On the stability of capacitance-diaphragm gauges with ceramic membranes
K. Joustena兲Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany

Simon Naefb兲
INFICON AG, Alte Landstrasse 6, 9496 Balzers, Liechtenstein

共Received 2 July 2010; accepted 29 November 2010; published 4 January 2011兲
Capacitance-diaphragm gauges with ceramic membranes or diaphragms have been on the market for
about 15 years. The long-term stability of these devices with full scales from 13 Pa to 133 kPa
has been tested in the past decade by the calibration of gauges used by the manufacturer as reference
gauges on the production line. These reference gauges were calibrated annually on a primary
standard. It was found that the reproducibility of these devices depends on their full scale. For
13 Pa, the annual reproducibility near full scale varied between 0.02% and 0.05%, and for full scalesof 133 Pa and higher, it varied between 0.005% and 0.03% of full scale. The reproducibility of theceramic capacitance-diaphragm gauges for full scales of 133 Pa and 1.3 kPa was significantly lower
than the uncertainty of a primary standard applying the static-expansion method. © 2011 American
Vacuum Society. 关DOI: 10.1116/1.3529023兴

I. INTRODUCTION
In the past 15 years, capacitance-diaphragm gauges
共CDGs兲 with ceramic membranes, also called diaphragms,
have become popular for pressure measurements in manydifferent applications such as etching, chemical-vapor deposition, physical-vapor deposition, thin-film deposition, andfor use as transfer standards. INFICON, a well-known manufacturer of such gauges, started a cooperation with the
Physikalisch-Technische Bundesanstalt 共PTB兲 in 2000 in order to qualify their CDGs as reference standards and to ensure the measurement specifications of the production line.
CDGs with full scales 共FSs兲 from 13.3 Pa up to 133 kPa
were calibrated annually at PTB. Since typically four CDGs
were calibrated at the same time, changes common to allgauges gave PTB the chance to check the reproducibility of
their primary standard as well.

II. CAPACITANCE-DIAPHRAGM GAUGES WITH
CERAMIC MEMBRANES
Capacitance-diaphragm gauges have been established as
the most precise commercial vacuum-measurement device
suitable for process applications. The measurement principle
is based on the deflection of a diaphragm under a differential
pressure across it.
Instead of having an all-metal-based sensor design, INFICON’s ceramic-diaphragm gauge technology is based on sintered alumina 共Al2O3兲. The diaphragm and entire housing are
made of ⬎99.5% pure Al2O3.
The diaphragm is bonded with the housing using a glass
solder. The upper housing, the getter dome, and the diaphragm form a reference cavity, which is kept in a low
vacuum range by a nonevaporable getter. The lower housinga兲Electronic mail: karl.jousten@ptb.de
Electronic mail: simon.naef@inficon.comb兲011011-1

J. Vac. Sci. Technol. A 29„1…, Jan/Feb 2011

with the diaphragm forms the measurement cavity. The electrodes are located on the reference vacuum side and form thecapacitor 共see Fig. 1兲.
A capacitance-diaphragm gauge measures the pressure
difference between the reference cavity and the measurement
cavity. The membrane bends if pressure is applied; the deflection is directly related to the applied pressure. The two
extreme cases are shown in Fig. 2. Figure 2共a兲 shows thefull-scale pressure deflection of the membrane, and Fig. 2共b兲shows the “zero” deflection of the membrane.
Beyond the full-scale pressure, the membrane is supported by the upper housing of the sensor cell that results ingood overpressure resistance.
The deflection within the zero pressure and the full-scalepressure is described as fixed circular plates under a uniform
load. The deflection is proportional to the pressure p as longas the deflection is significantly less than the membranethickness. The diaphragm deflection ␻ in the center of thediaphragm can be calculated by the following equation:1

␻共p兲 =

冋册

p · r4 · 3 · 共1 − v2兲
Pa · m4m=,
16 · E · t3
Pa · m3

共1兲

where ␯ is the Poisson ratio 共unitless兲, E is the Young modulus, t is the thickness of the diaphragm, and r is the freeradius of the diaphragm.
The typical deflection at full-scale pressure is adjusted toa few micrometers, which, in relation to a several hundred
micron-thick membrane, is only about 1%. The sensitivity topressure is varied by the diaphragm’s thickness.
In the center of the upper housing, a measurement electrode is located. The counter electrode is on the membrane.
The distance change due to pressure change is measured by
the resultant capacitance change,20734-2101/2011/29„1…/011011/7/$30.00©2011 American Vacuum Society

011011-1

011011-2 K. Jousten and S. Naef: On the stability of capacitance-diaphragm gauges
Measuring capacitance

011011-2

The tested reference gauges were of the standard 45 ° Cthermally stabilized ceramic-diaphragm gauge type 共INFICON CDG045兲 with full scales from 13.3 Pa up to 133 kPa.

Getter pump

Electrodes

Sensor cell

III. CALIBRATION

Reference vacuum

Al2O3

Diaphragm

Glass solder
NEG getter
Metallization(electrodes)

FIG. 1. 共Color online兲 Structure of INFICON ceramic-diaphragm gauge.

⌬Cmeas共␻兲 =冋册␧0 · AAs As · m2
− C0 F =,=d0 + ␻
V Vm · m

共2兲

where d0 is the distance at zero pressure, ␧0 is the dielectric
permittivity, A is the area of the housing electrode, ⌬Cmeas is
the resultant capacitance change, and C0 is the capacitance atzero deflection.
The electronics measures the capacitance change due topressure change and scales the raw signal into a linear
0–10 V signal output. The relation of the indicated pressure
pind and voltage measured at signal output voltage U and forfull scale FS is given by3
pind 共Pa兲 =U 共V兲 · FS 共Pa兲.
10.0 V

共3兲

Besides the heat controller and the internal power supply, theelectronics processes the raw capacitance reading throughfive defined stages. The first stage is the capacitance measurement, which is based on a sigma-delta capacitance/
voltage converter. The second stage consists of prescaling of
the raw signal.
A feedback loop for linearization is the third stage since
the capacitance measurements add some nonlinearity causedby the hyperbolic relationship of distance to capacitance 共seeFig. 3兲.
The fourth stage is the temperature compensation. The
temperature compensation applies to zero 共temperature effecton zero兲 and the span 共temperature effect on span兲. Finally,
the output stage changes the output impedance and contains
all protection devices against electromagnetic compatibility
and reverse polarity.

Full-scalepressure

Electrodes

Upper housing

Electrodes
d

d


(a)

Zero
pressure

=0

Lower housing(b)

FIG. 2. Schematic diaphragm bending.
J. Vac. Sci. Technol. A, Vol. 29, No. 1, Jan/Feb 2011

The CDGs were calibrated annually by standards for low
and medium vacuums at the PTB with nitrogen as the testgas. For CDGs with full scales up to 1.3 kPa, two primary
standards were used, namely, the SE2 static-expansion system and the FRS5 pressure balance 共Furness Control, Inc.兲.
In the static-expansion system, SE2 pressures are established by expanding a known gas amount from a small volume into much larger volumes. The pressure in such a system can be calculated and compared to the indication of avacuum gauge to be calibrated.4,5 SE2 covers the range from
0.1 Pa to 1.3 kPa.4,6
In the FRS5 pressure balance, the pressure is measured by
the force acting on a piston, where the lower side of thepiston is in high vacuum.7 The force is measured by a force
meter. The FRS5 can accurately measure pressures from 30
Pa up to 11 kPa,8 but in this investigation, it was used only
for calibrations up to 1.3 kPa.
Beyond 1.3 kPa, a 7010 quartz Bourdon spiral was usedas the secondary standard for calibration. The 7010 is traceable to the mercury manometer of PTB.9
The voltage output 0–10 V of the CDGs was measured bya calibrated digital voltmeter. Typically, four CDGs were
calibrated at the same time. The value in volts was converted
to the pressure unit in millibar 共1 mbar= 100 Pa兲 by a respective multiplier, which was 1.33322 times full scale intorr divided by 10. The calibration range covered 3 decades
from 0.1% to 100% of full scale, where the target points
were set to 共0.1%, 0.5%, 1%, 5%, 10%, and 20% through100%兲.
The measurand to be determined was the error of readinge defined ase=pind − pcal
,
pcal

共4兲

where pind is the pressure indicated by the CDG as describedabove and pcal is the pressure defined by the primary standard or measured by the secondary standard of PTB.
Four gauges for each full scale were shipped under atmospheric pressure conditions. Between recalibrations, two
CDGs of each full scale were stored in a cabinet under atmospheric pressure conditions as a backup, whereas theother two pieces of each full scale were used for the calibration of the production tools at INFICON.
For economical reasons, only one measurement series was
taken for each CDG. An additional uncertainty was added tocover the repeatability of the measurements. An example of acalibration curve for a CDG with a full scale of 1.3 kPa 共10
torr兲 is shown in Fig. 4.
The uncertainties related to the calibration are as follows:011011-3 K. Jousten and S. Naef: On the stability of capacitance-diaphragm gauges
Ceramic Sensor

Measuring board

011011-3

Scaling+V

Unlinearity
correction(stage 3)-V

Ceramic cell
Capacitancemeasurement(stage 1)

Pre-offset
pre-span(stage 2 )Internal
power
supllyOutputstage(stage 5)

Vcc
SupplySupply common
SupplySignal output
Signal common

Temperaturecompensation(stage 4)+V
Heat controller
Heater-V

FIG. 3. Electronics concept of heated ceramic-diaphragm gauge.

共1兲 the uncertainty of the calculated pressure in the respective primary standard or the measurement uncertainty ofthe secondary standard,
共2兲 the repeatability of the measurements, and共3兲 the measurement uncertainty of the CDG undercalibration.
The relative uncertainties u of the calculated pressures in
the primary standard SE2 ranged from 0.094% 共standard uncertainty, coverage interval is about 68%, k = 1, k being theso called coverage factor as a multiple of the standard uncertainty兲 at 0.1 Pa to 0.074% at 1.3 kPa. For the FRS5, thevalues ranged from u = 0.072% at 30 Pa to 0.0029% at 1.3
kPa. The u of the 7010 was between 0.019% at 1.4 kPa and0.014% at 130 kPa.

3.5
3.0
2.5
CDG 1.3 kPae in %

2.0
1.5
1.0
0.5
0.0
-0.5
100
1E+00

1

10
1E+01

2

10
1E+02

3

10
1E+03

4

10
1E+0

The repeatability of the measurements 共k = 1兲 with SE2
was considered to be 0.08% for pressures p ⬍ 10 Pa and0.03% for 10 Paⱕ p ⬍ 1.4 kPa and with 0.01% for the measurements with the 7010. These values were estimated fromrepeated measurements on the same day of several CDGs of
the same type. The repeatability is both due to the reference
standard and the device under calibration, but in the case ofSE2, dominated by the primary standard. Since the newly
established FRS5 had a better repeatability than the SE2, a
new investigation was conducted, which is described in thefollowing section.
During calibration, the uncertainty due to the CDG itself
was mainly caused by the drift and measurement of the offset. Typically, this amounted to a few parts of 105 of the
full-scale reading and dominated the total uncertainty in thelowest of the three calibration decades. The digitizing errorof the digital voltmeter could be neglected.
IV. REPEATABILITY
To assess the repeatability of the ceramic CDG with
1.3 kPa 共10 torr兲 full scale, three identical devices 共j= 12, 22, 23兲 were repeatedly 共16 times, l = 1 , . . . , 16兲 calibrated at the same time by the FRS5 at 30 Pa and 1.2 kPa.
Between each measurement, the pressure was pumped down
to below the resolution limit of the device. The 16 calibrations were performed one after the other within 3 h. For each
CDG j, the mean error of reading ē j and the experimental
standard deviation as estimate of the repeatability were determined,

p in Pa

FIG. 4. Calibration curve of a capacitance-diaphragm gauge with full scaleof 1.3 kPa. e is the relative error of indication. Calibration below 30 Pa was
performed by the static-expansion system at PTB above 30 Pa by use of apressure balance. At higher pressures, the uncertainty bars for the 95% confidence interval are smaller than the size of the symbols.
JVST A - Vacuum, Surfaces, and Films

sj =

冑

16

1
兺 共elj − ē j兲2 .
15 l=1

共5兲

The results are given in Table I. At 30 Pa, the mean repeatability of the three gauges is 0.027%, which is practically011011-4 K. Jousten and S. Naef: On the stability of capacitance-diaphragm gauges
TABLE I. Repeatability of 16 calibrations of three ceramic capacitancediaphragm gauges with full scale of 1.3 kPa against an FRS5 pressure balance at two different pressures p of 30 and 1200 Pa. The repeatability isdefined in Eq. 共5兲.
p
共Pa兲

Device 12
共%兲

Device 22
共%兲

Device 23
共%兲

Mean
共%兲

30
1200

0.020
0.00250.029
0.00160.032
0.0081

0.027
0.004

identical to the one with SE2. At 1200 Pa, however, it ismuch lower, at 0.004%.
The values in Table I include both the repeatability of the
FRS5 and of the CDGs. If, however, several gauges are calibrated at the same time, it is possible to distinguish between
the repeatability of the FRS5 reference standard and the
CDGs by employing a statistical model. This is currently
being investigated, and the results will be reported elsewhere.

V. LONG-TERM INSTABILITY
The long-term instability was evaluated near full scale forall types of CDGs and additionally at 5 Pa for the CDGs withfull scale at or below 133 Pa and at 7 Pa for the 1.3 kPa fullscale.
To quantify the long-term instability for the annual recalibrations, we use the following two approaches:
共1兲 the experimental standard deviation s about the all-timemean ē of a gauge and共2兲 the mean of absolute 共non-negative兲 changes between¯.
recalibrations ⌬The two quantities are defined as
s=

冑

n

1
兺 共ei − ē兲2 ,n − 1 i=1

共6兲011011-4兺i=1 兩ei+1 − ei兩
n−1

¯=
⌬

n−1

,

共7兲

where ei is the error of reading in year i and n is the total
number of annual recalibrations.
When n is not too small and the changes are purely random, the two values are very similar. When a systematic drift
is observed over several years in addition to random varia¯ will be smaller than s.
tions, ⌬It was evident after the recalibrations 共Fig. 5兲 that theuncertainty of the calibration with the SE2 static-expansion
system was too high to evaluate the long-term stability of thedevices with a full scale of 1.33 kPa directly. In addition to
the four ceramic sensors by INFICON, a check standard of
PTB was calibrated, which was an Inconel-type CDG by
MKS Instruments with the same full scale. All five CDGs
were calibrated at the same time each year and showed similar systematic changes from year to year. Although thechanges from year to year are within the measurement uncertainty, they indicate a common effect which was the generated calibration pressure pcal in SE2. For this reason, it wasmore complicated to estimate the long-term instability of the
CDGs with full scale 1.33 kPa and below with the calibration
at SE2.
To estimate the long-term stability in this case, it is necessary to distinguish between the influence of the primary
standard and the influence of possible annual shifts of theindication of the gauges under calibration. Normally, it is notpossible to distinguish between the two effects. In this case,however, when four gauges are calibrated at the same time,an estimate is possible; although the gauges were all of thesame type, it can be expected that long-term shifts are different from gauge to gauge. Hence, it can be assumed thatthe shift of the mean value of all gauges can be attributed topcal, which can vary within its uncertainty, and the scatter ofa single gauge around this mean shift can be attributed to thespecific gauge. So, we calculated the mean value of all errorof readings in year i and ēi by

FIG. 5. 共Color online兲 Error of reading at full scale for
CDGs with full scale of 1.3 kPa for 8 years calibrated
with the SE2 primary standard. Standard measurement
uncertainty u 共k = 1兲 was 0.08%.

J. Vac. Sci. Technol. A, Vol. 29, No. 1, Jan/Feb 2011

011011-5 K. Jousten and S. Naef: On the stability of capacitance-diaphragm gauges

011011-5

TABLE II. Apparent long-term instability of ceramic CDGs with full scale 1.33 kPa in percent of pressure nearfull scale. Different equations defined in the third column were applied. The recalibration period was one year;
data were observed within 9 years. The results with the FRS5 as standard are based on four successive years¯ calculated by Eqs. 共6兲 and 共7兲 do include the uncertainty ofonly. The rows with SE2 as standard and s and ⌬the standard and are not suitable to characterize the CDGs’ long-term instability.
Standard

Quantity

Equation

s
¯
⌬
sj
¯␦

Eq. 共6兲

0.062

0.062

0.051

0.074

0.062

Eq. 共7兲
Eq. 共12兲

0.050
0.010

0.049
0.015

0.050
0.009

0.046
0.010

0.049
0.011

Eq. 共13兲
Eq. 共6兲

0.009
0.009

0.010
0.005

0.009
0.009

0.012
0.012

0.010
0.009

Eq. 共7兲

0.013

0.006

0.012

0.008

0.010

SE2
SE2
FRS5

s
¯
⌬

Device 10

Device 11N共8兲

where eij is the error of reading of gauge j in year i and N is
the number of gauges. The shift from year i to i + 1 for themean is denoted by
共9兲

di+1 = ēi+1 − ēi ,and for a single gauge with

␦i+1,j = ei+1,j − eij .

共10兲

If no scatter due to the gauges occurs,␦i+1,j − di+1 = 0 all j.

共11兲

So, the root-mean-square deviation冑

Device 13兺i=1 兩␦i+1,j − di+1兩

Mean

n−1

1
ēi = 兺 eij ,
N j=1

sj =

Device 12n−11兺 共␦i+1,j − di+1兲2
n − 1 i=1

共12兲

gives a reasonable estimate of the long-term instability of thecalibrated CDG j. Similar to Eq. 共7兲, we can also observe thequantity

¯␦ =
j

n−1

,

共13兲

which is the average change per year over the recalibration
period. A more rigorous treatment would need to consider
the random variations of di as well, but since we are interested in a rough estimate only and have already carried out
eight recalibrations, this is of minor significance.
Table II shows the results of the two approaches according to the Eqs. 共6兲, 共7兲, 共12兲, and 共13兲, respectively. When the
reproducibility of the SE2 apparatus of about 0.058% 共standard deviation of di兲 is considered by the Eqs. 共12兲 and 共13兲,the long-term instabilities for the CDGs are much lower andmore realistic.
In 2006, the realization of the pressure scale above 30 Pa
was improved by establishing the FRS5 pressure balance.8
The four CDGs with full scale 1.33 kPa were calibrated by
the FRS5, in addition to the calibration at SE2. The observedchanges from year to year for a single gauge decreased by afactor of 5, and there were no clear common systematicchanges for all four gauges 共Fig. 6兲. The results from thesecalibrations directly give realistic values for the long-term
instability of the CDGs. In the case of full scale 1.33 kPa,e in % at full scale

0.100

0.050

u = 0.01%
Device 10
11
12
13

0.000

CDG, full scale 1.33 kPa
Ceramic type
Calibration with FRS5 pressure balanceu (k =1) = 0.01%-0.050
2005

2006

2007

2008
Year

JVST A - Vacuum, Surfaces, and Films

2009

2010

FIG. 6. 共Color online兲 Error of reading at full scale for
CDGs with full scale of 1.3 kPa for 4 years calibrated
with the FRS5 pressure balance. Standard measurement
uncertainty u 共k = 1兲 was 0.01%.

011011-6 K. Jousten and S. Naef: On the stability of capacitance-diaphragm gauges

011011-6

TABLE III. Long-term instability of ceramic CDGs with full scales from 13 Pa to 133 kPa in percent of pressurenear full scale. For each full scale, the values for four or five devices are given 共in total of 21 different devices兲.
The equation of the quantity for the long-term instability is given in the third column. The recalibration period
was one year; data were generally observed within 9 years. The results for the 1.33 kPa full scale CDGs are
based on four successive years only. For two CDGs with a full scale of 133 kPa 共devices 3 and 4兲, data wereignored when recalibration showed a change of about ⫺1% in 2 years 共device 20兲 or 1 year 共device 21兲.
FS

Quantity

Equation

Device 1

Device 2

Device 3

Device 4

Device 5

Mean

13 Pa

sj
¯␦

Eq. 共12兲

0.040

0.038

0.021

0.042

0.041

0.036

Eq. 共13兲

0.037

0.029

0.014

0.033

0.031

0.029

FS

Quantity

Equation

Device 6

Device 7

Device 8

Device 9

Mean

133 Pasj¯␦

Eq. 共12兲

0.014

0.015

0.012

0.009

0.013

Eq. 共13兲

0.009

0.011

0.009

0.008

0.009

FS

Quantity

Equation

Device 10

Device 11

Device 12

Device 13

Mean

1.33 kPas¯⌬

Eq. 共6兲

0.009

0.005

0.009

0.012

0.009

Eq. 共7兲

0.013

0.006

0.012

0.008

0.010

FS

Quantity

Equation

Device 14

Device 15

Device 16

Device 17

Mean

s
¯
⌬

Eq. 共6兲

0.009

0.011

0.015

0.016

0.013

13.3 kPa

Eq. 共7兲

0.007

0.008

0.010

0.011

0.009

FS

Quantity

Equation

Device 18

Device 19

Device 20

Device 21

Mean

Eq. 共6兲

0.006

0.017

0.040

0.015

0.019

133 kPas¯⌬

Eq. 共7兲

0.005

0.021

0.026

0.010

0.016

they should be similar to the ones calculated from above.
The last two rows in Table II show that this is indeed thecase.
Table III summarizes the observed values of s 关Eq. 共6兲兴¯ 关Eq. 共7兲兴 or s 关Eq. 共12兲兴 and ¯␦ 关Eq. 共13兲兴, respectively,
and ⌬over 9 years for CDGs from 13 Pa to 133 kPa full scale,except for CDGs with 1.33 kPa full scale, where only 4 years
serve as the database for the reason described above.
The lowest long-term instability was 0.005% 共device 11
with full scale 1.33 kPa and device 18 with full scale 133
kPa兲. The highest long-term instability was 0.042% for the
13 Pa full-scale range 共device 4兲.
Two of the four ceramic CDGs with full scale 133 kPa
showed a change of ⫺1% after 6 共device 20兲 and 7 共device

21兲 years, respectively, of recalibrations between successive
years. These data were ignored in Table III. These two devices had an accessible potentiometer for the full-scale adjust
which were mistakenly misadjusted. Both devices could bereadjusted and recalibration was resumed.
In Table IV, the values of s and ¯␦ at a pressure of 5 Pa
are shown for CDGs with a full scale of 13 and 133 Pa.
In the case of 13 Pa full scale, these values are a factor of
1.6 higher than the ones at full scale, whereas in the case of
133 Pa, they are larger by a factor of about 3.5. The reason isthat the variability of the offset due to drift and its measurement already affected the value at 5 Pa for the 133 Pa full¯ at a pressure
scale. This is also true for the values of s and ⌬TABLE IV. Long-term instability of ceramic CDGs with full scales of 13 Pa and 133 Pa in percent of pressure
at 5 Pa. s j and ¯␦ are defined in Eqs. 共12兲 and 共13兲. The recalibration period was 1 year; data were observed
within 8 years 共13 Pa兲 or 9 years 共133 Pa兲.
Full scale

Quantity

Device 1

Device 2

Device 3

Device 4

Device 5

Mean

sj
¯␦

0.085

0.062

0.025

0.058

0.060

0.058

13 Pa

0.072

0.052

0.018

0.047

0.044

0.047

Full scale

Quantity

Device 6

Device 7

Device 8

Device 9

Mean

sj
¯␦

0.022

0.071

0.040

0.038

0.043

133 Pa

0.020

0.057

0.030

0.030

0.034

J. Vac. Sci. Technol. A, Vol. 29, No. 1, Jan/Feb 2011

011011-7 K. Jousten and S. Naef: On the stability of capacitance-diaphragm gauges

011011-7

TABLE V. Long-term instability of ceramic CDGs with full scales of 1.33 kPa in percent of pressure at 7 Pa. s¯ are defined in Eqs. 共6兲 and 共7兲. The recalibration period was 1 year; data were observed within 9 years.
and ⌬Full scale

Quantity

Device 10

Device 11

s
¯
⌬

0.124

0.097

0.131

0.098

0.113

1.33 kPa

0.144

0.095

0.162

0.083

0.121

of 7 Pa for the 1.33 kPa full scale 共Table V兲, where 7 Pa isonly 0.5% of full scale. In this case, Eqs. 共6兲, 共12兲, 共7兲, and共13兲, respectively, delivered very similar values. This indicates that the uncertainty of the primary standard did notplay a significant role at pressures of 0.5% of full scale.

VI. DISCUSSION
This is the first investigation of the long-term stability of
CDGs with a ceramic diaphragm. Previous investigations
published data on the long-term stability of CDGs with ametal diaphragm.10,11 In the study by Hyland and Tilford,10
the authors found changes in the error of indication for recalibrations near full scale between 0.05% and 0.86% for
full scales of 133 kPa, 0.07%–0.24% 共13.3 kPa兲, 0.1%–1%
共1.33 kPa兲, and 0.1%–2% 共133 Pa兲 with unequal recalibration periods between 0.4 and 4.5 years. In the study by
Grosse and Messer,11 similar changes of 0.03%–0.25% for133 Pa and 0.09%–0.34% for 1.33 kPa full scale were reported for several gas species, but only one gauge each.
These values for metal CDGs seem to indicate that thelong-term instability near full scale is higher than that ofceramic CDGs. This is also the experience of the vacuum
metrology laboratory at PTB gained from repeated customer
calibrations. Since the long-term instability is the dominant
uncertainty for measurements and calibrations with CDGs inmany cases, PTB will publish these data on metal CDGs in
the near future. Despite the better long-term stability nearfull scale of the ceramic CDGs, it must be mentioned, however, that the accuracy of high-resolution CDGs with a metal
diaphragm below 1% of full scale is significantly better,compared to the CDGs with a ceramic membrane.
In comparison with resonance silicon gauges,12 the longterm shifts of ceramic CDGs are about a factor of 3 higher
for pressures below 1.3 kPa and a factor of 10–100 higher forpressures up to 100 kPa. Similar to ceramic CDGs and staticexpansion systems, resonance silicon gauges seem to be so

JVST A - Vacuum, Surfaces, and Films

Device 12

Device 13

Meanstable that their true long-term instability at 100 kPa cannot
be determined with the uncertainty of a high-level mercury
primary standard.
VII. CONCLUSION
The technology of ceramic CDGs has gained a great dealof maturity, and the long-term instability is within 0.01%–
0.02% 共full scale ⱖ133 Pa兲, which is so low that the uncertainties of the primary standards of the static-expansion type
are too high to observe the true long-term instability directly.
Near full scale, ceramic CDGs can be recommended as very
stable transfer standards. It must be noted, however, that the
CDGs tested here were stored, transported, and used underrelatively pure conditions with either atmospheric air aroundthem or nitrogen as the test gas. The results of this investigation are not representative for CDGs in contaminating process environments.
ACKNOWLEDGMENTS
The careful acquiring of data by Christian Buchmann andMarco Schulz of PTB, discussions with Clemens Elster of
PTB, and Per Björkman of INFICON are gratefully acknowledged.
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