# How do indirect pressure vacuum gauges work?

## Vacuum gauges with gas-dependent pressure reading

This type of vacuum gauge does not measure the pressure directly as an area-related force, but indirectly by means of other physical variables that are proportional to the number density of particles and thus to the pressure. The vacuum gauges with gas-dependent pressure reading include: the decrement gauge, the thermal conductivity vacuum gauge and the ionization vacuum gauge having different designs.

The instruments consist of the actual sensor (gauge head, sensor) and the control unit required to operate it. The pressure scales or digital displays are usually based on nitrogen pressures; if the true pressure pT of a gas (or vapor) has to be determined, the indicated pressure pI must be multiplied by a factor that is characteristic for this gas. These factors differ, depending on the type of instrument, and are either given in tabular form as factors independent of pressure (see Table 3.2) or, if they depend on the pressure, must be determined on the basis of a diagram (see Fig. 3.11).

Table 3.2 Connection factors

Fig 3.11 Calibration curves of THERMOVAC gauges for various gases, based on nitrogen equivalent reading

In general, the following applies:
True pressure pT = indicated pressure pI · correction factor
If the pressure is read off a “nitrogen scale” but not corrected, one refers to “nitrogen equivalent” values.

In all electrical vacuum gauges (they include vacuum gauges that are dependent on the type of gas) the increasing use of computers has led to the wish to display the pressure directly on the screen, e.g. to insert it at the appropriate place in a process flow diagram. To be able to use the most standardized computer interfaces possible, so-called transmitters (signal converters with standardized current outputs) are built instead of a sensor and display unit (e.g. THERMOVAC transmitter, Penning transmitter, IONIVAC transmitter etc.). Transmitters require a supply voltage (e.g. +24 volts) and deliver a pressure-dependent current signal that is linear over the entire measuring range from 4 to 20 mA or 0 – 10 V. The pressure reading is not provided until after supply of this signal to the computer and processing by the appropriate software and is then displayed directly on the screen.

## Thermal conductivity vacuum gauges

Classical physics teaches and provides experimental confirmation that the thermal conductivity of a static gas is independent of the pressure at higher pressures (particle number density), p > 1 mbar. At lower pressures, p < 1 mbar, however, the thermal conductivity is pressure-dependent.

It decreases in the medium vacuum range starting from approx. 1 mbar proportionally to the pressure and reaches a value of zero in the high vacuum range. This pressure dependence is utilized in the thermal conductivity vacuum gauge and enables precise measurement (dependent on the type of gas) of pressures in the medium vacuum range.

The most widespread measuring instrument of this kind is the Pirani vacuum gauge. A current-carrying filament with a radius of r1 heated up to around to 212 to 302°F (100 to 150°C) (Fig. 3.10) gives off the heat generated in it to the gas surrounding it through radiation and thermal conduction (as well as, of course, to the supports at the filament ends). In the rough vacuum range the thermal conduction through gas convection is virtually independent of pressure (see Fig. 3.10). If, however, at a few mbar, the mean free path of the gas is of the same order of magnitude as the filament diameter, this type of heat transfer declines more and more, becoming dependent on the density and thus on the pressure. Below 10-3 mbar the mean free path of a gas roughly corresponds to the size of radius r2 of the measuring tubes. The sensing filament in the gauge head forms a branch of a Wheatstone bridge.

3.10 Dependence of the amount heat dissipated by a heated filament (radius r1) in a tube (radius r2) at a constant temperature difference on the gas pressure (schematic diagram).

I Thermal dissipation due to radiation and conduction in the metallic ends
II Thermal dissipation due to the gas, pressure dependent
III Thermal dissipation due to radiation and convection

In the THERMOVAC thermal conductivity gauges with constant resistance which are the dominant type today, the sensing filament is also a branch of a Wheatstone bridge. The heating voltage applied to this bridge is regulated so that the resistance and therefore the temperature of the filament remain constant, regardless of the heat loss. This means that the bridge is always balanced. This mode of regulation involves a time constant of a few milliseconds so that such instruments, in contrast to those with variable resistance, respond very quickly to pressure changes. The voltage applied to the bridge is a measure of the pressure. The measuring voltage is corrected electronically such that an approximately logarithmic scale is obtained over the entire measuring range. Thermal conductivity vacuum gauges with constant resistance have a measuring range from 10-4 to 1013 mbar. Due to the very short response time, they are particularly suitable for controlling and pressure monitoring applications. In the most sensitive range, i.e. between 10-3 and 10 mbar, this corresponds to around 15 % of the pressure reading. The measurement uncertainty is significantly greater outside this range.

As in all vacuum gauges dependent on the type of gas, the scales of the indicating instruments and digital displays in the case of thermal conductivity vacuum gauges also apply to nitrogen and air. Within the limits of error, the pressure of gases with similar molecular masses, i.e. O2, CO and others, can be read off directly. Calibration curves for a series of gases are shown in Fig. 3.11.

An extreme example of the discrepancy between true pressure pT and indicated pressure pI in pressure measurement is the admission of air to a vacuum system with argon from a pressure cylinder to avoid moisture (pumping time). According to Fig. 3.11, one would obtain a pI reading of only 40 mbar on reaching an “Ar atmospheric pressure” pT with a THERMOVAC as a pressure measuring instrument. Argon might escape from the vessel (cover opens, bell jar rises). For such and similar applications, pressure switches or vacuum gauges that are independent of the type of gas must be used.

## Ionization vacuum gauges

Ionization vacuum gauges are the most important instruments for measuring gas pressures in the high and ultrahigh vacuum ranges. They measure the pressure in terms of the number density of particles proportional to the pressure. The gas whose pressure is to be measured enters the gauge heads of the instruments and is partially ionized with the help of an electric field. Ionization takes place when electrons are accelerated in the electric field and attain sufficient energy to form positive ions on impact with gas molecules. These ions transmit their charge to a measuring electrode (ion collector) in the system. The ion current, generated in this manner (or, more precisely, the electron current in the feed line of the measuring electrode that is required to neutralize these ions) is a measure of the pressure because the ion yield is proportional to the particle number density and thus to the pressure.

The formation of ions is a consequence of either a discharge at a high electric field strength (cold-cathode being the umbrella term for penning/inverted magnetron discharge, see direct pressure measurement) or the impact of electrons that are emitted from a hot cathode (the umbrella term for Bayard-Alpert/Extractor/triode) (see direct pressure measurement)

Under otherwise constant conditions, the ion yield and thus the ion current depend on the type of gas since some gases are easier to ionize than others. As all vacuum gauges with a pressure reading that is dependent on the type of gas, ionization vacuum gauges are calibrated with nitrogen as the reference gas (nitrogen equivalent pressure, see direct pressure measurement). To obtain the true pressure for gases other than nitrogen, the read-off pressure must be multiplied by the correction factor given in Table 3.2 for the gas concerned. The factors stated in Table 3.2 are assumed to be independent of the pressure, though they depend somewhat on the geometry of the electrode system. Therefore, they are to be regarded as average values for various types of ionization vacuum gauges (see Fig. 3.16).

### Cold-cathode ionization vacuum gauges

Ionization vacuum gauges which operate with cold discharge are called cold-cathode or Penning/inverted magnetron vacuum gauges. The discharge process in a measuring tube is, in principle, the same as in the electrode system of a sputter ion pump. A common feature of all types of cold cathode ionization vacuum gauges is that they contain just two unheated electrodes, a cathode and an anode, between which a so-called cold discharge is initiated and maintained by means of a d.c. voltage (of around 2 kV) so that the discharge continues at very low pressures. This is achieved by using a magnetic field to make the paths of the electrons long enough so that the rate of their collision with gas molecules is sufficiently large to form the number of charge carriers required to maintain the discharge. The magnetic field (see Fig. 3.12) is arranged such that the magnetic field lines of force cross the electric field lines. In this way the electrons are confined to a spiral path. The positive and negative charge carriers produced by collision move to the corresponding electrodes and form the pressure-dependent discharge current, which is indicated on the meter. The reading in mbar depends on the type of gas. The upper limit of the measuring range is given by the fact that above a level of several 10-2 mbar the cold cathode discharge changes to a glow discharge with intense light output in which the current (at constant voltage) depends only to a small extent on the pressure and is therefore not suitable for measurement purposes. In all cold cathode gauges there is considerably higher gas sorption than in ionization vacuum gauges that operate with a hot cathode. A cold cathode measuring tube pumps gases similarly to a sputter ion pump (S ≈ 10-2 l/s). Here again the ions produced in the discharge are accelerated towards the cathode where they are partly retained and partly cause sputtering of the cathode material. The sputtered cathode material forms  a gettering surface film on the walls of the gauge tube. In spite of these disadvantages, which result in a relatively high degree of inaccuracy in the pressure reading (up to around 50 %), the cold-cathode ionization gauge has three very outstanding advantages. First, it is the least expensive of all high vacuum measuring instruments. Second, the measuring system is insensitive to the sudden admission of air and to vibrations; and third, the instrument is easy to operate.

Fig 3.12 Cross-section of PENNINGVAC PR25 gauge.

1. Small flange DN 25 KF; DN 40 KF
2. Housing
3. Ring anode with ignition pin
4. Ceramic washer
6. Connecting bush
7. Anode pin
8. Cathode plate

### Hot-cathode ionization vacuum gauges

Generally speaking, such gauges refer to measuring systems consisting of three electrodes (cathode, anode and ion collector) where the cathode is a hot cathode. Cathodes used to be made of tungsten but are now usually made of oxide-coated iridium (Th2O3, Y2O3) to reduce the electron output work and make them more resistant to oxygen. Ionization vacuum gauges of this type work with low voltages and without an external magnetic field. The hot cathode is a very high-yield source of electrons. The electrons are accelerated in the electric field and receive sufficient energy from the field to ionize the gas in which the electrode system is located. The positive gas ions formed are transported to the ion collector, which is negative with respect to the cathode, and give up their charge there. The ion current thereby generated is a measure of the gas density and thus of the gas pressure. If i- is the electron current emitted by the hot cathode, the pressure-proportional current i+ produced in the measuring system is defined by:

(3.3)

(3.3a)

The variable C is the vacuum gauge constant of the measuring system.  For nitrogen this variable is generally around 10 mbar-1. With a constant electron current the sensitivity S of a gauge head is defined as the quotient of the ion current and the pressure. For an electron current of 1 mA and C = 10 mbar-1, therefore, the sensitivity S of the gauge head is:

Hot-cathode ionization vacuum gauges also exhibit gas sorption (pumping action), which, however, is considerably smaller than with cold cathode systems, i.e. approx. 10-3 l/s. Essentially this gas sorption takes place on the glass wall of the gauge head and, to a lesser extent, at the ion collector. Here use is made of nude gauges that are easy to operate because an external magnet is not needed. The upper limit of the measuring range of the hot cathode ionization gauge is around 10-2 mbar (with the exception of special designs). It is basically defined by the scatter processes of ions at gas molecules due to the shorter free path at higher pressures (the ions no longer reach the ion collector = lower ion yield). Moreover, uncontrollable glow or arc discharges may form at higher pressures and electrostatic discharges can occur in glass tubes. In these cases the indicated pressure pI may deviate substantially from the true pressure pT

At low pressures the measuring range is limited by two effects: by the X-ray effect and by the ion desorption effect. These effects results in loss of the strict proportionality between the pressure and the ion current and produce a low pressure threshold that apparently cannot be crossed (see Fig. 3.14).

Fig 3.14 Apparent low pressure limit due to X-ray effect in a normal ionization vacuum gauge.

I - Pressure reading without X-ray effect
II - Apparent low pressure limit due to X-ray effect
III - Sum of I and II

#### The X-ray effect (see Fig. 3.15)

Fig 3.15 Explanation of the X-ray effect in a conventional ionization gauge. The electrons e- emitted by the cathode C collide with anode A and trigger a soft X-ray radiation (photons) there. This radiation strikes, in part, the ion collector and generates photoelectrons e–s there.

C - Cathode
A - Anode
I - Ion collector

The electrons emitted from the cathode impinge on the anode, releasing photons (soft X-rays). These photons, in turn, trigger photoelectrons from surfaces they strike. The photoelectrons released from the ion collector flow to the anode, i.e. the ion collector emits an electron current, which is indicated in the same manner as a positive ion current flowing to the ion collector. This photocurrent simulates a pressure. This effect is called the positive X-ray effect, and it depends on the anode voltage as well as on the size of the surface of the ion collector.

Under certain circumstances, however, there is also a negative X-ray effect. Photons which impinge on the wall surrounding the gauge head release photoelectrons there, which again flow towards the anode, and since the anode is a grid structure, they also flow into the space within the anode. If the surrounding wall has the same potential as the ion collector, e.g. ground potential, a portion of the electrons released at the wall can reach the ion collector. This results in the flow of an electron current to the ion collector, i.e. a negative current flows which can compensate the positive ion current. This negative X-ray effect depends on the potential of the outer wall of the gauge head.

#### The ion desorption effect

Adsorbed gases can be desorbed from a surface by electron impact. For an ionization gauge this means that, if there is a layer of adsorbed gas on the anode, these gases are partly desorbed as ions by the impinging electrons. The ions reach the ion collector and lead to a pressure indication that is initially independent of the pressure but rises as the electron current increases. If such a small electron current is used so that the number of electrons incident at the surface is small compared to the number of adsorbed gas particles, every electron will be able to desorb positive ions. If the electron current is then increased, desorption will initially increase because more electrons impinge on the surface. This finally leads to a reduction in adsorbed gas particles at the surface. The reading falls again and generally reaches values that may be considerably lower than the pressure reading observed with a small electron current. As a consequence of this effect in practice, one must ascertain whether the pressure reading has been influenced by a desorption current. This can be done most simply by temporarily altering the electron current by a factor of 10 or 100. The reading for the larger electron current is the more precise pressure value.

In addition to the conventional ionization gauge, whose electrode structure resembles that of a common triode, there are various ionization vacuum gauge systems (Bayard-Alpert system, extractor system) which more or less suppress the two effects, depending on the design, and are therefore used for measurement in the high and ultrahigh vacuum range. Today the Bayard-Alpert system is usually the standard system.

Fig 3.16 Schematic drawing of the electrode arrangement of various ionization vacuum gauge measuring systems.

a) Bayard-Alpert ionization vacuum gauge system
b) Conventional ionization vacuum gauge system.
c) ionization vacuum gauge system for higher pressures (up to 1 mbar)
d) extractor ionization vacuum gauge system

I - ion collector
Sc - screen
M - modulator
A - anode
C - cathode
R - reflector

##### a) Bayard-Alpert ionization vacuum gauge (the standard measuring system used today)

To ensure linearity between the gas pressure and the ion current over as large a pressure range as possible, the X-ray effect must be suppressed as far as possible. In the electrode arrangement developed by Bayard and Alpert, this is achieved by virtue of the fact that the hot cathode is located outside the anode and the ion collector is a thin wire forming the axis of the electrode system (see Fig. 3.16 a). The X-ray effect is reduced by two to three orders of magnitude due to the great reduction in the surface area of the ion collector. When pressures in the ultrahigh vacuum range are measured, the inner surfaces of the gauge head and the connections to the vessel affect the pressure reading. The various effects of adsorption, desorption, dissociation and flow phenomena cannot be dealt with in this context. By using Bayard-Alpert systems as nude gauge systems that are placed directly in the vessel, errors in measurement can be extensively avoided because of the above mentioned effects.

##### b) The conventional ionization vacuum gauge

A triode of conventional design (see Fig. 3.16 b) is used as the gauge head, but it is slightly modified so that the outer electrode serves as the ion collector and the grid within it as the anode. With this arrangement the electrons are forced to take very long paths (oscillating around the grid wires of the anode) so that the probability of ionizing collisions and thus the sensitivity of the gauge are relatively high. Because the triode system can generally only be used in high vacuum on account of its strong X-ray effect, the gas sorption (pumping) effect and the gas content of the electrode system have only a slight effect on the pressure measurement.

##### c) The high-pressure ionization vacuum gauge (up to 1 mbar)

A triode is again used as the electrode system (see Fig. 3.16 c), but this time with an unmodified conventional design. Since the gauge is designed to allow pressure measurements up to 1 mbar, the cathode must be resistant to relatively high oxygen pressure. Therefore, it is designed as a so-called non-burnout cathode, consisting of an yttria-coated iridium ribbon. To obtain a rectilinear characteristic (ion current as a linear function of the pressure) up to a pressure of 1 mbar, a high-ohmic resistor is installed in the anode circuit.

##### d) Extractor ionization vacuum gauge

Disruptive effects that influence pressure measurement can also be extensively eliminated by means of an ion-optical system first suggested by Redhead. With this extractor system (see Fig. 3.16 d) the ions from the anode cylinder are focused on a very thin and short ion collector. The ion collector is set up in a space, the rear wall of which is formed by a cup-shaped electrode that is maintained at the anode potential so that it cannot be reached by ions emanating from the gas space. Due to the geometry of the system as well as the potential of the of individual electrodes, the disruptive influences through X-ray effects and ion desorption are almost completely excluded without the need of a modulator. The extractor system measures pressures between 10-4 and 10-12 mbar. Another advantage is that the measuring system is designed as a nude gauge with a diameter of only 35 mm so that it can be installed in small apparatus.

## Spinning rotor gauge (SRG)

Fig 3.9 Cross-section of the gauge head of a spinning rotor gauge (SRG).

1. Ball
2. Measuring tube, closed at one end, welded into connection flange 7
3. Permanent magnets
4. Stabilization coils
5. 4 drive coils
6. Bubble level
7. Connection flange
Pressure-dependent gas friction at low gas pressures can be utilized to measure pressures in the medium and high vacuum range. In technical instruments of this kind a steel ball that has a diameter of several millimeters and is suspended without contact in a magnetic field (see Fig. 3.9) is used as the measuring element. The ball is set into rotation through an electro magnetic rotating field: after reaching a starting speed (around 425 Hz), the ball is left to itself. The speed then declines at a rate that depends on the prevailing pressure under the influence of the pressure-dependent gas friction. The gas pressure is derived from the relative decline of the speed f (slowing down) using the following equation:

(3.2)

p = gas pressure
r = radius of the ball ρ = density of the ball material
c- = mean speed of the gas particles, dependent on type of gas
σ = coefficient of friction of the ball, independent of the type of gas, nearly 1.

As long as a measurement uncertainty of 3 % is sufficient, which is usually the case, one can apply σ = 1 so that the sensitivity of the spinning rotor gauge (SRG) with rotating steel ball is given by the calculable physical size of the ball, i.e. the product radius x density r · ρ (see equation 3.2). Once a ball has been “calibrated”, it is suitable for use as a “transfer standard”, i.e. as a reference device for calibrating another vacuum gauge through comparison, and is characterized by high long-term stability.

While in the case of the kinetic theory of gases with SRG the counting of particles directly represents the measuring principle (transferring the particle pulses to the rotating ball, which is thus slowed down).
With other electrical measuring methods that are dependent on the type of gas, the particle number density is measured indirectly by means of the amount of heat lost through the particles (thermal conductivity vacuum gauge) or by means of the number of ions formed (ionization vacuum gauge).

## Combination vacuum gauges

With all the above gauge types, you are limited in the range that can be measured. With the drive to smaller and smaller equipment, the space to have multiple ports to accommodate different gauge types to cover the full range has become untenable. Therefore, you now see gauges with combinations in order to cover the full ranges. These are typically Pirani / cold cathode, Pirani / Hot cathode to cover atmosphere to High/Ultra high vacuum. Or you will also see Pirani/Piezo gauges where by the piezo increases the accuracy at the atmospheric end of the measuring.

# Fundamentals of Vacuum Technology

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## References

Vacuum symbols

### Vacuum symbols

A glossary of symbols commonly used in vacuum technology diagrams as a visual representation of pump types and parts in pumping systems

Glossary of units

### Glossary of units

An overview of measurement units used in vacuum technology and what the symbols stand for, as well as the modern equivalents of historical units

References and sources

### References and sources

References, sources and further reading related to the fundamental knowledge of vacuum technology

### Vacuum symbols

A glossary of symbols commonly used in vacuum technology diagrams as a visual representation of pump types and parts in pumping systems

### Glossary of units

An overview of measurement units used in vacuum technology and what the symbols stand for, as well as the modern equivalents of historical units