WO2012103942A1

WO2012103942A1 - Sensor arrangement

Info

Publication number: WO2012103942A1
Application number: PCT/EP2011/051479
Authority: WO
Inventors: Pascal Nicolay; Werner Ruile; Xavier PEROIS
Original assignee: Epcos Ag
Priority date: 2011-02-02
Filing date: 2011-02-02
Publication date: 2012-08-09
Also published as: DE112011104825T5; DE112011104825B4

Abstract

The present invention concerns a sensor arrangement (SAN) for measuring a pressure of an environment comprising an atmosphere. The sensor arrangement comprises a resonator (RES), a heating element (HE) that is thermally coupled to the resonator (RES), and means to measure the resonance frequency of the resonator (RES). The present invention further concerns methods to measure a pressure of an environment comprising an atmosphere using this sensor arrangement.

Description

Sensor arrangement

The present invention concerns a sensor arrangement for measuring a pressure of an environment comprising an

atmosphere and corresponding methods to measure a pressure an environment comprising an atmosphere.

During manufacturing of MEMS devices, vacuum chambers of various sizes are used in clean-rooms all across the world. Contamination of the vacuum and leak detection are important issues in this environment. There is a big need for precise and fast monitoring of the pressure in every vacuum chamber.

During manufacture of a MEMS device, a vacuum chamber can be connected to a processing machine, then opened. The pressure inside the processing machine should equal the pressure inside the vacuum chamber. Otherwise, cross-contamination can occur when gas move from the machine into the vacuum chamber and vice-versa. A sensor arrangement that is included into the vacuum chamber allows to monitor the pressure inside the vacuum chamber. In particular, the sensor arrangement allows to verify that pressure inside the vacuum chamber equals the pressure inside the processing machine prior to the opening of the vacuum chamber.

Moreover, leaks can occur in a vacuum chamber and these leaks can also cause a contamination of the vacuum chamber. If the vacuum chamber comprises a pressure sensor, the contamination can be detected before the vacuum chamber is connected to a manufacturing facility. Otherwise, a contaminated vacuum chamber can contaminate the whole facility. Sensor arrangements to monitor a pressure are also commonly used as part of a processing unit. They allow to monitor the processing. A typical application is a vacuum chamber that is pumped empty, e.g. for manufacturing a semi-conductor device. The sensor arrangement monitors the pressure inside the chamber and determines when a sufficient vacuum has been reached so that the next processing step can be started.

Especially in a mass production, a sensor arrangement with a fast response time is crucial for an efficient monitoring.

Nowadays, Pirani sensors or thermocouple-based gauges are used for this purpose. In both cases, the gauge use the pressure dependence of the thermal conductivity of a gas to infer pressure there from. In the case of thermocouple-based gauges, sensing is basically done by plunging a piece of heated matter inside a gas and then monitoring its pressure- dependent equilibrium temperature, using thermocouples. Pirani gauges are based on the same measurement principle.

Here, the heated element is a hot wire which constitutes one arm of a Wheatstone bridge. The wire loses heat to the gas as the gas molecules collide with the wire removing heat. If the gas pressure is reduced, the number of molecules present will fall proportionately and the wire will rise in temperature due to the reduced cooling effect. This breaks the balance of the bridge because the wire resistivity changes with the temperature. A feed-back loop on the heating power then allows for increasing or decreasing the wire temperature in order to keep it constant. Once the bridge balance is

restored, the pressure can be deduced by measuring the injected heating power. Further, EP 1944595 A2 discloses a sensor arrangement, wherein a heated SAW filter is used as a sensor element.

However, this sensor arrangement suffers from a slow response time as the temperature capacity of the device is rather big.

It is an object of the present invention to provide a sensor arrangement that is small enough to be used in a miniature vacuum, e. g. a very small cleanroom or vacuum chamber, and that provides a fast response time. It is a further object of the present invention to provide a sensor arrangement that can be used over a wide pressure range.

A sensor arrangement according to claim 1 and a method to measure the pressure of an environment comprising an

atmosphere according to one of claims 19, 21 or 22 provide solutions for these objects. The dependent claims disclose advantageous embodiments of the present invention.

The present invention provides a sensor arrangement for measuring a pressure of an environment comprising an

atmosphere. The sensor arrangement comprises a resonator that is heated during a measurement and means to measure the resonance frequency of the resonator. The present invention is based on the idea that the thermal conductivity of gases is strongly and almost linearly

dependent on the pressure in a certain pressure range. This pressure range is called Knudsen regime. The Knudsen regime is characterized in that pressure is low enough so that gas molecules do not collide with each other. Here, thermal conduction happens when a gas molecule collides with the heated resonator, then the gas molecule collides with the walls of the vacuum chamber. Accordingly, there is a direct heat transmission from the resonator to the walls. Therefore, in Knudsen regime, there is no conduction through gas nor convection. In this regime, thermal conduction is directly proportional to the number of molecules, that is to the pressure.

Preferably, a resonator is chosen wherein the resonance frequency of the resonator is highly temperature dependent. When a gas molecule collides with the resonator, the

resonator is cooled. Accordingly, in an environment with a high pressure, there will be more thermal conduction between the resonator and the gas. Further, the sensor arrangement comprises means to measure the resonance frequency of the resonator. A pressure change causes a change in the thermal conduction between the resonator and the gas. This causes a corresponding change of the resonator operating temperature. Therefore, measuring the temperature-dependent resonance frequency of the resonator exposed to a gas atmosphere allows deducing the pressure of the gas atmosphere.

During a measurement the resonator is heated up. For this purpose, the sensor arrangement can comprise a heating element that is thermally coupled to the resonator. Alternatively, an RF power can be applied to the resonator. Due to energy losses inside the resonator, the resonator is heated by dissipation energy. In a typical SAW resonator, dissipation energy increases the temperature of the resonator by 30°K per applied Watt. However, it is possible to increase this value up to 50 to 80 °K/W. This effect is called self- heating. The self-heating is higher if more power is injected into the resonator. The self-heating can also be increased if the dimensions of a SAW resonator are reduced and the applied power is constant.

Accordingly, the resonator can be heated by a heating element that is thermally coupled to the resonator or by using the self-heating . Heating by a thermally coupled heating element and by self-heating can also be combined in one sensor arrangement . The temperature-dependency of the resonance frequency of a resonator, e. g. a resonator based on acoustic waves or a MEMS resonator, is discussed based on the example of a surface acoustic wave (SAW) resonator. In a SAW resonator, the wavelength of an acoustic wave at the resonance frequency is defined by the distance between two neighboring fingers in an Inter Digital Transducer (IDT) deposited on a

piezoelectric crystal. If the SAW device is heated up the crystal will expand, causing a longer distance between two electrode fingers. This equals a longer wavelength of the acoustic wave and therefore a smaller resonance frequency. On the other hand, cooling the SAW device increases the

resonance frequency as the device contracts.

Further, the resonance frequency of a SAW resonator is proportional to the celerity of the acoustic wave inside the resonator. If the resonator is heated the elasticity

coefficients of its constituting material change. In general, the material becomes less stiff. This causes a decrease in the celerity of the acoustic wave and therefore a further decrease of the resonance frequency. Cooling will make the resonator material more stiff, thereby increasing the

celerity and the resonance frequency. The sensor arrangement according to the present invention is sensitive over a pressure range that ranges from O.OlmTorr to multiples of the atmospheric pressure. However, as will be discussed in the following, the sensitivity of the sensor arrangement changes in this pressure range.

The sensitivity of a sensor arrangement according to the present invention is high in medium vacuum, almost zero in a rough vacuum, and small near atmospheric pressure. A medium vacuum is characterized thereby that it is a Knudsen regime. Typically, the pressure range of a medium vacuum ranges from 1 mTorr to 25 Torr. However, means to extend the medium vacuum character to higher pressure ranges will be discussed in the following. A rough or low vacuum is defined thereby that the thermal conductivity does not depend on pressure anymore. In an atmospheric pressure, convection is the dominant form of thermal conductivity. Here, the thermal conductivity again depends on pressure. The sensor arrangement has the highest sensitivity in a high or medium vacuum which corresponds to a pressure range of 0.01 mTorr to 25 Torr. Means to extend the medium vacuum character to pressures up to 50 Torr and above will be discussed later on. In this pressure range, the gas is in a Knudsen regime so that there is no thermal conduction by convection. There is also no thermal conduction through gas, that is no thermal gradient from resonator surface to the surrounding chamber walls. For a pressure range of 50 Torr to 500 Torr, the sensitivity of the sensor arrangement is based on the hydrostatic

pressure sensitivity. The atmosphere of the environment exerts a pressure on the resonator and thereby makes the elastic coefficient of its constituting piezoelectric

material change. In general, a higher pressure makes the resonator more compact and harder. In a SAW resonator, this causes a geometrical contraction of the wavelength and a change in the celerity of the acoustic wave. This causes therefore a change in the resonance frequency. This change can again be monitored and the pressure can be deduced there from. However, the effect of the hydrostatic pressure in rough vacuum is smaller compared to the effect of thermal conductivity in Knudsen regime. Accordingly, the sensitivity above 50 Torr is smaller than the sensitivity between 0.01 mTorr and 50 Torr.

Further, the sensor arrangement according to the present invention can also be used in an environment of atmospheric pressure, but the sensitivity will again be smaller.

In one embodiment, the means to measure the resonance

frequency of the resonator comprises means to apply an RF signal to the resonator and means to measure the impedance, the admittance or the S-parameters of the resonator at the frequency of the applied RF signal. The impedance is minimal at the resonance frequency. In one embodiment, the resonator is a surface acoustic wave (SAW) resonator or a bulk acoustic wave (BAW) resonator. A BAW resonator can be a (Thin) Film Bulk Acoustic Wave

resonator (FBAR) , a high-overtone bulk acoustic resonators (HBAR) or a surface mounted resonator (SMR) .

In particular, the resonator can be a one-port SAW resonator. SAW resonators provide numerous advantages, like very good reproducibility, a high resonance-frequency, a high quality factor and a high resolution.

To improve the sensitivity, the thermal resistance of the resonator to the atmosphere should be as small as possible, whereas the thermal resistance of the resonator to a

substrate should be as high as possible. Further, the thermal capacity of the sensor arrangement needs to be as small as possible in order to allow for an as fast as possible

response time. Therefore, it is preferable to flip-chip mount the SAW resonator on a substrate. Here, the arrangement can provide a chip-sized-package (CSP) . A chip-sized-package requires less chip material compared to other modules. A small amount of chip material is equivalent to a small thermal capacity.

A flip-chip mounted SAW resonator can be fixed to a substrate by bumps. Thereby, an intermediate gap "layer" between the SAW resonator and the substrate is defined. The intermediate gap layer comprises gas at the same pressure as the

environmental atmosphere. The substrate may be adapted in size to the SAW resonator. The heating element and the electrode fingers of the SAW resonator can be placed on the surface of the chip and next to the intermediate gap layer. Accordingly, the heat exchange between the SAW resonator and the gas happens in this intermediate gap layer. The

intermediate gap layer can be in pressure contact with the atmosphere . The thickness of the intermediate gap layer is defined by the height of the bumps. Typically, a bump is about 60 μιη high. If the mean free path of gas molecules is bigger than the dimensions of a chamber containing the gas, gas will be in Knudsen regime. Accordingly, thermal conduction is pressure- dependent in this case. Therefore, by reducing the size of the bumps, the thickness of the intermediate gap layer can be reduced to about 5 to 10 μιη which allows extending the

Knudsen regime to higher pressures.

In one embodiment, the thickness of the intermediate gap layer can be smaller than the mean free path of a gas molecule in a pressure range from 0.01 mTorr to 50 Torr.

Accordingly, the conditions providing a medium vacuum

character can be extended in the intermediate gap layer up to pressures of 50 Torr.

In a pressure range above 50 Torr, the sensor arrangement is sensitive based essentially on its hydrostatic pressure sensitivity until pressure becomes high enough for convection to start thereby restoring pressure-dependant thermal conductivity .

The intermediate gap layer between the SAW resonator and the surface of the substrate needs to be in direct contact to the atmosphere of the environment. A chip that is flip-chip mounted on a substrate can be covered by a protection layer, providing a hermetic sealing of the chip. However, in this case, the intermediate gap layer is not in contact with the environment. Therefore, in one embodiment, the substrate can comprise a hole connecting the intermediate gap layer and the environment. The protection layer provides mechanical robustness of the sensor arrangement. Alternatively, if there is no protection layer covering the chip the substrate does not necessarily comprise a hole. In one embodiment, the chip is made of Lithium niobate, of the so-called black-yellow kind. It is preferable that the resonator has a high temperature dependency of its resonance frequency. Lithium niobate shows a high temperature

coefficient of frequency (TCF) of roughly 100 ppm/°K.

Alternatively, the chip can be made of Lithium tantalate, showing a TCF of about 50 ppm/°K. Lithium tantalate is also preferably of the black-yellow kind. The high temperature sensitivity of LN- or LT-based high-frequency SAW devices allows a more precise pressure measurement with an inventive sensor arrangement compared to resistivity-based Pirani sensors . The absolute sensitivity of the sensor arrangement increases linearly with the used frequency. For a one-port SAW

resonator, frequencies up to 3 GHz are easily achievable. Although more difficult to achieve, resonance frequencies up to 8GHz have already been demonstrated. In one embodiment, the SAW resonator has a resonance frequency of 2.45 GHz, to work in the 2.4GHz ISM-band.

In one embodiment, the sensor arrangement comprises means to readjust the voltage that is applied to the heating element so that the resonator has a constant temperature.

At the beginning of a measurement, a certain start voltage can be applied to the heating element. Further, a desired resonance frequency of the resonator is chosen. If the measured resonance frequency is below the chosen resonance frequency, the heating voltage that is applied to the heating element is decreased. A lower temperature of the resonator infers a contraction of the resonator which equals a smaller wavelength and further a higher wave celerity. Thereby the resonance frequency is increased. Alternatively, if the measured resonance frequency is higher than the chosen resonance frequency, the heating voltage that is applied to the heating element is increased, thereby decreasing the resonance frequency of the resonator. The resonance frequency of the resonator can be tuned as described above by tuning the applied heating voltage until the resonance frequency equals the chosen frequency. This also infers that the resonator and the atmosphere have a certain equilibrium temperature .

Accordingly, the sensor arrangement can comprise means to determine the applied heating voltage and means to tune the voltage that is applied to the heating element so that the resonator has a constant temperature. As the voltage that is needed to heat the resonator to a constant temperature depends on the amount of heat exchange between the resonator and the gas molecules of the environment, determining the applied voltage easily gives away the pressure of the

environment .

Alternatively, if the heating is based on self-heating by energy dissipation, the sensor arrangement can comprise means to readjust the RF power that is applied to the resonator.

At the beginning of a measurement, a certain start RF power can be applied to the resonator. Further, a desired resonance frequency of the resonator is chosen. If the measured

resonance frequency is below the chosen resonance frequency, the RF power that is applied to the resonator is decreased. Accordingly, the heating due to energy dissipation in the resonator is decreased and thus the resonance frequency is increased. Alternatively, if the measured resonance frequency is higher than the chosen resonance frequency, the RF power that is applied to the resonator is increased, thereby decreasing the resonance frequency of the resonator. The resonance frequency of the resonator can be tuned as

described above by tuning the applied RF power until the resonance frequency equals the chosen frequency. This also infers that the resonator and the atmosphere have a certain equilibrium temperature.

Accordingly, the sensor arrangement can comprise means to determine the applied RF power and means to tune the RF power that is applied to the resonator so that the resonator has a constant temperature. As the RF power that is needed to heat the resonator to a constant temperature depends on the amount of heat exchange between the resonator and the gas molecules of the environment determining the applied RF power easily gives away the pressure of the environment. In an alternative embodiment, a constant voltage is applied to the heating element. Here, measuring the resonance

frequency of the resonator allows to directly deduce the pressure of the environment. In one embodiment, the resonator can be a suspended MEMS resonator. In particular, the resonator can be a MEMS ring, a MEMS fork or a suspended MEMS plate. The resonance frequency of MEMS resonators is also temperature-dependent. Accordingly, the resonance frequency of the suspended heated MEMS resonator can be monitored. This allows to deduce the temperature of the resonator and further to deduce the pressure of the environment as the heat exchange between resonator and environment is pressure-dependent.

In one embodiment, the heating element is a meander-shaped conducting structure.

Moreover, the present invention concerns three methods to measure the pressure of an environment comprising an

atmosphere with a sensor arrangement as previously discussed.

The first method comprises the steps of exposing the sensor arrangement to the environment, applying an RF signal to the resonator, measuring the impedance of the resonator, and deducing the pressure of the atmosphere from the impedance of the resonator.

If the sensor arrangement comprises a heating element, the method further comprises the step of applying a voltage to the heating element.

The resonator can be connected to a network analyzer. The network analyzer applies RF signals at different frequencies to the resonator and monitors the impedance of the resonator for each frequency. This allows to track the resonance frequency of the resonator.

The second method comprises the steps of exposing the sensor arrangement to the environment, applying an RF signal to the resonator, applying a heating voltage to the heating element, measuring the impedance of the resonator, readjusting the heating voltage so that the resonator has a certain

impedance, and deducing the pressure of the atmosphere from the known heating voltage. Again the resonator can be connected to a network analyzer that allows tracking the resonance frequency as discussed above .

The third method comprises the steps of exposing the sensor arrangement to the environment, applying an RF signal to the resonator, measuring the impedance of the resonator,

readjusting the applied RF signal so that the resonator has a certain impedance, and deducing the pressure of the

atmosphere from the known heating voltage.

The impedance can be measured by connecting the resonator to a network analyzer. The network analyzer determines the impedance for RF signals with different frequencies that are applied to the resonator.

In general, the pressure can be deduced based on a given parameter, like impedance at a certain frequency or heating voltage for a certain frequency, with the help of look-up tables. A look-up table can give the pressure of the

atmosphere if all parameters are known. Alternatively, the pressure can be deduced after measuring a certain parameter by calculation based on a model describing the temperature dependency of the resonance frequency.

The present invention will become fully understood from the detailed description given herein below and the accompanying schematic drawings. In the drawings:

FIG. 1 shows a sensor arrangement according to the present invention . FIG. 2 shows an alternative embodiment of the sensor arrangement according to the present invention.

FIG. 3 shows a top view of a CSP SAW resonator.

FIG. 4 shows a close-up view of a one-port resonator and a heating element.

FIG. 1 shows the cross section of a sensor arrangement SAN according to the present invention vertical to a substrate plane. The sensor arrangement SAN comprises a chip CH that is flip-chip mounted on a substrate SU. The substrate SU is a multi-layer substrate. The substrate SU comprises dielectric ceramic layers CL and structured metallization layers. The metallization layers ML are contacted with each other by via holes VH. The substrate SU further comprises contact pads CP which are placed on the surface of the substrate SU facing to the chip CH. Bumps BU are placed above the contact pads CP. The contact pads CP may be provided by the top surface of the metallization of the via.

Further, the chip CH comprises bumping pads BP which are on the bottom surface of the chip CH facing the substrate SU. The bumping pads BP of the chip CH are contacted to the contact pads CP of the substrate SU by the bumps BU.

The chip CH is an SAW resonator RES and further comprises a heating element HE. The electrodes of the SAW resonator RES and the heating element HE are placed on the surface of the chip CH that is facing to the substrate SU. Between the chip CH and the substrate SU, there is an intermediate gap layer IL containing gas molecules MOL . The height of the intermediate gap layer IL is defined by the height TH of the bumps BU.

The gas in the intermediate gap layer IL and the gas in the environment of the sensor arrangement SAN are in physical contact to each other. The heating element HE heats up directly the SAW resonator RES. In the intermediate gap layer IL, a heat exchange between the SAW resonator RES and the gas molecules MOL happens when a gas molecule MOL collides with the SAW resonator RES. If the pressure increases, more gas molecules MOL will collide with the SAW resonator. Therefore, a pressure increase causes a temperature decrease of the SAW resonator RES. As already discussed, a linear temperature dependency of the resonance frequency of the SAW resonator RES extends only over a certain pressure range. This is the so-called Knudsen regime. Further, at pressures near atmospheric pressure, the SAW resonator RES also shows a pressure-dependent

characteristic.

Normally Knudsen regimes comprise conditions wherein the mean free path of a gas molecule MOL is bigger than the dimensions of the chamber in which the gas molecules MOL are placed. As the thickness TH of the intermediate gap layer IL is rather small, the Knudsen regime can extend to higher pressures. For a bump height of 5 to 10 μιτι, the Knudsen regime can extend up to pressures of 50 Torr. FIG. 2 shows a sensor arrangement SAN in an alternate

embodiment in a side-view. Here, a protective layer PL is laminated over the chip and seals to the surface of the substrate in an edge portion surrounding the chip. The protective layer PL provides mechanical stability and

robustness. However, the protective layer PL isolates the intermediate gap layer IL between the chip CH and the

substrate SU from the environment above the chip CH.

In the second embodiment, a hole HO is thus provided in the substrate SU to connect the environment and the intermediate gap layer IL. The diameter of the hole HO is chosen as small as possible.

FIG. 3 shows a top view of a SAW resonator RES. The SAW resonator RES comprises two electrodes El, E2, each having a number of electrode fingers interdigitally overlapping each other in an acoustic track. The acoustic track is located as far away as possible from the bumps BU as the bumps BU are heat sinks.

A heating element HE is placed in the middle of the SAW resonator RES. FIG. 4 shows a more detailed presentation of the heating element HE and the SAW resonator RES.

A signal is applied to electrode El. Electrodes E2a and E2b are positioned opposite to electrode El and are connected to ground. In the middle of the SAW resonator, a meander shaped heating element HE is placed. The heating element HE is a conducting structure wherein a DC voltage is applied to the heating element HE. The heating element HE has two contacts which can be connected to a DC voltage source. Further, the SAW resonator RES as shown in FIG. 3 comprises areas AMC of metal coating in order to decrease the radiative energy losses. This allows for increasing thermal transfer by gas therefore enhancing the sensor sensitivity. In a further alternative embodiment, the sensor arrangement SAN can comprise two SAW resonators RES. Here, one resonator RES can be heated and the other is not heated. Two resonators RES enable a differential mode which allows measuring a pressure more precisely.

In order to achieve an acceptable response time of about 100 ms with a sensor arrangement SAN according to the present invention, the chip CH has to be as thin and as small as possible to provide small thermal capacity. Thus, the chip CH is preferably a chip-sized-package . In one embodiment, the chip CH is 130 ym thick. The inventors have found that a sensor arrangement SAN comprising an SAW resonator RES works best for a temperature difference between sensor and gas of about 100-150 °C.

Reference numerals

SAN sensor arrangement

CH chip

SU substrate

CL ceramic layer

ML metallization layer

VH via hole

CP contact pad

BP bumping pad

RES resonator

HE heating element

IL intermediate gap layer

MOL gas molecule

TH thickness of the intermediate gap layer IL

PL protective layer

HO hole

El, E2 electrode

AMC area of metal coating

Claims

Claims (We claim)

1. Sensor arrangement (SAN) for measuring a pressure of an environment comprising an atmosphere, comprising:

- a resonator (RES) that is heated during a measurement, and

- means to measure the resonance frequency of the resonator (RES) . 2. Sensor arrangement (SAN) according to claim 1,

that comprises a heating element (HE) that is thermally coupled to the resonator.

3. Sensor arrangement (SAN) according to claim 2,

wherein the heating element (HE) is a meander-shaped conducting structure.

4. Sensor arrangement (SAN) according to one of claims 1-3, wherein an RF power is applied to the resonator (RES) and the resonator (RES) is heated by energy dissipation.

5. Sensor arrangement (SAN) according to one of claims 1-4, wherein the means to measure the resonant frequency of the resonator (RES) comprises means to apply an RF signal to the resonator (RES) and means to measure the impedance, admittance or S-parameters of the resonator (RES) at the frequency of the applied RF signal.

6. Sensor arrangement (SAN) according to one of claims 1-5, wherein the resonator (RES) is a surface acoustic wave -

SAW - resonator (RES) or a bulk acoustic wave - BAW - resonator . Sensor arrangement (SAN) according to claims 6,

wherein the resonator (RES) is arranged on the surface of a chip (CH) that is flip-chip mounted on a substrate (SU) , the arrangement providing a chip-sized-package .

Sensor arrangement (SAN) according to claim 7,

wherein there is an intermediate gap layer (IL) between the resonator (RES) and the substrate (SU) .

Sensor arrangement (SAN) according to claim 8,

wherein the thickness of the intermediate gap layer (IL) is smaller than the mean free path for a gas molecule (MOL) in a pressure range from 0.01 mTorr to 50 Torr. 10. Sensor arrangement (SAN) according to one of claims 8-9, wherein the heating element and the resonator (RES) are on the surface of the chip (CH) and next to the

intermediate gap layer (IL) . 11. Sensor arrangement (SAN) according to one of claims 8- 10,

wherein the chip (CH) is covered by a protection layer (PL), and wherein the substrate (SU) comprises a hole (HO) connecting the intermediate gap layer (IL) and the environment.

Sensor arrangement (SAN) according to one of claims 11,

wherein the chip (CH) is made of Lithium Niobate or Lithium Tantalate.

Sensor arrangement (SAN) according to one of claims 12, wherein the resonator (RES) has a resonance frequency of 2.0 - 8.0 GHz at room temperature.

Sensor arrangement (SAN) according to one of claims 1-4, wherein the resonator (RES) is a suspended MEMS

resonator .

Sensor arrangement (SAN) according to claim 14,

wherein the MEMS resonator is a MEMS ring, a MEMS fork or a suspended MEMS plate.

Sensor arrangement (SAN) according to one of claims 2- 15,

wherein a constant voltage is applied to the heating element (HE) .

Sensor arrangement (SAN) according to one of claims 2- 15,

wherein the sensor arrangement (SAN) comprises means to determine the voltage that is applied to the heating element (HE) and means to tune the voltage that is applied to the heating element (HE) so that the

resonator (RES) has a constant temperature.

Sensor arrangement (SAN) according to one of claims 1- 15,

wherein the sensor arrangement (SAN) comprises means to determine the RF power that is applied to the

resonator (RES ) and means to tune the RF power that is applied to the resonator (RES ) so that the resonator (RES) has a constant temperature.

19. Method to measure the pressure of an environment

comprising an atmosphere with a sensor arrangement (SAN) according to one of claims 1-16, comprising the steps:

- exposing the sensor arrangement (SAN) to the

environment,

- applying an RF signal to the resonator (RES) ,

- measuring the impedance of the resonator (RES) ,

- deducing the pressure of the atmosphere from the impedance of the resonator (RES) .

20. Method according to claim 19 to measure the pressure of an environment comprising an atmosphere with a sensor arrangement (SAN) according to one of claims 2-16, further comprising the step of:

- applying a voltage to the heating element (HE) .

21. Method to measure the pressure of an environment

comprising an atmosphere with a sensor arrangement (SAN) according to claims 2, 17 and one of claims 1-15, comprising the steps:

- exposing the sensor arrangement (SAN) to the

environment,

- applying a RF signal to the resonator (RES) ,

- applying a heating voltage to the heating element (HE) ,

- measuring the impedance of the resonator (RES) ,

- readjusting the heating voltage so that the resonator (RES) has a certain impedance,

- deducing the pressure of the atmosphere from the heating voltage.

22. Method to measure the pressure of an environment

comprising an atmosphere with a sensor arrangement (SAN) according to claim 18 and one of claims 1-15, comprising the steps:

- exposing the sensor arrangement (SAN) to the

environment,

- applying a heating RF signal to the resonator (RES) ,

- measuring the impedance of the resonator (RES) ,

- readjusting the applied RF power so that the resonator (RES) has a certain impedance,

- deducing the pressure of the atmosphere from the heating power.