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# Pressure Measurement Technical Notes

## Measuring Pressure

### Units of Measure

Sub-atmospheric pressures are measured in several units, including: Torr (also called millimeters of mercury, mmHg), milliTorr (mTorr but also called micron, μ), inches of mercury (" Hg), millibar (mbar), and pascal (Pa). In the U.S., three units are in common use: micron as the unit for pressures reached by backing pumps, Torr for high vacuum and UHV pumps, and inches of mercury for coarse vacuum pumps. In Europe, millibar is the common unit for all pressure measurements. Japan uses the pascal unit, but often has Torr as a secondary unit. Most authors of scientific/technical papers are urged to use the SI unit pascal, and some do.

The units are derived from:

• Pascal—the force of 1 newton (1 kg accelerating at 1m/sec./sec.) acting on 1 m2
• Millibar—1,000 times the force of 1 dyne (1g accelerating at 1cm/sec./sec.) acting on 1 cm2
• Torr—1/760 times the height of a mercury barometer under “standard” atmospheric pressure
• MilliTorr or micron—1,000th of 1 Torr
• Inches of Hg (vacuum)—1/29.92 times the height of a mercury barometer under “standard” atmospheric pressure (taking atmospheric pressure as 0" Hg)
• Inches of Hg (weather forecasts)—1/29.92 times the height of a mercury barometer under “standard” atmospheric pressure (taking no pressure as 0" Hg)

### Pressure Ranges

There is no “universal” gauge that can measure from atmosphere to UHV pressures (a dynamic range of 1015). There are, essentially, three mechanisms used in pressure measurement and the one chosen depends on the pressure range and the residual gases in the vacuum.

### Basic Technologies:

Mechanical Gauges have liquid or solid diaphragms that change position under the force of all the gas molecules bouncing off them. These gauges measure absolute pressures unaffected by gas/vapor properties. Unfortunately, this type of gauge is ineffective below 10-5 Torr.

Gas Property Gauges measure a bulk property, such as thermal conductivity or viscosity. They are dependent on gas composition and are effective over limited pressure ranges from atmosphere to 10-4 Torr.

Ionization Gauges For high vacuum and UHV measurements, charge collection is used. The residual gas molecules are ionized by electrons and the resulting ion current measured. Although such gauges will ionize vapors as well as permanent gases, their response depends on parameters other than ionization potential, making accurate total pressure measurement difficult in gas mixtures. Ionization gauges cover the pressure range from 10-4 Torr to 10-10 Torr.

The typical arrangement of two gauges covering the range of interest between atmosphere and 1 x 109 Torr leaves a poorly covered band at pressures widely used in sputtering, etching, CVD, etc. Fortunately, the precise measurements needed between 10-1 and 10-3 Torr for reproducible processing can be made by adding a third gauge—the capacitance manometer.

When choosing a gauge, in addition to pressure range, other features should be considered: the gauge’s pumping speed; how it is affected by radiation, magnetism, temperature, vibration, and corrosive gases; and the damage caused by switching it on at atmospheric pressure. These subjects are discussed below in the section "How to Spec in a Gauge", but can also be found in comprehensive vacuum texts such as John F. O’Hanlon’s A User’s Guide to Vacuum Technology.

## Vacuum Gauges

### Mechanical Gauges

A gas’s pressure is the sum of all the individual forces caused by each atom or molecule colliding with a surface at any instant. Mechanical gauges register this total force by monitoring the surface’s movement against the (restoring) force trying to keep the surface in its original place. Because mechanical gauges respond to molecular momentum only, they measure pressures of any gas or vapor. They can be very accurate or inaccurate depending on how the movement is registered.

### McLeod

This gauge, though seldom used, is employed mostly as a primary calibration standard for other gauges. In effect, a large known volume of gas at unknown pressure is captured in a glass bulb and compressed by raising the mercury level until the gas is confined in a small, closed capillary of known volume. Because the ratio between the original and final volumes is known and the final pressure can be measured, the original pressure is calculated by Boyle’s law (P1 x V1 = P2 x V2). McLeod gauges are particularly useful in the 1 Torr to 10-4 Torr range but, because of the compression, cannot be used to measure vapors.

### Bourdon

Bourdon

Typical Specifications:

• Gas Independent
• 1 to 760 Torr
• 10 to 15% accuracy
• Typical Operating Temperature: 0°C to 50°C

When a closed-end, curved, oval cross-section, copper alloy tube is connected to the vacuum, atmospheric pressure bends it to a greater or lesser degree, depending on the internal pressure. The mechanical force moves an indicator needle through a geared linkage. Bourdon gauges are used primarily in high-pressure measurement (most commonly attached to regulators on gas cylinders), but variations are built to indicate pressures from 0" Hg to 30" Hg and are used for freeze drying, “house” vacuum systems, vacuum impregnation, etc., where the major concern is whether vacuum exists rather than its accurate measurement.

### Piezo

Typical Specifications:

• Gas independent
• 0.1 to 1000 Torr
• 1% accuracy
• Typical Operating Temperature: 0°C to 40°C

Piezo-resistive pressure sensors are typically comprised of a silicon wafer that is machined on a surface that makes the crystal into a suitable deflecting diaphragm when subjected to a normal stress (pressure). The thickness of the silicon crystal at its minimum section is the primary factor that determines the pressure range of the gauge from 1,500 to 0.1 Torr. As the diaphragm deflects under pressure, the resistances of the piezo-resistive elements change in value, causing the Wheatstone bridge network to move out of balance. Applying a voltage to this bridge produces an output voltage that is proportional to the applied pressure. If the elements are of equal resistance, there will be a zero output voltage with no pressure differential across the diaphragm.

### Capacitance Manometers

Manometer

Typical Specifications:

• Gas Independent
• Reads in a four (4) decade range below the full scale (F.S.) value (i.e. a 1000 Torr Capactiance manometer = 1000 to 0.1 torr, a 0.1 Torr Capacitance manometer = 0.1 to 1e-5 Torr)
• 0.25 to 0.50% accuracy
• Ambient or heated versions
• Typical Operating Temperature: 0°C to 40°C

The deflection of a thin metal diaphragm separating a known pressure from an unknown pressure is a measure of the pressure difference between the two volumes. In the capacitance manometer, as the name suggests, the deflection is measured using the electrical capacitance between the diaphragm and some fixed electrodes. Capacitance manometers are the most accurate devices for measuring the differential or absolute pressure of all gases (including vapors that do not condense at the gauge’s operating temperature).

Gauge heads are specified by their maximum measured pressure (25,000 Torr down to 1 x 10-1 Torr), with each head having a dynamic range of approximately 104 below that. Accuracies of 0.25% gauge reading are common, with 0.08% available from high-accuracy products.

While gauges have a set operating temperature, capacitance manometers can be configured (prior to purchase) for above ambient operating temperatures. These "heated" units have a heater within the unit that internal heats the diaphragm to a set temperature (i.e. 100°C). This helps to maintain the accuracy of the capacitance manometer as well as helps reduce the condensation of vapors on the diaphragm (pending that the internal temperature compensation of the unit is higher than the process temperature).

### Diaphragm Manometers

Like the capacitance manometer, these gauges use the deflection of a thin metal (or silicon) diaphragm separating a known pressure from an unknown pressure. However, in this type of gauge, the deflection is sensed by a strain gauge attached to the diaphragm. While this limits the minimum measurable pressure to 1 Torr, it does provide a stable, repeatable, device reading pressures up to 1,200 Torr.

### Gas Property Gauges

The thermal conductivity or viscosity value for each specific gas is different and varies non-linearly with pressure. Gas property gauges, presented with the typical vacuum chamber gases, are inaccurate. This, and numerous other inherent error sources, suggest the gauge readings are acceptable for noting repeating pressure events but of little use in measuring absolute pressures.

Thermocouple

### Thermocouple (T/C)

Typical Specifications:

• Gas dependent
• 1e-3 to 760 Torr or 1e-3 to 1 Torr
• Typically passive (need a controller)
• 50% accuracy above 10 Torr, 15% below 10 Torr
• Constant current, variable temperature
• Typical Operating Temperature: 0°C to 100°C

A filament within a thermocouple gauge is heated to a certain temperature via a constant current. As molecules interact with the filament, heat is transferred at a given rate (dependent on the thermal conductivity of the molecules), which causes a temperature differential. This variable temperature is measured and translated into a voltage output, followed by a pressure. The higher the pressure (more molecules), the greater the temperature differential. Due to the design of the gauge and placement of the filament, thermocouple gauges are not generally used for measurements above 10 Torr, as the plethora of molecules tend to coalesce on a given part of the filament, causing an inaccuracy.

Over time, molecules will stick to the filament, causing an inaccurate measurement. Depending on what the gauge has been exposed to, the filament can be cleaned by pouring a small amount of solvent into the flange termination, making contact with the filament (while the gauge is off). This should be done after reviewing the SDS's of the solvent and the molecules used in the process. Once inside, the unit can be swirled around gently (not like a maraca) so that the solvent makes contact with the whole filament, in hopes of dissolving some, if not all, of the molecules that are stuck. The solvent will then be exposed of properly and any residual amounts allowed to evaporate. This can be sped up by turning on the unit, which will provide heat. This cleaning is not guaranteed to work, as some molecules may have corroded the filament. In this case, it is suggested to replace the gauge.

### Pirani

Pirani

Typical Specifications:

• Gas dependent
• 1e-4 to 1000 Torr
• 50% accuracy above 10 Torr, 10% accuracy below 10 Torr
• Constant temperature, variable current
• Typical Operating Temperature: 0°C to 40°C

In a Pirani gauge, two filaments, often platinum, are used as two arms of a Wheatstone bridge. The reference filament is immersed in a fixed-gas pressure, while the measurement filament is exposed to the system gas. Both filaments are heated by the current through the bridge but, unlike most T/Cs, the Pirani gauge does not use constant voltage or power, but constant filament temperature. Gas molecules hitting the immersed element conduct energy away that is detected and replaced by the feedback circuit to the power supply. A Pirani gauge will measure in a similar range as the Thermocouple gauge, but is extended to 1e-4 Torr. This gauge has the same issue as the thermocouple gauge above 10 Torr however.

Over time, molecules will stick to the filament, causing an inaccurate measurement. Depending on what the gauge has been exposed to, the filament can be cleaned by pouring a small amount of solvent into the flange termination, making contact with the filament (while the gauge is off). This should be done after reviewing the SDS's of the solvent and the molecules used in the process. Once inside, the unit can be swirled around gently (not like a maraca) so that the solvent makes contact with the whole filament, in hopes of dissolving some, if not all, of the molecules that are stuck. The solvent will then be exposed of properly and any residual amounts allowed to evaporate. This can be sped up by turning on the unit, which will provide heat. This cleaning is not guaranteed to work, as some molecules may have corroded the filament. In this case, it is suggested to replace the gauge.

Convection

### Convection Enhanced Pirani

Typical Specifications:

• Gas dependent
• 1e-4 to 1000 Torr
• 5% accuracy above 10 Torr, 10% accuracy below 10 Torr
• Constant temperature, variable temperature
• Typical Operating Temperature: 0°C to 40°C

A Convection Enhanced Pirani is very similar to the pirani gauge in that a current is supplied to the filament to maintain a constant temperature. As molecules interact with the filament, heat is removed from the filament and more current is needed to maintain the constant temperature. This current differential is translated into a voltage and then a pressure. This gauge design however allows for the even movement around the filament however due to convection (proper airflow). This minimizes pockets of molecules sticking to a specific portion of the filament, providing a more accurate reading. This helps maintain accuracy above 10 Torr.

Over time, molecules will stick to the filament, causing an inaccurate measurement. Depending on what the gauge has been exposed to, the filament can be cleaned by pouring a small amount of solvent into the flange termination, making contact with the filament (while the gauge is off). This should be done after reviewing the SDS's of the solvent and the molecules used in the process. Once inside, the unit can be swirled around gently (not like a maraca) so that the solvent makes contact with the whole filament, in hopes of dissolving some, if not all, of the molecules that are stuck. The solvent will then be exposed of properly and any residual amounts allowed to evaporate. This can be sped up by turning on the unit, which will provide heat. This cleaning is not guaranteed to work, as some molecules may have corroded the filament. In this case, it is suggested to replace the gauge.

## Ionization Gauges

With relatively minor differences, all ionization gauges use the same principle. Energetic electrons ionize the residual gases—the positive ions are collected at an electrode and the current is converted to a pressure indication. Hot filament gauges (Bayard-Alpert, Schulz-Phelps) use thermionic emission of electrons from a hot wire, while cold cathode gauges (Penning, Inverted Magnetron) use electrons from a glow discharge or plasma.

All ion-gauge measurements are seriously affected by gas composition. For example, a report in J. Vac. Sci. Tech. indicates an ion gauge's relative sensitivity (relative to N2 = 1) is 5 for acetone vapor and 0.18 for He. That is, the same absolute pressure of these pure (gaseous) materials will give a gauge indication differing by a factor of almost 28. Ionization gauges do not give accurate absolute pressure measurements unless recently calibrated with the exact gas mixture that is to be measured.

### Sensitivity

The term relative sensitivity used above should not be confused with the parameter called the 'gauge sensitivity.' The latter comes from the equation relating the gauge's positive ion current (ip) for a given electron emission (ie) at given gas pressure (P): ip = S x ie x P or P = 1/S x ip/ie

The constant of proportionality (S in units of reciprocal pressure) is the 'gauge sensitivity.' Practical (hot filament) ion gauges have gauge sensitivities ranging from 0.6 Torr-1 to 20 Torr-1. This is important when selecting an ion gauge controller because the gauge's sensitivity must be within the controller's available range. The higher the gauge sensitivity, the higher chance of ionizing a molecule.

### Hot Filament Gauges

Ion

Typical Specifications:

• Gas dependent
• 1e-9 to 1e-4 Torr (B-A) or 1e-11 to 1e-4 Torr (Nude UHV)
• 30% accuracy
• Typical Operating Temperature: 0°C to 40°C

The two common hot filament ion gauges, Bayard/Alpert (B-A) and Schulz-Phelps (S-P), differ only in the physical size and spacing of their electrodes. Both have heated filaments biased to give thermionic electrons of 70eV, energetic enough to ionize any residual gas molecules with which they collide. The positive ions formed move to an ion collector held at -150V. The current varies with the gas number density (the number of molecules in each cc), which is a direct measure of gas pressure.

Over time, the hot filament gauge will have collected a plethora of ionized molecules, which need to be removed to maintain accuracy of the gauge. This can be done easily by "degassing" the unit. This is a common practice with any hot filament gauge where a high current is sent through the grid and collector, essentially baking off these portions. This "bake-out" helps to remove these ionized molecules, bringing the unit back to a clean state. Degassing however does not guarantee to remove all molecules, as some will remain stuck to the collector or may have even caused erosion. In cases like this, it is recommended to replace the sensor.

Bayard-Alpert ion gauges have a reasonably linear response from 1e-9 to 1e-4 Torr, with gauge sensitivities from 5 to 20 Torr-1. B-A gauges are available with one or two filaments (the second acting as a spare) and with two filament materials thoria-coated iridium, used in oxygen-rich applications and for 'burn-out' protection if accidentally vented and tungsten, used for lower cost and in residual gases containing halogens.

The standard B-A gauge measures down to 1e-9 Torr. It does not go lower because primary electrons generate soft X-rays when they hit the grid. An X-ray hitting the ion collector electrode releases a photo-electron, which is indistinguishable from positive ions arriving there. Below 1e-9 Torr, photo-electron emission is a large enough fraction of the ion current to distort the pressure reading. Special B-A structures with ultra-thin ion collectors will reach 10-10 Torr and perhaps even into the 10-11 Torr range.

Nude UHV ion gauges act off the same principle as the standard Bayard-Alpert, but allow for a deeper vacuum measurement, 1e-11 to 1e-4 Torr. This change in base pressure is due to the design of the gauge, which includes a basket-style grid design and tight filaments.

### Cold Cathode Gauges

ColdCathode

Typical Specifications:

• Gas dependent
• 1e-10 to 1e-2 Torr
• 30% accuracy
• Typical Operating Temperature: 0°C to 55°C

In the cold cathode gauges, the ionizing electrons are part of a self-sustaining discharge. However, since the CCG has no (thermionic emission) filament, the discharge is initiated by stray field emission or external events (cosmic rays or radioactive decay). At low pressures, this can take minutes and CCGs are usually switched on at high pressure (1e-2 Torr or higher). Once started, the gauge's magnetic field constrain the electrons in helical paths, giving them long path lengths and a high probability of ionizing the residual gas. The ions are collected and measured to determine the gas pressure.

Many electrode geometries have been used—cylinders, plates, rings, rods, in various combinations with the magnetic field direction and strength chosen to maximize the measured current. If the gauge's central or 'end' electrodes are negative, the convention is to call this a magnetron. If the same electrodes are positive, the gauge is called an inverted magnetron.

Magnetron: The initial Penning design (cylindrical anode and end plate cathodes) was neither precise nor accurate and it was replaced by other geometries. However, the name Penning is still used even for magnetrons with central wire or ring cathodes. The operating voltage is limited (typically to ~2kV) to avoid field emission effects that cause increases in the ion current unrelated to pressure. While the newer magnetron designs are satisfactory, they are limited to the top of the high vacuum range and attract little commercial attention.

Inverted Magnetron: Largely due to the development efforts of Redhead and his colleagues, this design works into the UHV pressure range. Its axial central anode enters the cylinder/end plates cathode through voltage guard rings (to prevent field emission affecting the ion current measurement). The anode carries a much higher potential than the normal magnetron (~6kV) and is parallel to the gauge’s magnetic field. Some commercially available inverted magnetron designs have good linearity and operating characteristics down to 1 x 10-11 Torr. However, attempting to start one at such low pressures may take hours or days.

Unlike the hot filament gauge, the cold cathode gauge does not have the filaments or the grid to degas. Instead, some cold cathode gauges can be taking apart, exposing the ionization chamber and inside walls of the gauge. This exposure allows the user to literally scrub the inside walls of the cold cathode gauge, helping to remove molecules that have been "sputtered" onto the wall. This physical cleaning makes a cold cathode gauge generally more rugged than a hot filament gauge.

## Combination Gauges

Combination gauges, aka wide range gauges, are units where multiple technologies are used to provide a vast measurement range than any given, single technology. For instance, the most common wide range gauges are a cold cathode / pirani combination or a hot filament / convection enhanced pirani combination. These types will allow a measurement from UHV to atmosphere. Since these gauges combine different technologies, there is generally a transition region where one technology transitions into the next. The most common region between 10-2 and 10-3, where the pirani / convection enhanced pirani would transition into the cold cathode or hot filament ionization technology. These units are typically found within a single housing, which help minimize clutter and help to automate the pressure measurement, as the user will not need to manually activate a high vacuum technology.

## Residual Gas Analyzers

Special mass spectrometers designed to analyze gases remaining in a vacuum chamber are called residual gas analyzers or RGAs. The wealth of information about experimental or process conditions offered by an RGA makes a permanently attached unit a convenient, often necessary, diagnostic device.

Quadrupole RGAs, named for the four rods used in the mass filter section, are powered by mixed RF/DC voltages. Full operating details are beyond this text but are dealt with adequately in many books, such as Dawson’s Quadrupole Mass Spectrometry And Its Applications and the AVS’s monograph by Drinkwine, et al, Partial Pressure Analyzers and Analysis. The quadrupole analyzer (or sensor head) bolts to the vacuum system. It consists of an ionizer (ion source) connected to the mass filter, which in turn is attached to an ion detector, all mounted on a UHV flange (often a 2-3⁄4" O.D. CF) carrying the feedthroughs for power and signals. The combined RF/DC voltage is generated close to the sensor head. From here, only main power voltage and returning signal information connect to the control chassis and display or desktop PC. In the ionizer, neutral gas atoms and molecules are bombarded with 70eV electrons from a hot filament. The ionized species are extracted into the quadrupole, where only those ions with the appropriate mass-to-charge (m/e) ratio for the applied RF/DC voltages are transmitted. By varying the RF/DC voltage with time, the m/e ratios are scanned and the ion current at each mass is recorded as a spectrum.

Diagnosing vacuum problems with an RGA requires only a collection of fragmentation patterns from which the following may be quickly determined: the presence of air and water leaks; unacceptable levels of active gases such as O2, H2, and H2O, pump oil backstreaming, the presence of Fl or Cl compounds; the regeneration requirements of a cryopump, and the purity of backfill gases. Because an RGA operates at or below 10-4 Torr, high-pressure processes are analyzed with the RGA installed in an auxiliary vacuum system, often a mobile cart moved to various vacuum stations.

## Leak Detectors

Leak detectors are mass spectrometers that detect only helium ions at m/e = 4. Because they are specific, they detect extremely small concentrations of helium in the presence of large quantities of other gases. As the name implies, these devices determine the presence of leaks and help locate them. Excellent leak detection instructions are available in Harris’ book, Modern Vacuum Practice or available as part of our Lesker University curriculum.

The chamber under test and the leak detector are connected via a vacuum-tight tube and the chamber is evacuated using the leak detector’s own vacuum system. Helium is sprayed from a fine nozzle at the chamber’s surface where it displaces the air diffusing through the leak only while the probe is directed at the leak’s position. It is a common misconception that the pressure in the chamber must be low before leak testing can start. In fact, chamber pressures lower than 10-2 Torr are rarely needed. Once the leak detector inlet valve is fully open, further efforts to reduce pressure in the chamber only waste time. During one operator’s 11-year leak-checking experience, for example, most leaks were detected while the leak detector’s inlet valve was only partially cracked. Leaks larger than 1 x 10-5 atm cc/sec. are the most common—“some” leaks were in the 1 x 10-6 atm cc/sec. range, six leaks were in the 1 x 10-7 atm cc/sec. range, two in the 1 x 10-8 atm cc/sec. range, and only one in the 1 x 10-9 atm cc/sec range. Because most leak detectors have a minimum detectable leak rate of 1 x 10-10 atm cc/sec., detection sensitivity is rarely a problem for locating real leaks.