1. Introduction
Vacuum technology needs accurate pressure monitoring for different kinds of purposes, including thermal insulation and correct operation of manufacturing systems. Applications might vary from simply monitoring all or parts of a pump down cycle, carefully measuring and controlling a stringent target pressure, or supervising a critical industrial process. In the semiconductor industry, for instance, this enabled dramatic progress on several frontiers of contemporary electronics such as lifetime, precision, and reproducibility of devices that are currently ubiquitous. This capability originates essentially from better production and process control relying on, amongst others, accurate pressure sensors. However, the diversity of pressure ranges and of the required accuracies annihilates the possibility of implementing a single type of gauge that will be of use to all requirements. That is why several types of vacuum sensors based on different operating principles are commercially available operating from as low as 10
−10 Pa up to atmospheric pressure and far above. Nonetheless, a cheap sensor that would extend into the high vacuum range and tolerate atmospheric or even higher pressure without switching is highly desirable and not commercially available.
Table 1 shows the degree of vacuum with respect to pressure.
Conventional systems for measuring sub-atmospheric pressures include mechanical manometers, ionization gauges, and heat conductivity manometers. Mechanical manometers use some solid deflectable objects [
1] such as tubes, plates, or diaphragms to measure pressure. The system whose pressure is to be measured is connected to the deflecting object. Any change in pressure causes the object to deflect and this deflection is mechanically amplified using a suitable gear and linkage mechanism, indicated on a calibrated dial. Ionization gauges are vacuum gauges in which the pressure is indicated by the ionization current between two specified electrodes at a prescribed voltage [
2].
A heat conductivity pressure gauge is based on a heating element (wire, plate, or chip) inserted inside a chamber that transfers thermal energy to any gas molecules that come into contact with it, and that energy is again transferred to the walls of the chamber. With continuous motion of the gas molecules, a thermal equilibrium is reached as long as the number of gas molecules, i.e., the pressure, remains constant.
If, however, the pressure changes while the wire is being heated from a constant power source, a new thermal equilibrium is reached, and the temperature of the wire changes to indicate the new number of gas molecules that can carry heat away from it.
This means that the temperature of the wire can be used as an indication of the pressure inside the chamber. This is the basic principle of all thermal conductivity gauges to which Pirani sensors belong. They are known for their unsurpassed accuracy in the rough vacuum area. In practice, the heated element is an electrical resistance inserted inside a Wheatstone bridge. Therefore, the temperature variation is transduced into a precise voltage variation.
2. Theoretical Background
The Pirani principle operates when a heated element is inserted inside a vacuum chamber. When the Pirani element is supplied with a constant heating power P, it will transfer heat to its surroundings and reach an equilibrium temperature characteristic of the pressure. The Pirani element transfers heat by three means:
Solid conduction from the Pirani sensor to its carrier; the value of the thermal conductance depends on the geometry of the sensor’s carrier and its thermal conductivity.
Radiation from the sensor’s hot surface to the surface of the chamber; its value depends on the emissivity and the exterior surface of the sensor.
Solid to gas conduction from the sensor to the gas molecules that contact it, which effectively depends on pressure.
The equilibrium equation can be expressed as [
3]
where
is the heating power supplied to the sensor,
is the equilibrium temperature,
is the initial temperature,
is the radiative thermal conductance,
is the solid thermal conductance of the sensor’s carrier, and
is the gas conductance.
where
is the emissivity of the sensor exterior surface,
is the Stefan–Boltzmann constant, and
is the sensor’s emitting surface.
In the case where the sensor is suspended by one cylindrical wire, the solid conductance can be expressed as [
4]
where
is the thermal conductivity of the wire material,
is the radius of the wire, and
is the length of the wire. The gas conductance is expressed as follows [
3]:
with
the thermal conductivity of the gas at pressure
, and
the sensor’s surface.
where
represents the thermal conductivity of the gas at atmospheric pressure,
is the energy accommodation coefficient of the gas molecules,
is the pressure-dependent mean free path of the gas molecules, and
is the distance between the sensor’s heated surface and the cold ambient surface.
The change in pressure vs. wire temperature remains fairly linear over a pressure range of about 0.01 Pa to 100 Pa depending on the wire dimensions. Below this range, heat transfer is dominated by radiation from the wire’s surface and conduction from the wire to its carrier [
3,
5,
6]. Above this range, heat transfer is ruled by thermal convection [
7]. In addition to that, other heat transfer mechanisms, i.e., solid conduction from chip to carrier and radiation, overwhelm the pressure-dependent gas heat transfer.
Figure 1 shows the ratio of gas conductance over total conductance versus pressure (obtained from Reference [
3]). It can be seen that, below 10
−2 Pa, the gaseous conductance represents less than 10% of the total conductance and, above 100 Pa, it represents more than 99% of the total conductance.
Figure 1 shows the actual values of the gas conductance and the total conductance computed from Reference [
3].
Figure 2 depicts the gaseous heat transfer over the total heat transfer for the device introduced in Reference [
3].
A wide choice of sensors based on the Pirani principle is available in the literature. A list of references is given in
Table 2, which also includes the measurement principles and the range of the sensors. The devices are often made using microfabrication and semiconductor technologies [
3,
5,
8]. These sensors address different pressure ranges: from two decades of pressure up to seven decades of pressure for one single device [
5].
However, systematic investigations of Pirani wires identified limits of the process corresponding to saturation due to the pressure dependence of thermal conductivity in high vacuum and close to atmospheric pressure [
3,
5,
6].
A high vacuum process will need to be provided with gauging that follows the pump down cycle from atmospheric pressure through the volume zone and into the dry down zone. A thermal conductivity gauge can follow the pressure all the way through the volume zone; however, when the system goes into the dry down zone below about 10−2 Pa, where water vapor becomes the predominant residual gas, an ionization gauge becomes necessary. Usually, with the exception of some extended range gauge modifications, these two gauges together can be used to cover the full pump down cycle. This is why many electronic gauge controllers combine both types of gauges in the same unit. For instance, vacuum hybrid sensors such as Pirani Bayard–Alpert and Pirani–Magnetron increase the measurement range from atmospheric to the ultra-high vacuum. Consequently, the revived development of hybrid sensors combining two or more operating principles received much attention recently, since many combined Pirani gauges are commercialized (Canon Cold Cathode Pirani Gauge M-360 CP or BCG 450 from INFICON, for instance). In the present case, two different measurement techniques will be combined, namely the miniaturized Pirani principle and Surface Acoustic Waves (SAW).
Surface acoustic waves are elastic waves that propagate on the surface of piezoelectric crystals [
42]. Their propagation frequency and elastic constants are sensitive to the surrounding environment´s properties including temperature, pressure, and humidity. SAW devices and sensors are made of a piezoelectric crystal substrate with an interdigitated transducer (IDT) on its surface that converts voltage or other signals to SAW back and forth. An interdigitated transducer consists of a series of etched metallic electrodes whose dimensions determine the properties of the waves that they will generate. SAW devices offer opportunities for wireless operation, as well as self-heating effects [
43,
44]. Having an interdigitated transducer printed on their surface enables them to send and receive waves.
Figure 3 shows the principle structure of a SAW device. The SAW IDT is connected to an antenna, generating surface waves when a radio-frequency pulse signal is received. A series of reflectors is available. Reflected waves are received by the transducer, which makes the antenna radiate a return signal with characteristics determined by the reflectors. The reflector configuration can also be used for identifying the device. Many Industrial, Scientific and Medical radio bands are used to operate SAW devices, among which the 2.45-GHz used for the presented device. SAW devices can be operated passively with no need of power supply. Wireless operation is possible because the device can give relatively long delays, preventing overlap between interrogation signal and return signal.
Thanks to their sensitivity to pressure, SAW devices can also be used as pressure sensors. Pressure-induced bending of the piezoelectric crystal membrane generates a change in wave speed that is directly correlated to the pressure. This effect has good sensitivity over a restricted pressure range of one to two decades. Indeed, beyond two decades of pressure, the bending of the crystal will be too large and causes destruction of the crystal [
42].
5. Conclusions
The vacuum sensor presented here is new in the sense that it is extending the sensing range, while operating completely wirelessly. The performance was not tested in real-world applications, but it contains innovations compared to conventional Pirani wires or SAW sensors or even the SAW–Pirani sensors presented in the literature. The prototype still needs to be assembled and tested, which will state the actual performance of the sensor. Previous work on SAW–Pirani sensors was studied, and design directions such as the reduction of the thickness of the chip, the increase of the surface-to-volume ratio, and the increase of the operating frequency to obtain a higher thermal sensitivity of the chip were taken into account.
This work presents an innovative compact wireless SAW–Pirani sensor for microscopic and macroscopic applications. The combination of both surface acoustic waves and heat transfer in gases allows extending the sensing range of a vacuum sensor and to operate this sensor wirelessly, which can be advantageous in vacuum technology. The results given by simulation predict a sensitivity of 0.1 K for a pressure variation of 10−4 Pa, which could easily be detected by the available instruments in the lab. Furthermore, it is expected that further investigations concerning the modus operandi of the sensor will improve the sensitivity of the sensor in high vacuum and close to atmospheric pressure. For instance, applying pulsed heating instead of continuous heating could increase the sensitivity of the resonance frequency of the sensor to the pressure through the whole target range. A prototype of the described sensor design is currently being assembled and tested. The best modus operandi of the sensor still needs to be determined.
Further work, therefore, includes the investigation of the transformation of SAW signal in vacuum and its dependence on pressure. To support that, Sharipov et al. reported interaction between acoustic waves and thermal waves in vacuum [
50].