# 3.1.2 Indirect, gas-dependent pressure measurement

At extremely low pressures, the influence of the force on a diaphragm becoming negligible. This is why pressure is determined by means of the molecular number density, which is proportional to pressure. The status equation that applies for an ideal gas is: p = n · k · T (Formula 1-5). Thus, pressure is proportional to molecular number density where temperature T is identical. This formula is satisfied for the pressures that prevail in vacuum technology. Various physical effects, such as thermal transfer, ionization capacity or electrical conductivity, are measured for this purpose. These values are a function of both pressure as well as molecular weight. This results in a pressure measurement that produces differing results for different heavy gases

## Pirani (thermal transfer) vacuum gauges

Figure 3.3: Operating principle of a Pirani vacuum gauge
Source: Inficon 2000-2001 Catalog, p. 82

A Pirani vacuum gauge utilizes the thermal conductivity of gases at pressures p of less than 1 mbar. Wire (usually tungsten) that is tensioned concentrically within a tube is electrically heated to a constant temperature between 110 °C und 130 °C by passing a current through the wire. The surrounding gas dissipates the heat to the wall of the tube. In the molecular flow range, the thermal transfer is the molecular number density and is thus proportional to pressure. If the temperature of the wire is kept constant, its heat output will be a function of pressure. However it will not be a linear function of pressure, as thermal conductivity via the suspension of the wire and thermal radiation will also influence the heat output.

The limiting effects are:

• Thermal conductivity will not be a function of pressure in the range of 1 mbar to atmospheric pressure (laminar flow range)
• The thermal conductivity of the gas will be low relative to the thermal transfer over the wire ends at pressures below 10-4 mbar, and will thus no longer influence the heat output of the wire. Consequently, the measurement limit is approximately at 10-4 mbar
• Thermal radiation will also transfer a portion of the heat output to the wall of the tube

Figure 3.4 shows the different curves for various gases between 1 mbar and atmospheric pressure. While good linearity can still be seen for nitrogen and air, significant deviations are indicated for light (He) and heavy gases (Ar). In the case of gas-dependent measuring methods, it is also common to speak of the nitrogen equivalent that is displayed.

Figure 3.4: Pirani vacuum gauge curves

## Cold cathode ionization vacuum gauges

Cold cathode ionization vacuum gauges essentially consist of only two electrodes, a cathode and an anode, between which a high voltage is applied via a series resistor. Negatively charged electrons leave the cathode because of the high voltage, moving at high velocity from the cathode toward the anode. As they travel this path, they ionize neutral gas molecules, which ignites a gas discharge. The measured gas discharge current (Figure 3.5) is a parameter for pressure. However only few molecules are ionized with straight electron trajectories, which results in lower sensitivity and interruption of the gas discharge at approximately 1 mbar. A design that avoids this disadvantage is the inverted magnetron after Hobsen and Redhead. A metal pin (anode) is surrounded by a rotationally symmetrical measurement chamber (cathode) (Figure 3.5). An axially magnetized, cylindrical, permanent-magnet ring is placed on the exterior of the measurement chamber to generate a magnetic field within the chamber.

Figure 3.5: Design of an inverted magnetron

The electrons travel through the magnetic field on spiral trajectories (Figure 3.6). The electron paths extended in this manner increase the probability of collisions with the gas molecules and ensure that sufficient ions are generated to maintain the gas discharge, even at pressures of less than 1 mbar. The pressure reading will depend upon the type of gas in question due to the different ionization probabilities of the various gases. For example, a lower pressure will be indicated for helium than for air.

Figure 3.6: Operating principle of an inverted magnetron
Source: Jousten (publisher) Wutz, Handbuch Vakuumtechnik, Vieweg Verlag

Cold cathode vacuum gauges can be easily contaminated under the following conditions:

• If the device is activated at pressures p of more than 10-1 mbar
• Argon is often used for applications in sputtering systems. This results in sputtering of the cathode, as well, which can cause short circuits and thus failures of the gauges
• Gases are also gettered on the surfaces of the cathode. This produces a pumping effect that will falsify the measurement signal

When installing the gauge in a vacuum system, it is necessary to take the magnetic field into consideration, as it can interfere with sensitive equipment.

## Hot cathode ionization vacuum gauges

In this case, as opposed to cold cathode ionization vacuum gauges, electrons are generated with the aid of a heated cathode. Figure 3.7 shows the design of a gauge after Bayard-Alpert. A thin wire is arranged in the middle of the cylindrical, lattice-shaped anode; this wire serves as the ion collector. A voltage of approximately 100 V is applied between anode and cathode. This accelerates all emitted electrons toward the anode. The emission current is measured in the anode circuit, which can be set by means of the heat output of the cathode. As they travel toward the anode, gas molecules that strike the collector, which has the potential of the cathode, are ionized by electron collisions. The measured collector current is a parameter for pressure. Since the emission current is proportional to the ion current, it can be used to set the sensitivity of the gauges.

Figure 3.7: Design of a Bayard-Alpert vacuum gauge

Pressures can be accurately measured to 1 · 10-10 mbar with Bayard-Alpert sensors

Measuring errors result from the pumping effect of the sensor, as well as from the following two limiting effects:

• X-ray braking radiation. Electrons that strike the anode cage cause x-rays to be emitted, some of which strike the collector. This x-ray effect causes the collector to emit photoelectrons that flow off toward the anode. The resulting photoelectron current increases and falsifies the pressure-dependent collector current. Consequently the collector wire should be selected as thin as possible so that it collects only little x-ray radiation.
• ESD ions ESD (electron stimulated desorption) means that gas molecules deposited on the anode cage are desorbed and ionized by electrons. These ions also increase the pressure-proportional ion current.

A hot cathode vacuum gauge also measures independently of the type of gas in question. However the measurement results are significantly more accurate than those obtained with a cold cathode ionization vacuum gauge.

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