Pressure sensor based on a mechanical resonator

Abstract

Pressure sensor arrangement (10) for measuring a pressure in a vacuum pressure range, said pressure sensor arrangement comprising: - electrically conducting elements, and - a high-quality-factor mechanical resonator (4) comprising a displaceable part (5) able to oscillate between a first position (6) and a second position (7), wherein a strength of a capacitive coupling or of an inductive coupling between said electrical conducting elements is dependent on said position of said displaceable part and / or on a velocity of said displaceable part. Furthermore, the invention is directed to a method of operating the pressure sensor arrangement.

Description

[0001] PRESSURE SENSOR BASED ON A MECHANICAL RESONATOR

[0002] The invention addressed herein relates to the technical field of measuring a pressure, in particular to measuring a pressure in the vacuum pressure range. More specifically, the invention relates a pressure sensor arrangement. Under further aspects, the invention relates to a method of measuring a pressure and to a method of operating the pressure sensor arrangement.

[0003] One way to determine the pressure of a very dilute gas is to measure the energy loss of a sensor element to said dilute gas. As an example, so called Pirani vacuum gauges rely on the thermal energy carried away by the surrounding residual gas atmosphere. Another approach is to measure the ringdown of a mechanical oscillator, which is read out by means of a laser interferometer (cf. Reinhardt, C. et al. Calibration-less gas pressure sensor with a 10-decade measurement range. https: / / doi.org / 10.48550 / arXiv.2309.12044 & https : / / pubs .acs.org / doi / epdf / 10.1021 / acspho tonics .3c01488 )

[0004] According to this approach, a laser interferometer is used to measure the resonator oscillation and its quality factor. The quality factor is obtained by performing ringdown measurements and serves as an indirect pressure measurement. These ringdown measurements are observations of the resonator slowly losing energy to the environment and can take anywhere between seconds and hours. Since high

[0005] P220869 Q resonators have a minimi zed loss to the environment these measurements are very time consuming .

[0006] Another disadvantage of this approach is that a laser interferometer is needed, which due to its si ze renders the whole apparatus impractical for a lot of applications .

[0007] The obj ect of the present invention is to provide an apparatus or a method which overcomes at least a problem of the state of the art . More speci fically, the present invention aims at providing an alternative approach of measuring pressure in the vacuum pressure range .

[0008] This obj ect is achieved by a pressure sensor arrangement according to claim 1 .

[0009] The pressure sensor arrangement according to the invention is adapted to measure a pressure in a vacuum pressure range . The pressure sensor arrangement comprises :

[0010] - electrically conducting elements , and

[0011] - a high-quality- factor mechanical resonator comprising a displaceable part able to oscillate between a first position and a second position . The strength of a capacitive coupling or of an inductive coupling between said electrical conducting elements is dependent on said position of said displaceable part and / or on a velocity of said displaceable part .

[0012] With this invention, a readout of an oscillation of a high- quality factor oscillator is possible with simple means that require little space . The electrical conducting

[0013] P220869 elements may be supplied with a voltage such that they interact capacitively with each other . The electrical conducting element may be supplied with a current such that they interact with a magnetic field .

[0014] For the latter case , as an example , two metallic lines may be arranged on an edge of a membrane . The membrane including both metallic lines may be arranged in an external static magnetic field . By driving a current through on of the metallic lines , due to the magnetomotive force , the membrane may be driven in an oscillating movement . This movement on the other hand induces a voltage on the other metallic line , which voltage may be measured and / or fed back into a phase-locked-loop . Thus , various ways of electromagnetic coupling to the electrical conducting elements may be used for readout of the position or velocity of the displaceable part of the oscillator, as well as for applying a driving force to the displaceable part of the oscillator .

[0015] The mechanical resonator may be a micro-mechanical resonator or a nano-mechanical resonator . The mechanical resonator may be a high-Q resonator having an intrinsic Q- factor above 104, preferably above 106. Such a high-Q means low intrinsic loss , such that it is very susceptible to its environment . The Q- factor may in particular be selected low enough that the dominant damping ef fect is due to the interaction with the residual gas , rather than the intrinsic loss . The mechanical resonator may the geometry of a trampoline or of a string or of a ribbon . The

[0016] P220869 displaceable part may be flat , mainly extending perpendicular to direction between first and second positions .

[0017] The resonance frequency of the mechanical oscillator may be in the kHz to MHz frequency range .

[0018] The high-quality- factor mechanical resonator may comprise a resonator element of an elastic material under tensile stress and a clamping structure supporting the resonator element and upholding the tensile stress . The resonator and the support structure may be formed and dimensioned to establish a soft-clamping condition . This means that elastic waves of the frequency of the operational oscillation mode and of the polari zation of the operational oscillation mode decay when entering into the clamping structure . More speci fically, the clamping structure may be configured to exhibit a phononic density of states having a bandgap in the frequency range including the operational oscillation mode of the high-quality- factor mechanical resonator .

[0019] The resonator element and the clamping structure may be made of the same elastic material under tensile stress . Structuring of this material , e . g . by etching through holes across a flat piece of this material and leaving connection parts unetched, may be applied to produce the resonator and the clamping structure from one piece .

[0020] The elastic material under tensile stress may be one of silicon nitride , diamond, quartz , aluminum nitride , silicon carbide , gallium arsenide , indium gallium arsenide ,

[0021] P220869 aluminum gallium arsenide , aluminum, gold, graphene , polymer materials , or combinations thereof .

[0022] In one embodiment of the pressure sensor arrangement according to the invention, which may be combined with any of the embodiments still to be addressed unless in contradiction, it comprises a first and a second electrical ly conducting element forming a capacitor, wherein said first and second conducting element are arranged such that the capacitance of said capacitor is higher when said displaceable part is in said first position as compared to when said displaceable part is in said second position .

[0023] In one embodiment of the pressure sensor arrangement , which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in contradiction, said first electrical conducting element is arranged on said displaceable part .

[0024] In one embodiment of the pressure sensor arrangement , which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in contradiction, a third conducting element is isolated from said first and said second conducting element and said third conducting element is arranged on said displaceable part .

[0025] P220869 In this embodiment , no electrical connection to the displaceable part is necessary . The third conducting element acts passively and modi fies the capacitance between the first and second conducting element only due to its distance to these elements .

[0026] In one embodiment of the pressure sensor arrangement , which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in contradiction, said displaceable part consists of or comprises a material having a relative permittivity srof at least 2 . Preferably sr> 10 .

[0027] In one embodiment of the pressure sensor arrangement , which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in contradiction, the pressure sensor arrangement further comprises means of measuring a parameter of an oscillation of a capacitance in real time . This parameter may be an amplitude of the oscillation of the capacitance , a frequency of the oscillation of the capacitance or a phase shi ft of the oscillation of the capacitance . The pressure sensor arrangement may be able to measure time variations of said parameter on a millisecond timescale .

[0028] In one embodiment of the pressure sensor arrangement , which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in

[0029] P220869 contradiction, the pressure sensor arrangement may further comprise means for driving an oscillation of said mechanical resonator .

[0030] Such means for driving an oscillation may be reali zed by a piezo actuator or by driving an electrode by electrical force , such as e . g . by applying a voltage between said first and second electrical conducting elements . As an alternative , driving an oscillation may be achieved by driving a current through an electrical conductor element , which is arranged on the displaceable part of the resonator, such as e . g . a membrane . For this latter case , a static magnetic field may be provided, which magnetic field is oriented such that the Lorentz- force acting on the current carrying element is directed into the direction of the oscillation movement .

[0031] Examples of means for driving an oscillation of the mechanical resonator are laser pressure force , motion induced by a piezo-electric device , electrical field driving charges on the surface , electromagnetic force (Lorentz force due to current in a conductive element on the membrane ) , etc .

[0032] Further in the scope of the invention lies a method according to claim 8 .

[0033] It is a method of measuring a pressure . It is performed by means of a pressure sensor arrangement according to the invention . The method comprises the steps of

[0034] - defining an amplitude setpoint for the oscillation of said mechanical resonator,

[0035] P220869 acting with a driving force on said mechanical oscillator,

[0036] - measuring a parameter indicative of the amplitude of said oscillation,

[0037] - adapting by means of a feedback control loop a drive strength of said driving force such that the amplitude is driven towards said amplitude setpoint ,

[0038] - evaluating said drive strength to derive a pressure value .

[0039] In conclusion, an apparatus is proposed that uses any high- Q resonating device with a metallic coating ( fully or locali zed) to enable capacitive readout of the resonator device , which of fers a cheaper and more space-ef ficient readout than the interferometer-based readout .

[0040] Furthermore , using the below proposed feedback loop or Q- control in a pressure gauge with such high quality factors has not been demonstrated or published before .

[0041] As a possible form of pressure measurement , the use of the amplitude ( Z O ) as an indirect pressure measurement instead of ringdown measurements is proposed . The amplitude can be directly related to the quality factor ( Q) with an ef fective mass (m) obtained from simulations and the angular mode frequency w , according to the formula

[0042] Z O = ( F - Q) / (m - w2) .

[0043] P220869 Therefore , i f we drive with a constant force ( F) we can indirectly measure the pressure by measuring the amplitude since it is directly proportional to the quality factor . This way and by using a mechanical model of our sensor, it is possible to correlate the amplitudes of the sensor with pressure over the governing physics . This means that calibration for every single sensor is not required with this method, which is a further advantage of the present invention .

[0044] Alternatively, instead of the amplitude measurement , a feedback loop can be employed where the power used to drive the membrane oscillation to a constant amplitude serves as an indirect pressure measurement . This is also a consequence of the previous formula . By keeping Z 0 constant , we can relate Q to the needed force or driving strength .

[0045] Further in the scope of the invention lies a method according to claim 9 . It is a method of measuring a pressure , which may be combined with the above-mentioned method .

[0046] I f the method above does not work for the entire measurement region, e . g . because the driving strength gets too small to measure , one can use a method termed "Q- control" . To control the quality factor, the oscillator ' s excitation is measured and the scaled measurement signal is used as a feedback signal to drive the oscillator .

[0047] Depending on the phase shi ft between the measured signal and the feedback signal the ef fective quality factor can be

[0048] P220869 tuned. Note that this does not have an adverse effect on the sensing limits.

[0049] The method comprises

[0050] - acting with a driving force on said mechanical oscillator to excite an oscillation,

[0051] - measuring an instantaneous displacement of said displaceable part of the mechanical oscillator to produce a time-dependent signal z (t) ,

[0052] - applying a phase shift ( ) to said time-dependent signal ,

[0053] - multiplying the phase-shifted time-dependent signal with a gain-factor, and

[0054] - feeding back the multiplied and phase-shifted signal (G • z ( t- / o ) ) to the driving force.

[0055] The basic excitation may be accomplished by a time-harmonic force, e.g. having a cosine shaped time dependence with an angular frequency co close to a resonance of the mechanical oscillator, i.e. being proportional to cos(ot) . The instantaneous displacement may, e.g., in the case of a mechanical oscillator in form of a cantilever, be the deflection of the tip of the cantilever. By applying a phase-shifted feed-back signal to the excitation force, in addition to the basic excitation, an effective quality factor of the oscillator being higher than the intrinsic mechanical quality factor of the oscillator may be achieved. As it turns out, a phase lag of about 90° maximizes the effective quality factor.

[0056] P220869 Correspondingly, a phase lag of about - 90 ° minimi zes the ef fective quality factor, which is desirable in the present case , in order to have a fast response to the pressure value . The strength of the ef fect to the quality factor may be adj usted by an appropriate value of the gain factor . Phase shi ft and / or gain factor may be controlled by an additional feedback-loop, for example keeping the ef fective quality factor at a constant value .

[0057] The invention furthermore allows for electrical control and manipulation of membrane oscillation . It also eliminates the need for optical access to the resonator, allowing novel applications where space and optical access is a limiting factor . The present invention may, for example , be directly employed on wafers that are moved .

[0058] Electrical control is also anticipated to be more energy ef ficient than interferometer-based solutions .

[0059] The control mechanism is much faster than waiting for quality factor measurements to complete . Especially the Q- control makes a pressure readout much faster . Further advantage of using Q-control in such a pressure sensor is that the linewidth of the resonator' s resonance is much wider and therefore easier to measure .

[0060] The invention shall now be further exempli fied with the help of figures . The figures show :

[0061] P220869 Fig. 1, in sub-figures l.a) and l.b) a schematic and cross-sectional view of two embodiments of the pressure sensor arrangement;

[0062] Fig. 2 a flow-chart of a variant of a method of operating the pressure sensor arrangement;

[0063] Fig. 3 a schematic, perspective view on an embodiment of the pressure sensor arrangement;

[0064] Fig. 4 a schematic, perspective view on another embodiment of the pressure sensor arrangement;

[0065] Fig. 5 a schematic, perspective view on another embodiment of the pressure sensor arrangement illustrating two positions of the oscillating movement .

[0066] Fig. l.a) shows schematically and simplified, a pressure sensor arrangement 10. A high-quality-factor mechanical resonator 4, here in form of a cantilever, comprises a displaceable part 5, here realized as the free end of the cantilever, is able to oscillate between a first position

[0067] 6, here indicated with dashed lines and a second position

[0068] 7, the position which is captured in the figure here. The displaceable part carries an electrical conducting element 2, which is arranged opposite to an electrical conducting element 1. The two electrical conductor elements form a capacitor. Both are connected by electrical connectors to optional means 8 for measuring a parameter of an oscillation, such as e.g. a voltmeter. A driving force 9 is symbolized by an arrow.

[0069] P220869 Fig . l . b ) shows a similar embodiment as Fig . l . a ) . In this embodiment , however, the two electrical conducting elements 1 and 2 forming a capacitance , are arranged on the part of the sensor, which is not oscillating . A third electrical conductor element 3 i s arranged on the displaceable part of the oscillator . Depending on its position, it influences the capacitance between elements 1 and 2 .

[0070] Figure 2 shows a flow-chart of a method 20 of operating the pressure sensor arrangement . The method comprises defining 21 an amplitude setpoint , defining 22 a drive strength, a reaction 23 of a resonator amplitude to the drive strength and a measurement 24 of the amplitude . In a feedback control loop 25 ( e . g . defined by proportional-integral- di f ferential parameters , PID) , the result of the measurement of the amplitude is fed back into the definition of the drive strength . Use is made of the drive strength as a measure of pressure , as indicated by block 26 of the flow chart . The advantage of this operational scheme is that the drive strength determined this way provides a fast information about the pressure value and its changes over time .

[0071] Figure 3 shows a geometric configuration of an embodiment of the pressure sensor arrangement , wherein the resonator 4 having a high quality factor has the form of a trampoline resonator . The displaceable part is a small square held on its corners by four long strings attached to a square frame . On the displaceable part is the second electrical conductor element 2 , shown in light gray, which together

[0072] P220869 with the first electrical conductor element 1 , which is a larger circular element on the bottom plate , a capacitor . Not visible in this figure is an electrical connection leading along at least one of the strings to the second electrical conductor element 2 . Alternatively, the complete trampoline oscillator may be coated with a conductive layer, to provide an electrical connection to the electrical conductor element 2 .

[0073] Figure 4 shows a geometric configuration of another embodiment of the pressure sensor arrangement . Di f ferent to the embodiment shown in Fig . 3 , here the first 1 and the second 2 electrical conductor element are formed as semicircular plates and are both arranged on the bottom plate . They are isolated from each other and form a capacitor . A third electrical conductor element is arranged on the displaceable part of the trampoline oscillator . Its exact position influences the capacitance between the first and second electrical conductor elements .

[0074] Figure 5 shows extremal positions 6 , 7 of the displaceable part of a trampoline oscillator 4 .

[0075] P220869 List of reference signs

[0076] 1 first electrically conducting element

[0077] 2 second electrically conducting element

[0078] 3 third electrically conducting element

[0079] 4 mechanical resonator (having high quality factor )

[0080] 5 displaceable part

[0081] 6 first position ( of displaceable part )

[0082] 7 second position ( of displaceable part )

[0083] 8 means of measuring a parameter of an oscillation

[0084] 9 driving force

[0085] 10 pressure sensor arrangement

[0086] 20 method of operating the pressure sensor arrangement

[0087] 21 defining amplitude setpoint

[0088] 22 defining drive strength

[0089] 23 resonator amplitude reacts to drive strength

[0090] 24 measurement of amplitude

[0091] 25 feedback control ( e . g . defined by proportional- integral-di f ferential parameters , PID)

[0092] 26 use of drive strength as a measure of pressure

[0093] P220869

Claims

Claims1. Pressure sensor arrangement (10) for measuring a pressure in a vacuum pressure range, said pressure sensor arrangement comprising:- electrically conducting elements, and- a high-quality-factor mechanical resonator (4) comprising a displaceable part (5) able to oscillate between a first position (6) and a second position (7) , wherein a strength of a capacitive coupling or of a inductive coupling between said electrical conducting elements is dependent on said position of said displaceable part and / or on a velocity of said displaceable part.

2. Pressure sensor arrangement (10) according to claim 1, comprising a first (1) and a second (2) electrically conducting element forming a capacitor, wherein said first and second conducting element are arranged such that the capacitance of said capacitor is higher when said displaceable part is in said first position as compared to when said displaceable part is in said second position.

3. Pressure sensor arrangement according to claim 2, wherein said first electrical conducting element is arranged on said displaceable part.P2208694 . Pressure sensor arrangement according to claim 2 , wherein a third conducting element is isolated from said first and said second conducting element and wherein said third conducting element is arranged on said displaceable part .5 . Pressure sensor arrangement according to any one of claims 1 to 4 , wherein said displaceable part consists of or comprises a material having a relative permittivity of at least 2 , preferably of at least 10 .6 . Pressure sensor arrangement according to any one of claims 1 to 5 further comprising means of measuring a parameter of an oscillation of a capacitance in real time , in particular, wherein said parameter is an amplitude of the oscillation of the capacitance , a frequency of the oscillation of the capacitance or a phase shi ft of the oscillation of the capacitance , preferably being able to measure time variations of said parameter on a milli second timescale .7 . Pressure sensor arrangement according to any one of claims 1 to 6 further comprising means for driving an oscillation of said mechanical resonator .8 . Method of measuring a pressure by means of a pressure sensor arrangement according to any one of the claims 1 to 7 , wherein the method comprisesP220869- defining an amplitude setpoint for the oscillation of said mechanical resonator,- acting with a driving force on said mechanical oscillator to excite an oscillation,- measuring a parameter indicative of the amplitude of said oscillation,- adapting by means of a feedback control loop a drive strength of said driving force such that the amplitude is driven towards said amplitude setpoint ,- evaluating said drive strength to derive a pressure value .

9. Method of measuring a pressure by means of a pressure sensor arrangement according to any one of the claims 1 to 7 , wherein the method comprises- acting with a driving force on said mechanical oscillator to excite an oscillation,- measuring an instantaneous displacement of said displaceable part of the mechanical oscillator to produce a time-dependent signal z ( t ) ,- applying a phase shi ft ( ) to said time-dependent signal ,- multiplying the phase-shi fted time-dependent signal with a gain- factor , and- feeding back the multiplied and phase-shi fted signal to the driving force .P220869

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