A primary standard high vacuum calibration station for

I

A primary standard high vacuum calibration station for industrialapplications

P. D. Levine and J. R. SwedaLockheed Martin Missiles & Space, Sunnyvale, California 94088

(Received 29 September 1995; accepted 18 December 1995)

The Metrology Laboratory at Lockheed Martin Missiles & Space in Sunnyvale, CA, has developeda primary standard high vacuum calibration station. Maintaining an in-house capability forcalibrating Bayard-Alpert gauge tubes and spinning rotor gauges (SRGs) at the primary leveleliminates the need for external sources of calibration. This not only significantly reduces costs butalso provides for continuous monitoring of the reference standards used to support researchprograms and manufacturing processes. A constant volume, pressure drop flowmeter is used togenerate known pressures in a vacuum chamber partitioned by an orifice of calculable conductance.Data are presented which show vacuum chamber pressure to be directly proportional to flowmeterpressure drop in the three decades of vacuum spanned by the SRGs (10-3-10 -6 Torr). Using a SRGcalibrated at the National Institute of Standards and Technology, the proportionality constant isdetermined and shown to agree well with the constant calculated from system fixed parameters andmeasured pressure ratios. A new design of flowmeter is discussed. An estimate of when the systemwill be fully utilized as a primary reference will be made. © 1996 American Vacuum Society.

I. INTRODUCTION

The Lockheed Martin Missiles & Space Metrology Labo-ratory maintains a broad base of primary calibration stan-dards in support of manufacturing and testing throughout thecorporation. Commercial services are also offered. Vacuumgauge calibration comprises a substantial portion of theworkload. As such, a program was undertaken to develop astandalone capability for the calibration of high vacuumgauges in order to improve accuracy and reliability and tolower costs. I The development phase of the program verifiedthe system function and established operating parameters andprocedures. The current work was focused on creating a trueprimary calibration capability and estimating the magnitudeof uncertainty inherent to the system.

II. SYSTEM OVERVIEW

An ultrahigh vacuum calibration chamber is constructedfrom two 12-in.-diam cylinders of 304 stainless steel, 15 in.long connected by a 14 in. Conflat-type flange. This flange ismachined to accept a specially designed orifice plate. Thesection of the chamber above the flange provides measure-ment ports for 10 gauges and access to the orifice plate,which is demountable. A pumping bypass connects the upperto the lower section through gate valves to allow for rapidpumpdown of the entire chamber. The lower chamber hasfour ports for the mounting of gauges. The entire chamber isevacuated using a twin opposed rotor, turbomolecular pumpof 510 /Is pumping speed. Figure 1 shows details of thevacuum chamber.

The orifice is machined into a 3.75-in.-diam stainless steelplate 0.5 in. thick. The orifice geometry is based on a Na-tional Institute of Standards and Technology (NIST) design.'Given molecular flow conditions and constant pumpingspeed, the conductance of the orifice can be calculated basedon its measured dimensions, by applying the work of

Clausing? A pressure drop will develop across the orifice forgas flowing through it from the upper to the lower chamber.The value of the drop depends only upon the flow rate andthe calculated conductance:

Pa- Pb= QIC,

where P a = pressure above orifice (upper chamber),Pb=pressure below orifice (lower chamber), Q=flow rate,and C=conductance.

As such, the overall molecular distribution for a particulargas flowing through the chamber is strictly defined by theorifice conductance. Thus, if steady flow conditions areachieved, the ratio of upper to lower chamber pressuresshould remain constant regardless of flow rate or absolutepressure, provided the conditions for molecular flow are metand that the pumping speed remains constant. Therefore, thepressure in the upper chamber can be calculated directlyfrom the flow rate once the pressure ratio has been deter-mined:

Pa= QRIC(R-l),

where R=P)Pb.

A precision gas flowmeter supplies ultrahigh purity(99.9997%) nitrogen gas to the upper chamber through anadjustable leak valve. The pressure drop in the supply vol-ume is monitored as a function of time. The flow rate is theproduct of gas supply volume and the rate of pressure drop.The flow rate can also be expressed as the product of leakvalve conductance and instantaneous supply volume pres-sure, such that

Q=VdPldt=-CLP (P~Pa),

where V=supply volume, P=supply volume pressure, andCL = leak valve conductance.Therefore supply volume pressure can be represented as

P = Po exp( - CL 1V) t,

1297 J. Vac. Sci. Technol. A 14(3),May/Jun 1996 0734-2101196/14(3)/1297/6/$10.00 ©1996American Vacuum Society 1297

(1)

(2)

(3)

(4)

1298 P. D. Levine and J. R. Sweda: Industrial primary vacuum standard 1298

FIG. 1. Ultrahigh vacuum calibration chamber.

where Po=supply volume initial pressure and t=elapsedtime.

Expanding the exponential in a Taylor series to the qua-dratic term:

If PI Po:%0.9875 during the time t, which corresponds to a1.25% drop in supply pressure, the quadratic term is 0.63%of the linear term, higher terms in the exponential can there-fore be neglected. Upper chamber pressure is directly pro-portional to flow rate [Eq. (2)], thus the average rate of sup-ply pressure drop is directly proportional to the mean of theupper chamber pressure during the measurement interval tothe extent that the supply pressure drop is linear in time(0.63%). The proportionality constant is dependent upon sys-tem fixed parameters only and does not change as a functionof flow rate. Thus, the relationship between flow rate andupper chamber pressure is established empirically. The con-stant is also calculated from orifice conductance, flowmetervolume, and the ratio of upper to lower chamber pressures.Figure 2 is a schematic representation of the relationshipbetween the flowmeter and vacuum chamber.

III. INSTRUMENTATION AND DATA ACQUISITION

Pressure in the flowmeter volume is measured using ca-pacitance diaphragm gauges (CDGs). CDG heads of 100 or1000 Torr full scale absolute are used depending upon theflow rate. Supply pressures and valve openings which main-tain low leak valve conductance were determined during thedevelopment phase. Upper chamber pressures are measuredusing spinning rotor gauges (SRGs). Initial measurements

J. Vac. Sci. Technol. A, Vol. 14, No.3, May/Jun 1996

VARIABLE LEAKC,

UPPER CHAMBER

P,

R=P/P,FLOWMETER

P,=QRlC(R.I) Q=VdP/dl=-CL P

vORIFICEC

1p=p oexp( -CLN)t

LOWER CHAMBER

P,

FIG. 2. System schematic.

(5)

were made using a NIST calibrated SRG in an effort to es-tablish the proportionality constant empirically.

Data acquisition software is designed to monitor twoSRGs and three CDG heads sequentially over the IEEE-488bus of an HP 9000 series instrument controller. SRG integra-tion time is adjusted according to the level of pressure beingmeasured. Pressures to 5X 10- 5 Torr require integrationtimes of 30 s and use an interval of 2000 s. Pressures above5X 10-5 and below 5X 10-4 Torr utilize integration times of15 s with an interval of 1000 s; above 5XlO-4 integrationtimes of 8 s are used with measurement intervals of 500 s.The parameter values above were determined to ensure thatthe supply pressure drop does not exceed 1.25% during themeasurement interval and that a statistically significantamount of data is acquired.

IV. CALIBRATION OF SRGs

The SRG consists of a magnetically suspended steel ballof roughly 4.5 mm diameter which is spun up and allowed tocoast, the rotational frequency is maintained to within 405-415 Hz. Gas molecules impact the rotor causing it to decel-erate. In addition to gas drag, the interaction of suspensionand monitoring fields also decelerate the rotor; this is knownas the residual drag. By monitoring the deceleration rate rela-tive to the rotational frequency the pressure is calculatedfrom the following formula:

P= (Xpl u){[ (dwldt)1 wJ - RD}, (6)

where w is the rotational frequency of the rotor, [dwldt)lw]is the relative deceleration, RD is the residual drag, Xp is aconstant determined from the density and diameter of therotor, and a is the coupling constant between the gas and


5.25e-05

c, 5.20e-05c,0.:.:w 5.15e-05a:::JUJUJ 5.10e-05wa:0..a: 5.05e-05wm::E<!IU 5.00e-05

4.95e-05'0 1000+-----------------~----------------~------~78.8

2000

£0.0

r,79.8 c,o.j.J~

ELAPSED TIME (secs)

o SRG 4!J. SRG 3

FLOWMETER COG.--------.-4. 320027e-04*X +80.03751

FIG, 3, Typical graph of data,

rotor.' Once RD is determined and the mass and diameter ofthe rotor are measured SRG calibration is simply the deter-mination of if.

The residual drag constitutes an offset in the pressuremeasurement. It is dependent upon spin frequency. In orderto correct for the offset, each gauge is monitored at thechamber base pressure for several days and a fit of residualdrag versus frequency is made. During the course of actualpressure measurements the spin frequency is recorded andwhen measurements are completed the offset is automati-cally subtracted based on the curve fit of residual drag versusfrequency.

Four SRGs were utilized in this work, one of which wascalibrated at NIST. The NIST gauge was used to establish therelationship between flowmeter pressure drop and upperchamber pressure. Measurements were made at upper cham-ber pressures from 1X 10-6 to 1X 10-3 Torr. Flowmeter andindicated upper chamber pressure were graphed versus time(see Fig. 3), A straight line fit was made to the flowmeterCDG data to yield a value of ap/ at. Mean upper chamberpressure during the measurement interval' was determinedfrom the SRG data. At least five points per decade wereobtained in this way. Mean upper chamber pressure withinthe measurement interval (at) was graphed versus aP / at(Fig, 4) for each point in the three decades of pressure mea-sured to obtain the overall system proportionality constantKcaJ' where

P cal= KcaiaP/ at.

Once a value of K cal was established, a measurement se-quence was initiated wherein all four gauges were measuredtwo at a time. The diameter and mass of each of the three

JVST A - Vacuum, Surfaces, and Films

unknown rotors were determined and if set to one. A previ-ously measured gauge was used to set upper chamber pres-sures by incorporating an average offset value. The pressuresindicated by the SRGs were graphed versus ap/ at in eachof the calibration sequences and a value of Kunk obtained asfor the calibrated gauge. The only variable to be determinedin SRG calibration is if. Therefore, the ratio Kunk/KcaJ can betaken as if of the unknown provided that aP /a t truly definesupper chamber pressure.

v. DATA AND ANALYSIS

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The four SRGs were denoted as SRG1, SRG2, SRG3,

SRG4, with the last one holding a recent NIST calibration.Data were first obtained for SRG4 and SRG3 vs ap/at. Thevalues of Kunkl and Kunk2 as determined for these two gaugesare shown in Fig. 4. Using the value of Kunkl for SRG4 asKcal (0.1203), a value of Kunk was obtained for SRG1 andSRG2 by monitoring them simultaneously vs ap/at. In thisway a if value was assigned to each of the three unknowngauges. This constituted a "calibration" of 'the unknowngauges based on the system constant Kcal as determined bythe NIST calibrated rotor.

The heart of the calibration system is the flowmeter. Fig-ure 2 is a schematic representation of the system showing therelationship of flowmeter pressure drop to upper chamberpressure. Pressures become completely defined providedrates of pressure drop can be accurately determined, Thus,evaluating the reproducibility of the system constant usingthe gauges as calibrated above is a measure of flowmeteraccuracy as all other system parameters are fixed. As such,all four gauges were compared to each other in combinations


1.00E-03

MEAN CHAMBER PRESSUREvs AP/At

I!

~

IA

o SRG 4 (Kunk1=O.1203)

'" SRG 3 (Kunk2=O.1164)III

'"

0

'"

lw0:: .ijl1.00E-04IIIwIf0::WIII:E<t::z::oz~ 1.00E-05

1.00E-061.00E-05 1.00E-04

PRESSURE DROPITIME (torr/sec)1.00E-021.00E-03

FIG. 4. Determination of system constant.

other than those used in establishing the initial calibration.Table I summarizes the data obtained for all gauges.

Rows 1 and 2 show the a values established for SRG!,SRGz, and SRG3 based on the initial value of KcaJ (Kunk! forSRG4) determined in run 1. Rows 3-6 show values of thesystem constant Kcal based on SRG vs ap/ at measurementsand the a values displayed in rows 1 and 2.

The mean of all values for the system constant obtainedusing calibrated rotors is 0.120 25 with a standard deviationof 0.73%. The overall variation as listed in rows 3-6, isabout 2.25% compared to this value. The largest variationseen in an individual gauge is 1.5% for SRG4. The smallestvariation is 0.5% for SRGz. There are two manufacturers ofSRGs, two from each were used in this work. One specifies± 1% for the accuracy and the other ± 1.5%. The reproduc-ibility is excellent and well within what can be expected ofthe gauges. In essence, flowmeter measurements were usedto transfer the calibration from the NIST rotor to the other

TABLEI. Data for determining system constant.

Run No. Gauge 1 Gauge 2 Kunk! Kunk2 u! U2

SRG4 SRG3 0.1203a 0.1164 0.980a 0.9672 SRG2 SRG! 0.1154 0.1165 0.960 0.9693 SRG! SRG3 0.1201 0.1202 0.969 0.9674 SRG4 SRG2 0.1210 0.120 0.980a' 0.9605 SRG2 SRG3 0.1206 0.ll97 0.960 0.9676 SRG4 SRG! 0.1185 0.1209 0.980a 0.969

"Value based on NIST calibration.


three. Thus it appears that ap/ at measurements are suffi-cient for determining calibration chamber pressures in thecurrent system configuration.

All that remains is to establish the system constant abso-lutely by virtue of orifice conductance calculations and flow-meter volume measurements.

VI. CALCULATION OF SYSTEM CONSTANT

The volume of the flowmeter was determined using astainless cylinder with a volume of 0.969 /. The cylinderwas calibrated to 0.5% traceable to NIST. It was connectedthrough a shut-off valve to the flowmeter output. The entiresystem was evacuated and the calibrated volume valved off.The flowmeter volume was then backfilled with ultrapurenitrogen to a pressure of approximately 1 Torr and thechange in pressure recorded. The shut-off valve was openedand the pressure allowed to equalize. The final pressure wasnoted such that the change in pressure due to the added vol-ume could be determined. The ratio of the two pressure dif-ferences and the value of the calibrated volume were thanused to calculate flowmeter volume. This process was re-peated in steps to 1200 Torr. The process was then reversedby pumping the flowmeter volume incrementally and thenallowing equalization to take place. These measurementsyielded a flowmeter volume of 1.2516 / with a standarddeviation of 0.26%.

Using Eqs. (2) and (3), it can be seen that

KcaJ= VR/(R-l)C, (8)


FIG. 5. Detail of calibration orifice.

where Q=V!:::.PI!:::.t, C=conductance, and V=flowmetervolume.

The orifice conductance for nitrogen is calculated throughthe use of Clausing factors and the aperture radius and can bewritten as

where W=Clausing factor for the orifice used (0.9971),K 1= 1, K2=correction factor for 70° conical surface belowthe spherical surface (0.9992), c = mean molecular velocityfor nitrogen at 294.3 K, and rl = radius of orifice entranceaperture (0.2133 in.),

This yields an orifice conductance (C) of 10.86 /'/s. Thepressure ratio (R) across the orifice has previously been de-termined to be 20.2 (see Ref. 1). Given these values Kcal iscalculated to be 0.12125. The value obtained empirically is0.1203. The difference between the calculated and measuredvalues of the system constant is 0.8% with respect to thecalculated value. Thus, it appears that the flowmeter mea-surements are accurate. Given the proper conditions, it ispossible to generate known pressures in a vacuum chamberwhich are directly proportional to the rate of pressure drop ina fixed volume. Figure 5 shows the details of the LMMSorifice.

VII. ESTIMATING SYSTEM UNCERTAINTY

There are several sources of uncertainty in the PrimaryVacuum Calibration Station. Uncertainties are evaluated ac-cording to the guidelines adopted by NISr and are classifiedinto two categories: type "A" and type "B." Type A uncer-tainties are those which are evaluated by statistical methodsand type B are those evaluated by other means. The rate ofpressure drop in the flowmeter is basically exponential asdescribed above. Parameters are chosen in such a way as toensure that the linear term in the exponential dominates. Theonly type A uncertainty arises from the extent to which therate of pressure drop is not linear-from Sec. II this can beseen to be 0.63%. The other components of uncertainty de-rive from the parameters used to calculate the pressure: theorifice conductance calculation (dimensional), flowmetervolume and pressure drop, the measured pressure ratio, andgas temperature. These components are all considered type Bas details of their distributions are not known.

The orifice conductance is thought to have no greater thana 0.2% uncertainty related to dimensional measurements; thecylinder used to calibrate the flowmeter volume has an un-

JVST A - Vacuum, Surfaces, and Films

TABLEII. System uncertainties.

Source Type Combined as Magnitude

Flowmeter !1PIt:J.t A A 0.63%Orifice BI B/J3 0.12%

condnctanceFlowmeter B2 BiJ3 0.29%

volumePressure ratio B3 B3/J3 0.09%Temperature B4 B41J3 0.14%Total U JA2+ '2. (B/J3j2 0.72%

UT=kU (k=2) 1.44%

certainty of 0.5%. The pressure ratio uncertainty is 0.15%, asmeasured. Ambient temperature within the laboratory wasobserved to vary by no more than ±0.75 °C or 0.25%throughout the course of the measurement program. The ef-fect is manifested directly as a variation in flowmeter supplyvolume gas pressure. This is the worst case as ambient tem-perature drift monitored during the longest measurement in-tervals (2000 s) was typically less than ±50 mK. Table IIlists the source, type, and magnitude of the uncertainty com-ponents and combines the type A and total B in quadrature.The type B uncertainties are normalized to a rectangular dis-tribution as only the limits of the distribution are known.

A coverage factor of k=24 is used to define the overalluncertainty in the generated pressure as 1.44%. The largestcontributor is the departure from linearity of the flow rate asa function of time. The standard deviation of the systemconstant as measured and the difference between the calcu-lated and measured system constant fall well within the es-timated overall uncertainty.

VIII. CONCLUSIONS AND FUTURE PLANS

A facility for the primary calibration of vacuum gauges inthe range from 10-3 to 10-6 Torr has been created and veri-fied. Known pressures are generated in a vacuum chamberwhich are directly proportional to the measured pressuredrop in a fixed volume flowmeter. The proportionality con-stant determined empirically using a gauge calibrated byNIST is in excellent agreement with that determined by vir-tue of dimensional, volumetric, differential pressure, andpressure ratio measurements only. The overall estimated un-certainty is ± 1.44% due mainly to departures from linearityin the determination of flow rate. This work has establishedthe calibration of three SRGs both absolutely and by com-parison to a NlST calibrated gauge. As such, these gaugescan now be used as reference standards from 10-3 to 10-6

Torr.A new flowmeter has been designed and is currently un-

der construction. It will experience smaller pressure dropsfor the same flowrates and provide higher resolution of !:::. PI!:::.t.This should reduce the contribution from nonlinear termsin the flow rate, thus reducing the uncertainty in the gener-ated pressure. The next generation flowmeter should also al-

1302 P. D. Levine and J. R. Sweda: Industrial primary vacuum standard1302

low for the extension of calibration to the 10-7 and 10-8Torr

range using Bayard-Alpert type ion gauge tubes. Integrationand verification should be completed within the next yearmaking the Lockheed Martin Missiles & Space PrimaryVacuum Calibration Station fully operational from 10-

3to

10-8 Torr.

Ip. Clausing, Ann. Phys. 12,961 (1932); English translation appears in J.Vac. Sci. Techno!. 8, 636 (1971).2S. Dittmann, "High Vacuum Standard and its Use," NIST Special Publi-

cation 250-34, March 19893R. P. Iczkowski, J. L. Margrave, and S. M. Robinson, J. Phys. Chern. 67,

229 (1963).4B. N. Taylor and C. E. Kuyatt, NIST Technical Note 1297, January 1993.


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A primary standard high vacuum calibration station for