of the Hz0 content of a gas sample at different background levels of Hz0 in the vacuum chamber. The desired sample gas signal for A4 = 18 is obtained as the difference between the signals recorded with the shutter open and closed (eqn. la). The inset shows that this difference stays constant in spite of large variations in the M = 18 background. 4. DISCUSSION
4.1. General aspects
We first note that the basic principle of the present gas inlet system, theoretically outlined in Section 2 and represented by eqns. 1 and 2, is verified by the experimental results. The ratio, R, between the local partial pressure increase in the ion source, due to the directed sample gas “beam”, and the isotropic background pressure created by the same sample gas, is 2 1 for the pumping speeds employed. This makes it quite straightforward to obtain the desired relative partial pressures of the sample gas, APdir, using periodic chopping and lock-in detection to measure the corresponding AIdir values. The sensitivity factors, K, converting the MS signals to (relative) partial pressures, are best obtained by calibration with known gas mixtures. Note that the K values are different to the “normal” sensitivity factors, y, used in residual gas analysis, because of the mass dependent velocity effect. The latter is the reason that R = Aldir/lcl (eqn. 2) is proportional to M”2. This explains the tendency of the R values to increase with increasing molecular mass (Table 1). Basically the reason is that the heavier molecules in the directed “beam” travel more slowly than the lighter ones, and therefore have a larger chance of being ionized. The trend in Table 1 predicted by this mechanism is, however, counteracted by the decreasing pumping speed, &,
12
with increasing M (see Table 2). Both these effects are accounted for by eqn. 2 and the plot of R/S,, vs. M’j2 gives a straight line. The M’12effect is an example of an interesting difference between conventional residual gas MS measurements and directed-beam measurements. Because of this effect the latter measurements have a relatively higher sensitivity for heavier molecules, partly counteracting the common loss of sensitivity at high mass numbers in quadrupole mass spectrometers. As discussed in the Introduction and Section 2, and illustrated by eqn. 2, the suppression of the background isotropic pressure (the latter created by the sample gas), is proportional to the pumping speed. Thus, additional suppression can, if necessary, be obtained by increasing the pumping speed. R values 2 10 can be obtained with pumping speeds 2 500 1s-’ which in some applications may make the chopper and lock-in detection unnecessary. In the analysis so far we have not explicitly treated the inherent system background gases present in the absence of sample gas. This is mostly a good approximation for a well baked system with a base pressure in the 10P9Torr region or lower, since the background partial pressures of interest created by the sample gas are then (usually) much larger: z 10-7-10-6Torr. Inclusion of the system background pressures does not change eqn. 1 or the basic conclusions, however, but modifies the third equality of eqn. 2, since the partial pressures, pCl , with the shutter/chopper closed now consist of two components: one due to the sample gas and the second due to the inherent system background pB. We now derive an expression including also PB. In order to simplify the analysis we assume that the system background pressure and the partial pressures created by Q, are additive”. Then the equality pcl = Q,/S,, used in eqn. 2 is replaced by pcl = Q,/S,, + pB 3 ps + pB, and eqn. 2 will be modified to read:
P
1
R = 7 & ~l+p”
PS
AiW2
=
Seff
1
(2’)
l+p”
PS
The modifying factor l/[ 1 + (pB /Pi)], in comparison with eqn. 2, is as mentioned above usually very close to unity for a well baked system, where
a The full treatment of the case with a non-negligible system background becomes quite complex and is beyond the scope of this paper. The complexity arises because _ns and pS in the general case cannot simply be added to each other, since the sample gas may release new background gases and since the effective pumping speeds will be dependent on both absolute pressure and time, due to wall pumping and degassing effects. It should be noted that these effects in no way affect the measurements based on eqn. 1 of the gas composition. They only affect the measurements of R, which were made only to compare the experimental results with the theoretical analysis.
13
pS B pB for most gases of interest. However, in some special cases or with a
system with a poor vacuum, 2 low6 Torr, we may have a system background (partial) pressure comparable to, or even larger than, the corresponding sample (partial) pressure. This does not in any way change the advantage of the directed-gas inlet system, but for individual partial pressures, pB may now be $pS which can make the signal to noise ratio significantly worse than when pB 4 pS. Also, the simple straight line R/S,, vs. M’/* would not be obtained in this case, since [l + (pB/ps)] in general has different values for different gases. It should be noted that pB above is not exactly the same as the system background partial pressures measured in the absence of sample gas, for the reasons mentioned in the Introduction. From a practical point of view this is a subtle point of minor interest, but it makes the division ofp,, into the pS and pe contributions artificial and somewhat questionable. In the practical measurement situation the only point of concern is that the sum pS + pB = pC, can be eliminated by chopping plus lock-in detection. 4.2. Sample gas collimation and ion source geometry The obtained sample gas signal, AIdir, is proportional to (~c#&)-’ QsM”* (see eqns. 1 and A5). Here (@&)-’ is the cross-section of the effective detection volume in the ion source. The degree of collimation of the sample gas obtained with the gas inlet tube, and thus the fraction of the total flow, Q,, which passes through the ion source, is vital for the signal magnitude Aldir and for the signal to background ratio, R. Dayton [7a] has shown that the degree of collimation is governed by a geometrical transmission function, T(8), for the inlet tube. T(0) is determined by the length L of the inlet tube and its radius Y. It is easily shown, using Dayton’s formulae, that the collimation increases substantially with increasing L/r for small ratios, but that very little change in collimation is achieved once L/r > 10. Figure 4 shows the amount of gas flow exiting within a polar angle, 8, normalized to the total gas flow, as a function of 8 for different L/r values. L/r M 10 gives sufficient collimation for all practical purposes. (For more details see Appendix A and ref. 7.) Once the L/r ratio is fixed it is possible to optimize the performance by positioning the tube exit closer to the ion source and thus allowing for a larger fraction of the total flow to pass through the ion source. However, one must then be careful not to distort the electric field in the ion source, since the electric field influences the production and collection of ions. Also the chopper/shutter must not perturb the electric fields since this will produce errors in signal detection and in the background subtraction. This must be tested individually for each MS unless the manufacturer can give advice on proper distances. An additional possible way of optimizing the performance involves a
9 (Degrees) Fig. 4. The integrated gas flux within polar angle 0 exiting from a tube of length, L, and inner radius, r, as a function off?, under molecular flow conditions (calculated using ref. 7a).
modification of the ion source. Since the directed sample gas signal, AZdir,is inversely proportional to the cross-section of the effective detection volume in the ion-source, it may be possible to increase this signal difference by diminishing the ionizing volume. An estimation for AZ,i, (based on Fig. 5 and eqn. A8) gives for small angles 8 and fixed L/r an increase of about 100% if the cross-sectional entrance area of the ionization volume is decreased by a factor of two without changing the ionization probability inside the ionization volume. We show elsewhere [8] how the volume of the ionizing volume can be varied by different settings of the ion source potentials. An appropriate final remark in this section is that we have found that small, cross-beam ion sources of several MSs always give satisfactory performance with R values 2 1. Ion sources with large ionization volumes are expected to give smaller R values. With differentially pumped gas inlet systems possible problems with mass separation, i.e. separation of molecules with different masses, have to be addressed. In the present case this is not a problem, however, since no differential pumping is employed. As long as the gas flow at the gas sampling point is viscous the gas composition will be conserved until it exits the MS. This was verified experimentally by measuring the MS signals for Ar and He for different original Ar/He ratios in the range z 0.1-10. The gas mixtures were made using a capacitance manometer. Figure 5 shows the measured MS signal ratio AZ,,/AZ,, as a function of the mixing ratio pAr/pHe. The linear relationship with a slope of one demonstrates that no mass separation occurs.
15
-I WI
0,l
1
10
100
Y4r’!He Fig. 5. A plot of the AZAro,= 36,/AZn,(M= 4, ratio vs. the P,/PHe ratio, measured for a number of different Ar/He gas mixtures using the gas inlet device shown in Fig. 1. PAr/PHeis the partial pressure ratio in the previous gas sample, whose total pressure was 700 Torr. The straight line with a unity slope shows that no mass separation occurs.
4.3. Measuring pumping speeds with the directed-gas inlet
Inspection of eqn. 2 (or 2’) reveals, as a side effect of the present gas inlet method, a very simple and elegant way of measuring pumping speeds. Initially this requires calibration of the gas inlet system + MS combination using a vacuum system with known pumping speeds for the gases of interest. This calibration is made once to obtain the instrumental constant A of eqn. 2 (from a plot like the one in Fig. 3).characterizing the gas inlet + MS combination. The calibration can then be used on any vacuum system to measure its pumping speeds for various gases. The pumping speeds are simply obtained by measuring the R values for the gases of interest and then using eqn. 2 (or 2’) to obtain the corresponding pumping speeds (depending on the prevailing vacuum conditions). The result will be more accurate if the system background pressure is sufficiently low such that eqn. 2 rather than eqn. 2’ can be used. 4.4. Some practical aspects The gas inlet system described here makes possible reliable, quantitative gas analysis even in the presence of interfering background gases, as examplified in Section 3.2 and Fig. 3 (see also [9]). Since no differential pumping is required the gas consumption is low (< 10e4 Torr 1SC’). If high accuracy is not required or if simple gases are analyzed one may use the present inlet system without a chopper or shutter and still have an advantage over conventional gas inlet methods. In this case a low system background pressure and
16
a high pumping speed give better results as can be seen by rewriting eqn. 1 as
The quantity of interest is ICAPdir = /3Q,and a correct gas analysis is obtained if this term dominates over ‘ypcl. A requirement to obtain correct results, which all the time has been implicitly assumed, is that the composition of the gas emerging at the vacuum end of the gas sampling system is the same as that sampled at the sampling position. This is a different type of problem than the one treated here but is of course not trivial. For example, with water vapour and other polar gases or with very reactive gases, molecules may adsorb, desorb, or react on the walls of the gas sampling device. Means of reducing or eliminating these effects are: proper choice of materials in the inlet system, and/or heating all surfaces in contact with the sample gas to an appropriate temperature to reduce “memory” effects. An example of the use of the present gas inlet system to study surface reactions, e.g., heterogeneous catalysis, in a small flow reactor will be published shortly [9]. 5. SUMMARY
The theoretical and experimental analysis above shows that the simple, directed-gas inlet system described here offers the following advantages over conventional non-directed gas inlets: (i) The measured signal contains no contribution from sample gas interaction with the walls of the vacuum system. (ii) It contains no contribution from the existing background gases in the vacuum system (except in the signal noise). (iii) It is independent of temporal variations in the pumping speed of the vacuum system and its walls. (iv) The sample gas consumption is only z 10e4 cm3 SK’ at 1 atm sample gas pressure. (v) The method can be used to measure pumping speeds. ACKNOWLEDGEMENT
We are grateful for many valuable discussions with I. Zoric and E. Tiirnqvist. Financial support from the Swedish National Board for Technical Development (Contracts 835405 and 6043 14) is gratefully acknowledged. REFERENCES 1 A. Hijghmd and L.G. Rosengren, Int. J. Mass Spectrom. Ion Processes, 60 (1984) 173. 2 E.L. Knuth, Direct-sampling studies of combustion processes, in G.S. Springer and D.J. Patterson (Eds.), Engine Emissions, Plenum Press, New York, 1973, p. 319.
17 3 S.N. Foner, Mass spectrometry of free radicals, in D.R. Bates and I. Easterman (Eds.), Advances in Atomic and Molecular Physics, Vol. 2, Academic Press, New York, 1966. 4 G. Stoles (Ed.), Atomic and Molecular Beam Methods, Vol. 1, Oxford University Press, New York, 1988. 5 B. Kasemo and K.-E. Keck, Swedish Patent 8404840-4, 1986. 6 B. Kasemo, Rev. Sci. Instrum., 50 (1979) 1602. 7 (a) B. Dayton, Trans. 2nd American Vacuum Society Vacuum Symposium, Pergamon Press, New York, 1961, p. 5. (b) S. Adamson and J.F. McGlip, Vacuum, 36 (1986) 227.. (c) P. Clausing, Z. Phys., 66 (1930) 471. 8 J. Hall, I. Zoric, M. Rinnemo and B. Kasemo, Rev. Sci. Instrum., in press. 9 S. Lundgren, K.-E. Keck and B. Kasemo, Time and space resolved gas analysis of gradients and transients in catalytic reactions, to be published.
APPENDIX
A: CALCULATIONS
OF A, B AND R
The theoretical treatment is essentially the same as for a molecular beam, but with the additional ingredient that we have to take the divergence of the gas flow at the exit of the gas sampling device in the MS chamber into account. The quantities we want to calculate are the relative magnitudes of the MS signals, l& and 1:,, corresponding to the partial pressure, or rather density, of a gas, i, with the shutter open and closed respectively. The difference, Al~ir, (see eqn. 1) between these two signals is the desired quantity. It contains only the contribution from gas molecules in the inlet gas which have not been in contact with the chamber walls. In the theoretical treatment, the MS signals are treated as d.c. signals when the shutter is open and closed. Extension of the theory to lock-in detection of chopped signals is straightforward. For conditions of molecular flow, Dayton [7a] has calculated the transmission of gas through a tube which connects two gas reservoirs. The angular distribution exiting from the tube at the lower pressure reservoir is given by F(8, L/r) do = T(8, L/r) cos 8 do
(Al) where T(8, L/r) is a transmission function which is determined by the ratio between the length, L, and the radius, r, of the tube and 8 is the angle about the tube axis. dco is an infinitesimal space angle about 8. For a hole in an infinitely thin wall, T(0, L/r = 0) = 1 and we get the well known cosine distribution. For a tube of finite length, T(8, L/r) will cause the angular distribution to peak in the forward direction. With do = sin 8 de d$, we may calculate the fraction of the flow which exits from the tube within a cone with half-angle 8 about the tube axis. This fraction increases rapidly with increasing L/r for small ratios, but saturates as L/r 2 10. In Fig. 4 a plot is shown of the integral (from zero to 0) of F(8, L/ r ) vs. 8, for different ratios of L/r. We will treat the tube exit as a point source and show that it is then possible to make a theoretical estimation which is in good agreement with the experi-
18
mentally obtained results b. The fraction H Q, of the total flow, Q,, that exits from the tube within the polar angle 8 about the tube axis is
HQs = Qs
1: F(O’, L/r) sin 8’ de’ j”y F(8’, L/r) sin 8’ de’
642)
In order to apply this equation we treat the effective ionization volume, A V,s, of the ion source as a cylindrical volume with diameter &s and with its axial parallel to the tube axis (Fig. 1). (We have shown [8] that the effective region is not actually cylindrical. However, knowledge of the exact shape of the effective ionization region is not necessary for the treatment below.) If z is the distance between the termination of the gas inlet tubing and the ionization volume (see Fig. l), we obtain an expression for the acceptance angle, c#+, of the ion source: 41s 22
8,s = arctan
(A3) ( ) Using 8,s as the integration limit in eqn. A2 we obtain the fraction HQ, that passes through the ion source. To proceed we now need to derive expressions for the MS signals with the shutter open and closed. The molecules within the tube will have a maxwellian velocity distribution corresponding to the tube temperature. However, the velocity distribution for molecules leaving the tube will be different from this distribution because the flow through the tube exit involves an extra factor, namely the velocity component along the tube axis. Thus the mean velocity for molecules leaving the tube is given by V = (~~T/EYz)‘/~, where T is the temperature of the tube and m is the molecular mass. Since the density of molecules within the ion source depends on their velocity, we may write the local density in the ionization volume, when the shutter is open, as consisting of two parts: n& =
&r
+
4
(A4)
where nai, = 4(4kT)-“2(7&)-’ (wz’)“~HQ~ is the local density in the ionization volume due to the molecules which pass directly from the tube through the ion source without interacting with the MS chamber walls. The term & is the isotropic density in the MS chamber, and it is related to the isotropic b It should be noted that the angular distribution function calculated by Dayton describes the total flow of molecules emerging from the exit of the tube in a given direction, 0, about the tube axis. It is thus possible to determine the fraction of the total flow emerging from the tube exit in the direction 0. It is, however, not possible to use Dayton’s expression when calculating the fraction of the total flow which passes through an area positioned in front of the tube exit. This is only possible when the radius of the tube exit is so small that it can be regarded as a point source.
19
pressure in the chamber by FZ;,= (kT)-‘p;,
(A3
where T is the temperature of the vacuum chamber. We assume that the temperatures of the inlet tube and the vacuum chamber are equal. The isotropic density, n,, , will be the same with the shutter closed and open. The mass spectrometer signal is proportional to the integral over the product of local density and position dependent detection efficiency in the ion source. In the case of a spatially non-varying density, the MS signal is given by Cl = e jAv,,K’,,(v)nh,dr= e(kT)-‘A&:,&p:,
(A6)
where A V,, is the effective volume of the ion source and pi, is the average MS detection efficiency factor for gas i. In the case of directed flow through the ion source, the local density variation becomes important. We have used Dayton’s formulae [7a], calculated the density variation and found that it is small for small angles 8. With this in mind we write the MS signal for directed flow as
= 4e(4kT)-“*AV,,(~~:,)-’
(m’)“*HQb~~ir
647) where heir is the average MS detection efficiency for the directed inlet. The last equality was obtained from eqn. lb. The detailed expression for Al~ir obtained above is not important for application purposes, since pi is calibrated for various gases i. However, it is useful in the following, where we estimate theoretically the relative order of magnitude of the signal due to the directed flow and the signal due to the isotropic background pressure. The ratio between the two signals AI~i, and Ii, is given by
The two average detection efficiency factors, &jr and pi,, are in general somewhat different since F& is the average detection efficiency factor for molecules moving essentially along the symmetry axis of the ionization volume and pi, is that for molecules with isotropically distributed velocity. However, the difference is expected to be rather small at thermal velocities. We put Eli, = PA,and rewrite R’ as
where u is the molecular weight unit and M’ is the molecular mass number.
20
We define the effective pumping speed according to the relation s;flp;, = Q;
(AlO)
We can then finally rewrite R’ as
(Al 1) where SLflis in Is-‘. In order to obtain quantitative values of A and R we put in numerical values. In the experimental system used for the measurements described in Section 3.1. we have z = 10 mm and an effective diameter of the ion source of 41s = 3Smm, yielding 8 = 10’. The fraction, H, of the total flow, Q, which passes through the ion source is now easily obtained from eqn. A2 or Fig. 4. The ratio between the length and the radius of the inlet tube is L/r = 200 in our system. This gives H = 0.12 for 8 = 10”. If the vacuum system is held at room temperature, we obtain a value of A = 4 x lop3 for the instrumental constant A of eqns. 2 and A9, in quite good agreement with the experimentally determined value of 5 x 10-3. The assumptions that the tube exit can be treated as a point source in the use of Dayton’s formulae for the angular distribution pattern results in an overestimation of the molecular flow through the effective volume of the ion source. However, our calculation does not include sample molecules which scatter from the walls of the ion source into the effective ionization volume. The latter results in an underestimation of the density of sample gas molecules within the ion source. It seems that these two effects are either small or partially cancel each other so that quite a good value for the constant A is calculated. Thus we obtain theoretical values for R’ in the range l-3 at pumping speeds of 80 1s-’ < Sirr < 200 1s-’ in good agreement with measurements (Table 1). APPENDIX
B: EXPERIMENTAL
DETERMINATION
OF PUMPING
SPEEDS
The pumping speeds required to plot R/S,, vs. (M)“’ (Fig. 3, eqn. 2) were measured in the following way. A gas supply volume of z 1 atm pressure feeds gas via an automatic leak valve into a second volume at a much lower pressure (PI = lo-*Torr). p, is continuously recorded by a capacitance manometer and is kept constant throughout the measurements by a feedback loop from the capacitance manometer to the automatic leak valve. A tube feeds gas from the volume at pressurep, into the vacuum chamber with the MS. The gas flow into the vacuum chamber is then Q, = C(p, - p,,(t)) where p,,(t) is the isotropic pressure in the vacuum system due to the gas flow Q,, and C is the conductance of the tube feeding the gas. Since pc, @ p, , Q, stays constant at
21
Q, = Cp, during the measurements. The vacuum chamber is equipped with a pneumatically operated gate valve which can be used to rapidly close off the chamber from the turbo pump. The latter has a nominal pumping speed for N, of 270 1s- ‘. The actual pumping speed is considerably lower because of the gate valve and a 6in. tube in series between the pump and the chamber and because of the splinter shield of the turbopump. The effective pumping speed of the chamber for various gases can now be determined by combining two measurements. The first one is just a measurement of the steady state vacuum system pressure, pz,, for each gas due to the gas leak, Q,. The accuracy of this measurement requires that the system background pressure is known or, in our case, is much less than pz, . (This was checked with the MS for each gas of interest.) The second measurement consists of closing the gate valve and following P,,(t) over a finite time, r. The two measurements are represented by the following two equations: PEI=
C(P, - P3
s
CP,
=r;
eff
dp,, =
C(P,
dt
PI BP:,
(Bl)
CP, V
032)
eff
-PC'(o) V
Z-
Combining these equations we obtain: s
=
eff
V(Pl - PZJ,, P3
with p,,(t) S
4 p,
V dpc,
z_----_--_
effPZI dt
PI - Pcq PI - Pcl(4
(f33)
, this simplifies to
v PC’(T) Pcq
7
(B4)
Several measurements were performed at different values of p and z. A variation of 5-10% was observed from run to run. Measurements were performed for the gases H,, CH,, N, and Ar with the results given in Table 2. These values produce a fairly smooth curve when plotted as a function of mass number. Pumping speeds for gases for which no pumping speed measurements were made were obtained by interpolation from such a plot to obtain the corresponding R/S,, values in Fig. 3 (filled squares).
Journal of Mass Spectrometry and Zon Processes, 108 (1991) 1-21
1
Elsevier Science Publishers B.V., Amsterdam
A gas inlet system for quantitative J. Hall, S. Lundgren,
mass spectrometry
K.E. Keck and B. Kasemo’
Department of Physics, Chalmers University of Technology, S-412 96 Giiteborg (Sweden)
(Received 28 November 1990; in final form 12 April 1991)
ABSTRACT A gas inlet system for quantitative mass spectrometry is described. The principle is to make the gas pass through the ion source using tubing terminating close to the ion source. With molecular flow conditions in the tubing a directed, reasonably collimated beam is achieved giving rise to a local pressure increase in the ion source. This local pressure increase is due to molecules that have not interacted with the chamber walls, and can easily be obtained for each gas species of interest by taking signal differences or by lock-in techniques if a shutter/chopper is positioned between the gas sample tubing and the ion source. The traditional plagues of quantitative mass spectrometry, namely background gases and wall gas-exchange effects are thus’eliminated. For stable gas species this gas inlet system offers essentially the same advantages as a molecular beam gas inlet, but at much lower cost and complexity and requiring much smaller gas samples for analysis. For example, no differential pumping is required. The properties and performance of the gas sampling system are analysed theoretically and demonstrated by experiments. Good quantitative agreement is obtained between theory and experiment. It is shown theoretically, and verified experimentally, that the ratio, R, between the local pressure rise in the ion source, due to the directed beam, and the average mass spectrometer (MS) chamber pressure varies as R 2 S Ml/2 where S is the pumping speed and M the molecular mass number. As a specific example it is demonstrated how the water vapour content of a gas sample can be correctly measured even in the presence of a high water background in the MS vacuum chamber. It is also shown how the gas inlet device can be used as a simple tool to measure pumping speeds in vacuum systems.
1. INTRODUCTION
Mass spectrometry is inherently an extremely sensitive method of measuring gas composition. In ideal cases it is possible to measure a relative gas concentration (of one gas diluted in another) of 1 x lo*, with a gas sample as small as 10P5cm3 at atmospheric pressure. However, the theoretical sensitivity rarely sets the limit for the measurement accuracy. The accuracy and sensitivity limits are instead usually determined by influences, e.g., from background gases, reactions or degassing in the ion source of the mass spectrometer (MS) analyser, and by temporal variations in pumping speed of the vacuum system. ’ Author
to whom correspondence
0168-1176/91/$03.50
0
should be addressed.
1991 Elsevier Science Publishers
B.V.
2
In the present paper we describe and analyse experimentally and theoretically a simple gas inlet system that greatly suppresses such effects. Basically it offers the same advantages over conventional gas inlet systems as molecular beam gas inlet systems, but at much lower cost and complexity and with much smaller gas consumption. For comparison purposes we first briefly describe some commonly used gas inlet methods in mass spectrometry. Then in Section 2 the principle of the gas inlet system described in this paper is outlined together with a theoretical analysis. A more detailed analysis is given in Appendix A. The third section describes measurements to test the theoretical predictions and also illustrates the performance for measurements of practical interest. These results and possible extensions and improvements are discussed in Section 4. In this section it is also shown how the gas inlet system can be used as a simple tool to measure pumping speeds. 1.1. Simple gas inlet methods
The simplest type of gas inlet system for MS analysis consists of a leak (sometimes differentially pumped) that introduces the gas sample into the MS system at a gas mass flow Q,. The magnitude of Q, and the pumping speed, S, are, if possible, chosen so that the total operating pressure, Q,/S, in the vacuum chamber lies in the region 10-6-10-5Torr, i.e., Q, is typically 10-3-10-4 Torr 1SC’.The pressure in the ion source is then made up of the sum of the system background pressure and the pressure created by Q,.The origin of the background partial pressures is: (a) degassing from the chamber walls and from components in the vacuum system; (b) reactions at hot filaments (ionization gauges, MS filament etc.); (c) back flow and/or gas release in the vacuum pump; and (d) exchange reactions at the walls due to the introduced sample gas. The precision by which a gas sample can be analysed depends to a large extent on how well such background effects can be controlled. The simplest approach to estimate these effects is to record a mass spectrum with the gas inlet closed and then subtract this spectrum from the one measured with an open gas inlet. The differential partial pressures obtained in this way are, however, generally different from the partial pressures of the inlet gas. The reason is that the background gas compositions with the sample gas inlet open and closed are usually different because exchange reactions on the chamber walls and reactions on surfaces in the chamber change the background gas composition (the inlet sample gas components can for example cause release of gas adsorbed on the chamber walls and in ion and cryopumps etc.). For many gases, particularly polar and reactive ones, these errors can be large and the simple background subtraction method then becomes unreliable. Additional measurement errors derive from variations over time in the
3
effective pumping speeds, S’ = Qi/$, of the different gases, i, which determine the corresponding partial pressures. The effective pumping speed is the sum of the pumping speed of the vacuum pump and the chamber walls. Since the latter temporarily may be as large as, or even larger than, the former and may also act as a gas source by release of previously adsorbed gas, large uncertainties may result in the quantitative gas analysis (the chamber walls effectively act as a capacitor for reactive and polar gases). All these effects may to a certain extent be checked and reduced by introducing a known gas mixture, which has a composition as close to the composition of the analysed gas as possible. By an iterative procedure this can give improved but still only approximative control over background effects. The method is tedious, time consuming, and useful only in simple cases. It is thus apparent that the simple gas inlet method discussed above is not generally satisfactory for quantitative MS gas analysis. 1.2. Molecular beam inlet A straightforward, but expensive, method to get around these problems is to use a gas inlet with a molecular beam so that a well collimated beam passes through the ion source [l-4]. The operating principle is the following. The gas is introduced via a nozzle feeding a suitable amount of gas (10-‘-l Torr 1s-‘) into a first vacuum chamber, where a conical aperture (skimmer) skims off most of the gas which is then pumped away. The remaining small gas fraction travels through the skimmer aperture into a second vacuum chamber where it is further collimated by a second aperture. Sometimes a third chamber and collimating aperture are used. In this way a well collimated beam of sample gas of diameter l-2 mm is created. By chopping the beam before it enters the ion source, the relevant background pressures can be readily eliminated. To discuss how this is achieved, we assume that the chopper is in fact a shutter with two positions, open or closed. We also assume for simplicity of notation that the beam contains a single gas species. In the open position the beam passes through the ion source; in the closed position it is stopped by the chopper. In the closed position the situation is then identical to the situation discussed previously, i.e. one has a diffuse leak creating an isotropic pressure, pc,, ( wh ere the subscript cl stands for closed). When the shutter is open the pressure in the MS chamber will be the same as in the closed position everywhere, except along the directed molecular beam where the local pressure, pop, (op for open) will be higher. If measurements are performed with the shutter open and closed and the difference between the two measurements is taken, we obtain the MS signal due to the increased local pressure, Apdir,in the ion source caused by the directed molecular beam. This
4
is exactly the quantity one wants to measure since this difference is proportional to the gas flow, Q,, in the gas inlet system (see eqn. lb below), which in turn, in the case of gas mixtures, gives the sample gas composition. (For a gas mixture the same analysis as above holds for each gas component i-just put a superscript i on p and Q,.) The proportionality -C(Pdir a Q, is not quite trivial. It is, however, correct when the gas flow at the sampling point is viscous and the exit flow is molecular. See also a comment at the end of Section 4.2 and ref. 6. The sensitivity factors in this type of measurement will be different compared with those in the simple gas analysis described previously, due to a mass dependent molecular velocity effect in a molecular beam [4]. The partial densities, or pressures, of the different gas components in the beam will be proportional to the initial sample gas densities multiplied by the square root of the mass of the molecules (provided no supersonic nozzle expansion and seeding effects occur, i.e. we assume a “thermal” beam [4]). This is because the thermal velocity of a molecule is proportional to the inverse square root of the mass of the molecule and the corresponding density in the beam is proportional to the inverse velocity of the molecule (see also Appendix A). To obtain numbers, we consider absolute values of the parameters involved in a realistic case. Let us assume a sample gas-beam flow of 10P6Torr 1s-‘, equivalent to about 3 x 1Ol3molecules s-‘, into the vacuum system, which we assume to be at room temperature. With an effective pumping speed of 100 1s-’ this creates a chamber pressure of z lo-* Torr. If we assume a beam area of 1 mm* and a molecular velocity of 500 m s-‘, we obtain a local beam pressure of 2 x lop6 Torr, from which we see that the local beam pressure can be about 100 times larger than the average chamber pressure created by the beam. Obtaining a corresponding signal increase over the background due to the beam requires that the beam fills up the sensitive region of the ion source entirely, which is seldom realized, but a local pressure increase of z x 10 is realistic with z 100 1SC’ pumping speed. By differential pumping around the MS ion source and/or an increased pumping speed of the analysis chamber, the background pressure in the ion source can be further reduced 2-3 orders of magnitude, with a corresponding improvement of (beam) signal to background ratio. There is essentially only one argument against using a molecular beam as the gas inlet, namely the cost. The gas consumption may also be much too large when only small gas samples are available. The beam forming stage requires two to three pumping stages with diffusion or turbo pumps plus forepumps, valves, pressure meters and maybe alignment mechanisms [l]. Below we describe a much simpler and much cheaper alternative, essentially offering the same advantages as the molecular beam inlet for detection of stable gas components and with a gas consumption 103-lo4 times smaller. The
5
only major limitation in comparison with a molecular beam mass spectrometer is that unstable molecules, e.g. radicals, cannot be detected in the same way as is possible with a molecular beam MS system [3]. 2. A DIRECTED
GAS INLET SYSTEM
2.1. Operating principle
The principle [5] of the gas inlet system, illustrated in Fig. la, is the same as for the molecular beam MS discussed above, but with the important difference that no differential pumping is needed. At the high pressure (gas sampling) end, the sample gas is introduced via a narrow hole (which could also be a permanent leak or a leak valve) into the tubing, which extends almost all the way to the ion source. The narrow hole, acting as a gas leak, controls the amount of gas which is fed into the MS chamber, and brings the flow of gas into the molecular flow regime in the tubing [6]. The angular distribution pattern for gas transmitted through, and exiting from, a tube under these conditions has been subject to both theoretical and experimental work [7]. These results show that the tubing causes considerable collimation of the gas flow at the exit C. With an arrangement where the termination of the tubing is sufficiently close to the ion source, an increased local pressure is therefore created in the effective region, E, (the ionization volume) of the ion source when the shutter/chopper is open. In the same way as described for a molecular beam MS, the local pressure rise in the ion source is obtained by taking the difference between the MS signal recorded with the shutter open and closed. This difference can be obtained electronically as a simple difference signal or by a standard lock-in detection technique if a periodic chopper is used instead of a shutter. The same signal analysis as for the molecular beam MS is applicable, the only difference being that the “beam” leaving the tubing is more divergent. The local pressure increase in the ion source, over the background, may therefore not become quite as large as in the molecular beam case. There may also be some wall collisions (in the ion source) of the beam molecules due to the beam divergence, unless additional collimation is employed. We now derive an expression for the difference, AZii,, between the mass spectrometer signals, I&, and ZJ,,when the shutter is open and closed respectively, to be used for comparison with experimental results described in Section 3. A more extensive theoretical analysis is given in Appendix A. To simplify the analysis we assume that the isotropic partial pressures in the analysis chamber, created by the sample gas flow Qd, are much larger than the system background partial pressures. Incorporation of the system background is fairly straightforward and is done in Section 4. The mass
UHV-chamber
(b) Masd Spectrometer
Orifice -.-
\ 10 mm _____-----_________ \ -___ _____----____--_____--______.
Fig. 1. (a) Principle of the directed-gas inlet system. The sample gas exits from the tube C under molecular flow conditions and is directed through the effective ionization volume, E, of the ion source. The “beam” exiting from C is divergent but strongly peaked in the forward direction for L/r $ 1 (see Fig. 4). A chopper/shutter is used to subtract the beam signal from the isotropic chamber pressure. (b) The experimental set-up used to evaluate the directed-gas inlet system and to measure the R values presented in Table 1 and Fig. 2.
7
spectrometer signals, I’, are proportional to the density (or pressure) of molecules, i, within the effective detection region of the ion source. When the shutter is open, the total partial pressure, p&, in the ion source is the sum of the contribution, Apair, created by molecules, i, which pass directly from the tube exit through the ion source, and the isotropic partial pressure, p:,, in the vacuum chamber due to the sample gas Q$. When the shutter is closed, only molecules which contribute to the isotropic pressure, pi,, are present in the ion source. This contribution is of course the same, independent of whether the shutter is open or closed (providing the shutter is inert with respect to the gas in the beam, and providing pumps are not unsuitably positioned). Thus, the difference in mass spectrometer signals, AZ~ir,with the shutter open and closed is given by A&
= ZAP- Z;, = a’p& - yip;, = JC~L\P;~,
(la)
The sensitivity factors c?, yi and ICY are different because of the mass dependent velocity in the directed beam discussed below and in the Introduction. yi are the normal sensitivity factors for residual gas analysis, ICY are essentially the sensitivities corresponding to the molecular beam mode of operation, and the ai values, which will take absolute values between the values of yi and K~,are defined from the last equality of eqn. la. Since the local “pressure” (or rather density) rise, Ap~ir,is proportional to the directed gas flow Qbwe also have the following equality: AZ& = D’Q;
(lb)
The molecular mass-dependent parameters 8’ relate the difference signals Apai, to the corresponding components, Qi, of the sample gas. The magnitudes of the pi values depend on how large the fraction of molecules i is that passes from the tube exit through the effective detection region of the ion source, on the volume of this effective region, and on the molecular velocity which varies as the square root of the mass. The pi values are easily determined experimentally by calibration for the various sample gases which are let into the system. A theoretical expression for /3’is derived in Appendix A. To estimate semiquantitatively the performance of the gas inlet system let us assume a gas sample flow of Qi = 10e4Torr 1SK’and a pumping speed of S’ = 100 1s-l, producing a background gas pressure ofpi, = 10P6Torr. (In the following we drop for simplicity the superscript i.) For the estimation we assume that the divergence of the gas leaving the inlet tube is such that 10% of the total flow, Q,, (equivalent to about 3 x 10’4moleculess-‘) passes through the effective region of the ion source when the shutter is open. (We show in a separate paper [8] that the cross-section of the effective detection region of the ion source used in this work is of the order of 10 mm’.) If we use 500 m s- ’ for the molecular velocity we get a local pressure increase in the ion
8
source of Apdir = 2 x 10e6Torr due to the directed gas “beam”. In experiments we thus expect to obtain a signal difference, A~dir,which is at least as large, or even larger than, the signal, I,, , when the shutter is closed. As we shall see below this is verified experimentally. In the next section we test experimentally the described gas inlet system and compare the experimental results with the calculations. 3. EXPERIMENTAL
RESULTS
The gas inlet system (Fig. 1) was evaluated experimentally in two different MS systems. The first system was used to test the principle and quantify the performance of the gas inlet system. The results obtained could then be compared with the results of the theoretical analysis presented above and in Appendix A. The second system was used to demonstrate the advantage of the present gas inlet system over conventional inlet systems by measurements of H,O in the inlet gas in the presence of a large HZ0 background. 3.1. Experimental test ofthe principle and quantitative results The vacuum system for the evaluation of the inlet system consists of a stainless steel vacuum chamber and a Balzers QMG 31 I/QMA 150 quadrupole mass spectrometer with a cross beam ion source. The total pressure is measured with an ion gauge. The vacuum chamber is pumped by a turbomolecular pump (Balzers TPU 270). The background pressure in the chamber is in the low 10p9Torr range after bakeout of the system. The gas inlet tube, 300 mm long and 3 mm in diameter, is mounted on a 6 in. flange together with a rotary manipulator, which controls the shutter in front of the ion source (see Fig. lb). The inlet tube is mounted so that its axis goes through the centre of the ion source, perpendicular to the quadrupole axis. The distance, z, between the exit of the inlet tube and the entrance side of the ion source is x 1Omm. The effective width, &, of the ionizing region of the ion source is 4,s z 3.5 mm [8]. The divergence of the sample gas leaving the tube exit, the tube diameter, the distance z and the effective volume of the ion source determine the fraction of the total flow Q, which passes through the ion source. This fraction is estimated theoretically to be about 10% (Appendix A). The performance of the inlet system was quantified by measurements of the ratio, R, between the signal due to the directed inlet sample gas, Al~i,, and the signal with the shutter closed, IC,, due to the isotropic pressure created by the inlet gas. From eqn. la and b we see that R for a given gas is given by
(2)
TABLE 1 Measured ratios R E AZdir/Zclfor different gases Gas Ri
He 1.75
H2 1.30
CH, 2.34
H,O 2.58
N, 2.64
02 3.00
Ar 2.84
COZ 2.93
where A is a constant and S,, is the effective pumping speed for the gas considered. The mass dependence of j3originates from converting the gas flow Q, to gas density (or “local pressure”), which requires dividing Q, by the average molecular velocity in the beam direction. (Note that the mass dependence of R vanishes if one can arrange that Sffvaries as l/M”*). The constant A depends on the size of the effective detection volume in the mass spectrometer ion source and on the geometrical arrangement of the inlet system, i.e., it is an instrumental constant. It can be determined relatively easily experimentally (see below) but is not needed for quantitative MS measurements. (We recall that we have dropped the superscript i. Equation 2 is actually a set of equations, one for each type of gas molecule of interest.) Using the pumping speed values determined as described in Appendix B and given in Table 2, the system performance can now be quantified and the theoretical estimates can be tested by measuring the ratio R of eqn. 2 for various gases. The measured R values are given in Table I. A plot of R divided by the corresponding S,., as a function of the square root of mass number is shown in Fig. 2. The data points are well fitted by a straight line in agreement with eqn. 2. The scattering of data points around the straight line is mainly due to uncertainties in the effective pumping speeds. The slope of the line gives 0.04
I
He/
0
2 2
4
(mass number)
6
8
In
Fig. 2. A plot of the measured R’/& ratio vs. the square root of molecular mass number for the gases given at the data points. (The measured R and S,, values are given in Tables 1 and 2 respectively.) The good straight line tit to the data verities eqn. 2.
10 TABLE 2 Measured and interpolated pumping speeds for different gases Gas &T cs-‘1 aInterpolated
H* 188
He 171”
CH, 122
Hz0 118”
N, 100
02 96
Ar 85
COZ 82”
values.
the instrumental constant A in eqn. 2. we obtain A = 5 x lop3 which is in good agreement with the theoretically estimated value of 4 x lop3 (eqn. 12 in Appendix A). These results are further discussed in Section 4. Note that measurements of R are only made to evaluate the performance, but are not necessary for quantitative gas analysis. The latter only requires measurements of the Aldir value corresponding to the gases of interest and knowledge (by calibration with known gas mixtures) of the sensitivity factors xi (eqn. la). 3.2. Application to measurements of H,O The system used for these measurements [9] was similar to the one described above, but employed a Balzers QMG 112/QMA 120 mass spectrometer with a cross beam ion source. The leak rate of the sample gas was in this case controlled by a quartz tube orifice leak [6] creating a steady state isotropic pressure of pC,= 10V6Torr. The shutter was replaced by a chopper which was electromechanically controlled from the outside of the vacuum chamber and could be used as a closed/open shutter or operated at a frequency of 20Hz when using lock-in detection. The importance of controlling the vacuum chamber background effects during gas analysis is illustrated by the following example. Air with low humidity was let into the vacuum chamber with the directed-gas inlet system. Figure 3 shows the H,O signal as a function of time, recorded with the shutter successively positioned in the “closed” and “open” positions. While feeding a constant flow of gas with constant H,O concentration through the directed-gas inlet system, the H,O background pressure in the vacuum chamber was increased at times A-J, by introducing humid air through a separate leak valve. The MS signal, representing the H,O concentration in the sample gas, is obtained as the difference between the curves marked “open” and “closed”. Note that the difference between the curves displayed in the inset of Fig. 3 (representing the sample gas) stays constant in spite of the increase of the background H,O pressure. With a conventional gas inlet, the lower (isotropic) pressure curve marked “closed” would always have been recorded, creating a severe error in the sample gas analysis.
11
H2Osignal
10
-
20
open
---
-_-
30
Ii -, I----
closed
I
j I I
G
10
20
30
40
t(mW
Fig. 3. Measurement of the Hz0 content of a gas sample at different background levels of Hz0 in the vacuum chamber. The desired sample gas signal for A4 = 18 is obtained as the difference between the signals recorded with the shutter open and closed (eqn. la). The inset shows that this difference stays constant in spite of large variations in the M = 18 background. 4. DISCUSSION
4.1. General aspects
We first note that the basic principle of the present gas inlet system, theoretically outlined in Section 2 and represented by eqns. 1 and 2, is verified by the experimental results. The ratio, R, between the local partial pressure increase in the ion source, due to the directed sample gas “beam”, and the isotropic background pressure created by the same sample gas, is 2 1 for the pumping speeds employed. This makes it quite straightforward to obtain the desired relative partial pressures of the sample gas, APdir, using periodic chopping and lock-in detection to measure the corresponding AIdir values. The sensitivity factors, K, converting the MS signals to (relative) partial pressures, are best obtained by calibration with known gas mixtures. Note that the K values are different to the “normal” sensitivity factors, y, used in residual gas analysis, because of the mass dependent velocity effect. The latter is the reason that R = Aldir/lcl (eqn. 2) is proportional to M”2. This explains the tendency of the R values to increase with increasing molecular mass (Table 1). Basically the reason is that the heavier molecules in the directed “beam” travel more slowly than the lighter ones, and therefore have a larger chance of being ionized. The trend in Table 1 predicted by this mechanism is, however, counteracted by the decreasing pumping speed, &,
12
with increasing M (see Table 2). Both these effects are accounted for by eqn. 2 and the plot of R/S,, vs. M’j2 gives a straight line. The M’12effect is an example of an interesting difference between conventional residual gas MS measurements and directed-beam measurements. Because of this effect the latter measurements have a relatively higher sensitivity for heavier molecules, partly counteracting the common loss of sensitivity at high mass numbers in quadrupole mass spectrometers. As discussed in the Introduction and Section 2, and illustrated by eqn. 2, the suppression of the background isotropic pressure (the latter created by the sample gas), is proportional to the pumping speed. Thus, additional suppression can, if necessary, be obtained by increasing the pumping speed. R values 2 10 can be obtained with pumping speeds 2 500 1s-’ which in some applications may make the chopper and lock-in detection unnecessary. In the analysis so far we have not explicitly treated the inherent system background gases present in the absence of sample gas. This is mostly a good approximation for a well baked system with a base pressure in the 10P9Torr region or lower, since the background partial pressures of interest created by the sample gas are then (usually) much larger: z 10-7-10-6Torr. Inclusion of the system background pressures does not change eqn. 1 or the basic conclusions, however, but modifies the third equality of eqn. 2, since the partial pressures, pCl , with the shutter/chopper closed now consist of two components: one due to the sample gas and the second due to the inherent system background pB. We now derive an expression including also PB. In order to simplify the analysis we assume that the system background pressure and the partial pressures created by Q, are additive”. Then the equality pcl = Q,/S,, used in eqn. 2 is replaced by pcl = Q,/S,, + pB 3 ps + pB, and eqn. 2 will be modified to read:
P
1
R = 7 & ~l+p”
PS
AiW2
=
Seff
1
(2’)
l+p”
PS
The modifying factor l/[ 1 + (pB /Pi)], in comparison with eqn. 2, is as mentioned above usually very close to unity for a well baked system, where
a The full treatment of the case with a non-negligible system background becomes quite complex and is beyond the scope of this paper. The complexity arises because _ns and pS in the general case cannot simply be added to each other, since the sample gas may release new background gases and since the effective pumping speeds will be dependent on both absolute pressure and time, due to wall pumping and degassing effects. It should be noted that these effects in no way affect the measurements based on eqn. 1 of the gas composition. They only affect the measurements of R, which were made only to compare the experimental results with the theoretical analysis.
13
pS B pB for most gases of interest. However, in some special cases or with a
system with a poor vacuum, 2 low6 Torr, we may have a system background (partial) pressure comparable to, or even larger than, the corresponding sample (partial) pressure. This does not in any way change the advantage of the directed-gas inlet system, but for individual partial pressures, pB may now be $pS which can make the signal to noise ratio significantly worse than when pB 4 pS. Also, the simple straight line R/S,, vs. M’/* would not be obtained in this case, since [l + (pB/ps)] in general has different values for different gases. It should be noted that pB above is not exactly the same as the system background partial pressures measured in the absence of sample gas, for the reasons mentioned in the Introduction. From a practical point of view this is a subtle point of minor interest, but it makes the division ofp,, into the pS and pe contributions artificial and somewhat questionable. In the practical measurement situation the only point of concern is that the sum pS + pB = pC, can be eliminated by chopping plus lock-in detection. 4.2. Sample gas collimation and ion source geometry The obtained sample gas signal, AIdir, is proportional to (~c#&)-’ QsM”* (see eqns. 1 and A5). Here (@&)-’ is the cross-section of the effective detection volume in the ion source. The degree of collimation of the sample gas obtained with the gas inlet tube, and thus the fraction of the total flow, Q,, which passes through the ion source, is vital for the signal magnitude Aldir and for the signal to background ratio, R. Dayton [7a] has shown that the degree of collimation is governed by a geometrical transmission function, T(8), for the inlet tube. T(0) is determined by the length L of the inlet tube and its radius Y. It is easily shown, using Dayton’s formulae, that the collimation increases substantially with increasing L/r for small ratios, but that very little change in collimation is achieved once L/r > 10. Figure 4 shows the amount of gas flow exiting within a polar angle, 8, normalized to the total gas flow, as a function of 8 for different L/r values. L/r M 10 gives sufficient collimation for all practical purposes. (For more details see Appendix A and ref. 7.) Once the L/r ratio is fixed it is possible to optimize the performance by positioning the tube exit closer to the ion source and thus allowing for a larger fraction of the total flow to pass through the ion source. However, one must then be careful not to distort the electric field in the ion source, since the electric field influences the production and collection of ions. Also the chopper/shutter must not perturb the electric fields since this will produce errors in signal detection and in the background subtraction. This must be tested individually for each MS unless the manufacturer can give advice on proper distances. An additional possible way of optimizing the performance involves a
9 (Degrees) Fig. 4. The integrated gas flux within polar angle 0 exiting from a tube of length, L, and inner radius, r, as a function off?, under molecular flow conditions (calculated using ref. 7a).
modification of the ion source. Since the directed sample gas signal, AZdir,is inversely proportional to the cross-section of the effective detection volume in the ion-source, it may be possible to increase this signal difference by diminishing the ionizing volume. An estimation for AZ,i, (based on Fig. 5 and eqn. A8) gives for small angles 8 and fixed L/r an increase of about 100% if the cross-sectional entrance area of the ionization volume is decreased by a factor of two without changing the ionization probability inside the ionization volume. We show elsewhere [8] how the volume of the ionizing volume can be varied by different settings of the ion source potentials. An appropriate final remark in this section is that we have found that small, cross-beam ion sources of several MSs always give satisfactory performance with R values 2 1. Ion sources with large ionization volumes are expected to give smaller R values. With differentially pumped gas inlet systems possible problems with mass separation, i.e. separation of molecules with different masses, have to be addressed. In the present case this is not a problem, however, since no differential pumping is employed. As long as the gas flow at the gas sampling point is viscous the gas composition will be conserved until it exits the MS. This was verified experimentally by measuring the MS signals for Ar and He for different original Ar/He ratios in the range z 0.1-10. The gas mixtures were made using a capacitance manometer. Figure 5 shows the measured MS signal ratio AZ,,/AZ,, as a function of the mixing ratio pAr/pHe. The linear relationship with a slope of one demonstrates that no mass separation occurs.
15
-I WI
0,l
1
10
100
Y4r’!He Fig. 5. A plot of the AZAro,= 36,/AZn,(M= 4, ratio vs. the P,/PHe ratio, measured for a number of different Ar/He gas mixtures using the gas inlet device shown in Fig. 1. PAr/PHeis the partial pressure ratio in the previous gas sample, whose total pressure was 700 Torr. The straight line with a unity slope shows that no mass separation occurs.
4.3. Measuring pumping speeds with the directed-gas inlet
Inspection of eqn. 2 (or 2’) reveals, as a side effect of the present gas inlet method, a very simple and elegant way of measuring pumping speeds. Initially this requires calibration of the gas inlet system + MS combination using a vacuum system with known pumping speeds for the gases of interest. This calibration is made once to obtain the instrumental constant A of eqn. 2 (from a plot like the one in Fig. 3).characterizing the gas inlet + MS combination. The calibration can then be used on any vacuum system to measure its pumping speeds for various gases. The pumping speeds are simply obtained by measuring the R values for the gases of interest and then using eqn. 2 (or 2’) to obtain the corresponding pumping speeds (depending on the prevailing vacuum conditions). The result will be more accurate if the system background pressure is sufficiently low such that eqn. 2 rather than eqn. 2’ can be used. 4.4. Some practical aspects The gas inlet system described here makes possible reliable, quantitative gas analysis even in the presence of interfering background gases, as examplified in Section 3.2 and Fig. 3 (see also [9]). Since no differential pumping is required the gas consumption is low (< 10e4 Torr 1SC’). If high accuracy is not required or if simple gases are analyzed one may use the present inlet system without a chopper or shutter and still have an advantage over conventional gas inlet methods. In this case a low system background pressure and
16
a high pumping speed give better results as can be seen by rewriting eqn. 1 as
The quantity of interest is ICAPdir = /3Q,and a correct gas analysis is obtained if this term dominates over ‘ypcl. A requirement to obtain correct results, which all the time has been implicitly assumed, is that the composition of the gas emerging at the vacuum end of the gas sampling system is the same as that sampled at the sampling position. This is a different type of problem than the one treated here but is of course not trivial. For example, with water vapour and other polar gases or with very reactive gases, molecules may adsorb, desorb, or react on the walls of the gas sampling device. Means of reducing or eliminating these effects are: proper choice of materials in the inlet system, and/or heating all surfaces in contact with the sample gas to an appropriate temperature to reduce “memory” effects. An example of the use of the present gas inlet system to study surface reactions, e.g., heterogeneous catalysis, in a small flow reactor will be published shortly [9]. 5. SUMMARY
The theoretical and experimental analysis above shows that the simple, directed-gas inlet system described here offers the following advantages over conventional non-directed gas inlets: (i) The measured signal contains no contribution from sample gas interaction with the walls of the vacuum system. (ii) It contains no contribution from the existing background gases in the vacuum system (except in the signal noise). (iii) It is independent of temporal variations in the pumping speed of the vacuum system and its walls. (iv) The sample gas consumption is only z 10e4 cm3 SK’ at 1 atm sample gas pressure. (v) The method can be used to measure pumping speeds. ACKNOWLEDGEMENT
We are grateful for many valuable discussions with I. Zoric and E. Tiirnqvist. Financial support from the Swedish National Board for Technical Development (Contracts 835405 and 6043 14) is gratefully acknowledged. REFERENCES 1 A. Hijghmd and L.G. Rosengren, Int. J. Mass Spectrom. Ion Processes, 60 (1984) 173. 2 E.L. Knuth, Direct-sampling studies of combustion processes, in G.S. Springer and D.J. Patterson (Eds.), Engine Emissions, Plenum Press, New York, 1973, p. 319.
17 3 S.N. Foner, Mass spectrometry of free radicals, in D.R. Bates and I. Easterman (Eds.), Advances in Atomic and Molecular Physics, Vol. 2, Academic Press, New York, 1966. 4 G. Stoles (Ed.), Atomic and Molecular Beam Methods, Vol. 1, Oxford University Press, New York, 1988. 5 B. Kasemo and K.-E. Keck, Swedish Patent 8404840-4, 1986. 6 B. Kasemo, Rev. Sci. Instrum., 50 (1979) 1602. 7 (a) B. Dayton, Trans. 2nd American Vacuum Society Vacuum Symposium, Pergamon Press, New York, 1961, p. 5. (b) S. Adamson and J.F. McGlip, Vacuum, 36 (1986) 227.. (c) P. Clausing, Z. Phys., 66 (1930) 471. 8 J. Hall, I. Zoric, M. Rinnemo and B. Kasemo, Rev. Sci. Instrum., in press. 9 S. Lundgren, K.-E. Keck and B. Kasemo, Time and space resolved gas analysis of gradients and transients in catalytic reactions, to be published.
APPENDIX
A: CALCULATIONS
OF A, B AND R
The theoretical treatment is essentially the same as for a molecular beam, but with the additional ingredient that we have to take the divergence of the gas flow at the exit of the gas sampling device in the MS chamber into account. The quantities we want to calculate are the relative magnitudes of the MS signals, l& and 1:,, corresponding to the partial pressure, or rather density, of a gas, i, with the shutter open and closed respectively. The difference, Al~ir, (see eqn. 1) between these two signals is the desired quantity. It contains only the contribution from gas molecules in the inlet gas which have not been in contact with the chamber walls. In the theoretical treatment, the MS signals are treated as d.c. signals when the shutter is open and closed. Extension of the theory to lock-in detection of chopped signals is straightforward. For conditions of molecular flow, Dayton [7a] has calculated the transmission of gas through a tube which connects two gas reservoirs. The angular distribution exiting from the tube at the lower pressure reservoir is given by F(8, L/r) do = T(8, L/r) cos 8 do
(Al) where T(8, L/r) is a transmission function which is determined by the ratio between the length, L, and the radius, r, of the tube and 8 is the angle about the tube axis. dco is an infinitesimal space angle about 8. For a hole in an infinitely thin wall, T(0, L/r = 0) = 1 and we get the well known cosine distribution. For a tube of finite length, T(8, L/r) will cause the angular distribution to peak in the forward direction. With do = sin 8 de d$, we may calculate the fraction of the flow which exits from the tube within a cone with half-angle 8 about the tube axis. This fraction increases rapidly with increasing L/r for small ratios, but saturates as L/r 2 10. In Fig. 4 a plot is shown of the integral (from zero to 0) of F(8, L/ r ) vs. 8, for different ratios of L/r. We will treat the tube exit as a point source and show that it is then possible to make a theoretical estimation which is in good agreement with the experi-
18
mentally obtained results b. The fraction H Q, of the total flow, Q,, that exits from the tube within the polar angle 8 about the tube axis is
HQs = Qs
1: F(O’, L/r) sin 8’ de’ j”y F(8’, L/r) sin 8’ de’
642)
In order to apply this equation we treat the effective ionization volume, A V,s, of the ion source as a cylindrical volume with diameter &s and with its axial parallel to the tube axis (Fig. 1). (We have shown [8] that the effective region is not actually cylindrical. However, knowledge of the exact shape of the effective ionization region is not necessary for the treatment below.) If z is the distance between the termination of the gas inlet tubing and the ionization volume (see Fig. l), we obtain an expression for the acceptance angle, c#+, of the ion source: 41s 22
8,s = arctan
(A3) ( ) Using 8,s as the integration limit in eqn. A2 we obtain the fraction HQ, that passes through the ion source. To proceed we now need to derive expressions for the MS signals with the shutter open and closed. The molecules within the tube will have a maxwellian velocity distribution corresponding to the tube temperature. However, the velocity distribution for molecules leaving the tube will be different from this distribution because the flow through the tube exit involves an extra factor, namely the velocity component along the tube axis. Thus the mean velocity for molecules leaving the tube is given by V = (~~T/EYz)‘/~, where T is the temperature of the tube and m is the molecular mass. Since the density of molecules within the ion source depends on their velocity, we may write the local density in the ionization volume, when the shutter is open, as consisting of two parts: n& =
&r
+
4
(A4)
where nai, = 4(4kT)-“2(7&)-’ (wz’)“~HQ~ is the local density in the ionization volume due to the molecules which pass directly from the tube through the ion source without interacting with the MS chamber walls. The term & is the isotropic density in the MS chamber, and it is related to the isotropic b It should be noted that the angular distribution function calculated by Dayton describes the total flow of molecules emerging from the exit of the tube in a given direction, 0, about the tube axis. It is thus possible to determine the fraction of the total flow emerging from the tube exit in the direction 0. It is, however, not possible to use Dayton’s expression when calculating the fraction of the total flow which passes through an area positioned in front of the tube exit. This is only possible when the radius of the tube exit is so small that it can be regarded as a point source.
19
pressure in the chamber by FZ;,= (kT)-‘p;,
(A3
where T is the temperature of the vacuum chamber. We assume that the temperatures of the inlet tube and the vacuum chamber are equal. The isotropic density, n,, , will be the same with the shutter closed and open. The mass spectrometer signal is proportional to the integral over the product of local density and position dependent detection efficiency in the ion source. In the case of a spatially non-varying density, the MS signal is given by Cl = e jAv,,K’,,(v)nh,dr= e(kT)-‘A&:,&p:,
(A6)
where A V,, is the effective volume of the ion source and pi, is the average MS detection efficiency factor for gas i. In the case of directed flow through the ion source, the local density variation becomes important. We have used Dayton’s formulae [7a], calculated the density variation and found that it is small for small angles 8. With this in mind we write the MS signal for directed flow as
= 4e(4kT)-“*AV,,(~~:,)-’
(m’)“*HQb~~ir
647) where heir is the average MS detection efficiency for the directed inlet. The last equality was obtained from eqn. lb. The detailed expression for Al~ir obtained above is not important for application purposes, since pi is calibrated for various gases i. However, it is useful in the following, where we estimate theoretically the relative order of magnitude of the signal due to the directed flow and the signal due to the isotropic background pressure. The ratio between the two signals AI~i, and Ii, is given by
The two average detection efficiency factors, &jr and pi,, are in general somewhat different since F& is the average detection efficiency factor for molecules moving essentially along the symmetry axis of the ionization volume and pi, is that for molecules with isotropically distributed velocity. However, the difference is expected to be rather small at thermal velocities. We put Eli, = PA,and rewrite R’ as
where u is the molecular weight unit and M’ is the molecular mass number.
20
We define the effective pumping speed according to the relation s;flp;, = Q;
(AlO)
We can then finally rewrite R’ as
(Al 1) where SLflis in Is-‘. In order to obtain quantitative values of A and R we put in numerical values. In the experimental system used for the measurements described in Section 3.1. we have z = 10 mm and an effective diameter of the ion source of 41s = 3Smm, yielding 8 = 10’. The fraction, H, of the total flow, Q, which passes through the ion source is now easily obtained from eqn. A2 or Fig. 4. The ratio between the length and the radius of the inlet tube is L/r = 200 in our system. This gives H = 0.12 for 8 = 10”. If the vacuum system is held at room temperature, we obtain a value of A = 4 x lop3 for the instrumental constant A of eqns. 2 and A9, in quite good agreement with the experimentally determined value of 5 x 10-3. The assumptions that the tube exit can be treated as a point source in the use of Dayton’s formulae for the angular distribution pattern results in an overestimation of the molecular flow through the effective volume of the ion source. However, our calculation does not include sample molecules which scatter from the walls of the ion source into the effective ionization volume. The latter results in an underestimation of the density of sample gas molecules within the ion source. It seems that these two effects are either small or partially cancel each other so that quite a good value for the constant A is calculated. Thus we obtain theoretical values for R’ in the range l-3 at pumping speeds of 80 1s-’ < Sirr < 200 1s-’ in good agreement with measurements (Table 1). APPENDIX
B: EXPERIMENTAL
DETERMINATION
OF PUMPING
SPEEDS
The pumping speeds required to plot R/S,, vs. (M)“’ (Fig. 3, eqn. 2) were measured in the following way. A gas supply volume of z 1 atm pressure feeds gas via an automatic leak valve into a second volume at a much lower pressure (PI = lo-*Torr). p, is continuously recorded by a capacitance manometer and is kept constant throughout the measurements by a feedback loop from the capacitance manometer to the automatic leak valve. A tube feeds gas from the volume at pressurep, into the vacuum chamber with the MS. The gas flow into the vacuum chamber is then Q, = C(p, - p,,(t)) where p,,(t) is the isotropic pressure in the vacuum system due to the gas flow Q,, and C is the conductance of the tube feeding the gas. Since pc, @ p, , Q, stays constant at
21
Q, = Cp, during the measurements. The vacuum chamber is equipped with a pneumatically operated gate valve which can be used to rapidly close off the chamber from the turbo pump. The latter has a nominal pumping speed for N, of 270 1s- ‘. The actual pumping speed is considerably lower because of the gate valve and a 6in. tube in series between the pump and the chamber and because of the splinter shield of the turbopump. The effective pumping speed of the chamber for various gases can now be determined by combining two measurements. The first one is just a measurement of the steady state vacuum system pressure, pz,, for each gas due to the gas leak, Q,. The accuracy of this measurement requires that the system background pressure is known or, in our case, is much less than pz, . (This was checked with the MS for each gas of interest.) The second measurement consists of closing the gate valve and following P,,(t) over a finite time, r. The two measurements are represented by the following two equations: PEI=
C(P, - P3
s
CP,
=r;
eff
dp,, =
C(P,
dt
PI BP:,
(Bl)
CP, V
032)
eff
-PC'(o) V
Z-
Combining these equations we obtain: s
=
eff
V(Pl - PZJ,, P3
with p,,(t) S
4 p,
V dpc,
z_----_--_
effPZI dt
PI - Pcq PI - Pcl(4
(f33)
, this simplifies to
v PC’(T) Pcq
7
(B4)
Several measurements were performed at different values of p and z. A variation of 5-10% was observed from run to run. Measurements were performed for the gases H,, CH,, N, and Ar with the results given in Table 2. These values produce a fairly smooth curve when plotted as a function of mass number. Pumping speeds for gases for which no pumping speed measurements were made were obtained by interpolation from such a plot to obtain the corresponding R/S,, values in Fig. 3 (filled squares).