Hoffman D.M., Singh B., Thomas J.H. (Eds). Handbook of Vacuum Science and Technology
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280
Chapter
3.1:
The
Measurement
of Low
Pressures
important gap. The linearity of the MGD is better than that of the ion gauge at
high pressure (10"^ to 10"^ torr) and is theoretically more stable than other
gauges at lower pressures [68].
In a MDG, the rate of change of the angular velocity of a freely spinning ball is
proportional to the gas pressure and inversely proportional to the mean molecular
velocity. Angular velocity is determined by removing the driving force and then
measuring the AC voltage induced in the pickup coils by the magnetic moment of
the ball (see Figure 21).
Fig. 21.
THE SPINNING ROTOR GAUGE
END VIEV
crass SCCTDI
Molecular Drag Gauge (Spinning Rotor)
3.1.3 Indirect Reading Gauges 281
Briefly, a small rotor (steel ball bearing) about 4.5 mm in diameter is magneti-
cally levitated and spun up to about 400 Hz by induction. The ball, enclosed in a
thimble connected to the vacuum system, is allowed to coast by turning off the in-
ductive drive. Then the time of a revolution of the ball is measured by timing the
signal induced in a set of pickup coils by the rotational component of the ball's
magnetic moment. Gas molecules exert a drag on the ball, slowing it at a rate set
by the pressure P, its molecular mass m, temperature T, and the coefficient of mo-
mentum transfer a, between the gas and the ball. A perfectly smooth ball would
have a value of unity. There is also a pressure-independent residual drag {RD)
caused by eddy current losses in the ball and surrounding structure. There are
also temperature effects, which cause the ball diameter and moment of inertia to
change.
In the region of molecular flow, the pressure can be determined from
TTp
ac I—0)' \
P = — RD-2ar] (3)
lOo-eft-
\
CO
J
where p is the density of the rotor
a is the radius of the rotor
(o'/(o
is the fractional rate of slowing of the rotor
c"
is the mean gas molecular velocity
a is the linear coefficient of expansion of the ball
T is the rate of change of the ball's temperature
All the terms in the first part of the equation can be readily determined except for
the accommodation coefficient a, which depends on the surface of the ball and
the molecular adhesion between the gas and the surface of the ball. The accom-
modation coefficient a must be determined by calibration of the MDG against a
known pressure standard or, if repeatability is more important than the highest
accuracy, by assuming a value of
1
for
cr.
Dittman et al. [68] have made repeated
measurements of a on many balls over several years. The values obtained ranged
from 0.97 to 1.06 for 68 visually smooth balls. Assuming a value of
1
for
cr
would
not introduce a large error and would according to Fremerey [66] allow the MDG
to be considered
a
primary standard. The controller [68] contains the electronics to
power and regulate the suspension and drive, detect and amplify the signal from
the pickup coils and then time the rotation of the ball. It also contains a data pro-
cessor that stores the calibration data and computes the pressure.
McCulloh et al. [69] have studied the zero stability of the MDG and have con-
cluded that the largest contribution to instabihty is temperature change of the ro-
tor. Changes in accommodation coefficient have been studied by Fremerey [66]
and Cosma et
al.
[70] and, although the value will not change more than a few per-
cent, it is difficult to predict how a specific ball will react to differing gas species.
282 Chapter
3.1:
The Measurement of Low Pressures
These difficulties notwithstanding, Dittman et al. [68] have indicated that the
short-term stability of MDG is much less than 1 percent, and the long-term sta-
bility is of the order of a few percent. Although these results were obtained under
near-ideal laboratory conditions, careful users will be able to reproduce these re-
sults.
The MDG is perhaps the best available transfer standard for the pressure
range of 10"-^ to 10"^ torr
(1
to 10"^ Pa), but as it is designed for laboratory use
in controlled relatively vibration free environments its use in industrial applica-
tions is severely limited. The MDG is expensive. Typically it requires several min-
utes to achieve accurate results under essentially static conditions and hence will
be found most often in research and standards labs.
3.1.3.6
Mass Spectrometers
The theory and practical applications of mass spectrometers are discussed in Sec-
tion 3.3.5 of this handbook. Calibration of mass spectrometers can be accom-
plished by equating the integral (the total area under all the peaks, taking into ac-
count the scale factors) to the overall pressure as measured by another gauge
(cold-cathode, B A, or MDG). Once calibrated, the mass spectrometer can be used
as a sensitive monitor of system
pressure.
It
is
also important when monitoring sys-
tem pressure to know what gases are present. Most gauges have vastly different
sensitivities to different gas species.
3.1.3.7
Vacuum-Measuring Instruments
SINGLE-MEASUREMENT INSTRUMENTS
Several manufacturers sell vacuum instruments that make single measurements
or that measure multiple sensors of the same type (see Figure 22). These are avail-
able with either analog or digital displays, analog "recorder" outputs and relays.
Some also have output to directly interface with computers for process control.
COMBINATION AND MODULAR INSTRUMENTS
Where a large range of pressures are to be measured, a combination of sensors are
required to cover the range. The vacuum instruments in this case must accommo-
date these multiple-sensor
types.
Combination instruments are then used. More re-
cently these combination instruments are of
a
modular design that accepts printed
circuit board "cards" for each type of sensor desired.
3.1.3 Indirect Reading Gauges
283
Rg.22a.
500 800 IK 2K
,400
SKiOK
20K
lOQICl
•200K
,
•300K
•;
^500K,
;
•760K
'
Rg, 22b.
284
Chapter
3.1:
The Measurement
of
Low Pressures
The various types of sensors that can be accommodated by one such modular
gauge are as follows:
1 to
10
bar
1 to 1000 torr
1,10, 100, 1000, 10,000 torr
1 millitorr to 1000 torr
1 to 20,000 millitorr
10-"^
to
10 ~'^
torr
10"i4olO~2torr
10~^Uo 10"-^ ton-
Diaphragm sensor (positive pressure)
Diaphragm sensor
Capacitance diaphragm sensors
Convection sensor
Thermocouple sensors
Cold-cathode sensors
Cold-cathode sensors
Hot-cathode sensors
Examples of these combination instruments as sold by several manufacturers are
shown in Figure 23a~e.
Fig.23a-b
Source: Photo a, courtesy of Varian Vacuum Products; photo b, courtesy of MKS Instru-
ments, Inc.
3.1.3 Indirect Reading Gauges
285
Fig.
23c--e.
^^i'}^}:^-}M^f^.
P
I
C. I
GAS
M BAR
TORR MICRONS
per
HOUR
TELEVAC
MM 200
Source: Photo
c,
courtesy
of
MKS
Instruments, HPS Division; photo
d,
courtesy
of
Granville-
Phillips Company; and photo
e,
courtesy
of
Televac.
286
Chapter
3.1:
The Measurement
of
Low Pressures
Rg.
24a,
b.
**^a«ai*'
Intelligent Gauges
INTELLIGENT GAUGE TUBES
For some applications, an instrument with a display is not
required.
In this case an
"intelligent" (or "smart" or "active") sensor is used. The sensor contains its own
electronics. It is powered from an external source and provides an output signal
(usually 0-10 volts or a digital communications interface). This signal then is
provided to the user's control system or computer (see Figure 24).
3.1.4
CALIBRATION
OF
VACUUM GAUGES
The calibration of
any
vacuum gauge is not a trivial undertaking, but increasingly
necessary as vacuum processes become more intricate. Certain processes per-
formed on military end use items require compliance with military standards that
include calibration of vacuum gauges with traceability to national standards labs.
The capability of obtaining gauges calibrated by national standards labs or labs
having traceability to national labs is a relatively recent occurrence.
In contemplating the calibration of a vacuum sensor, it is useful to
first
evalu-
ate
the
pressure range
that
is important
to
the procedure being performed. The next
and perhaps more difficult task is to determine (if possible) the sensitivity of the
process to pressure change. These data should allow an estimate of the accuracy
necessary to ensure operation within this pressure range. Certain operations such
as vacuum melting and simple evaporation may only require knowledge that the
operation is taking place at a pressure below a set limit. For that purpose, an ac-
3.1.4 Calibration of Vacuum Gauges 287
curacy of 10% or even 20% would be sufficient. Other operations involving back-
filling into essentially totally exhausted chambers may require a much higher de-
gree of accuracy of approximately 2%. Perhaps the most important feature of any
gauge is the repeatability.
One can calibrate a vacuum gauge by measuring it relative to a direct reading
standard gauge, or by measuring the gauge at a fixed known pressure.
In the region from atmospheric to about 0.5 torr, the use of U-tube manometers
of one sort or another, if corrected for local atmospheric pressure and tempera-
ture,
can provide a standard that can be used to calibrate other indirect gauges.
In the region from 0.5 torr to 10"^ torr, McLeod gauges with calibrated vol-
umes can be used as standards, but care must be taken to eliminate condensable
vapors and the possibility of mercury contamination of sensor and system. For
years it had been the practice to simply state that the sensor had been measured
relative to a trapped McLeod gauge. This practice is no longer considered practi-
cal due to the toxic nature of mercury and the difficulty in obtaining accurate re-
producible readings of the mercury meniscus. The MDG (spinning rotor gauge)
can also be used as a calibration standard, as mentioned earlier.
More recently various national standards laboratories have instituted programs
leading to the establishment of pressure standards and calibration services
whereby gauges can be certified by reference to these pressure standards [72]. A
few companies can now offer NIST-traceable calibration services. Other calibra-
tion services are also available [73]. The devices most often used by NIST (Na-
tional Institute for Standards and Technology) as a secondary calibration standard
in the region
10 ~^
torr and lower are the spinning rotor gauge (MDG) and the
tungsten filament Bayard-Alpert gauge [41]. Other national labs have used triode
gauges of their own design [74,75].
The basis of the standardization process is the production of an accurately
known pressure. The static method is the simplest in that a known small volume
of a known gas (usually nitrogen or argon) of known pressure measured by a di-
rect reading gauge such as a U-tube is allowed to expand into a large volume.
Then all, or in most cases a small volume, of the expanded gas is allowed to ex-
pand into a larger volume, and so on, until the desired pressure is obtained. With
care,
one can obtain known pressures as low as 10"^ torr, but more realistically,
10 ~^
to 10"^ torr. Gauges can be calibrated at the final pressure or at several
points in the expansion process.
The dynamic process is the method preferred and used by NIST [71,72], other
national standards labs and some companies. This method is somewhat more
complex in that a gas is introduced into a chamber at a constant throughput Q. At
the same time gas is pumped out at a constant pumping speed S, At equilibrium
P = Q/S. The complicated part is keeping Q and S known and constant. The man-
ufacture of such a system is an expensive and time-consuming enterprise and,
given the availability of calibrated instruments, largely unnecessary.
288 Chapter
3.1:
The Measurement of Low Pressures
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