Method for detecting a perturbation by hysteretic cycle using a nonlinear electromechanical resonator and device using the method

Abstract

A method is provided for detecting a perturbation with respect to an initial state, of a device including at least one resonant mechanical element exhibiting a physical parameter sensitive to a perturbation such that the said perturbation modifies the resonance frequency of the said resonant mechanical element. A device is provided for detecting a perturbation by hysteretic cycle having at least one electromechanical resonator with nonlinear behavior and means for actuation and detection of the reception signal via a transducer so as to analyze the response signal implementing the method. A mass sensor and a mass spectrometer using the device are also provided.

Claims

1. A method for detecting a perturbation of a device comprising resonant mechanical element exhibiting a physical parameter sensitive to the perturbation, said method comprising: exciting the resonant mechanical element to vibrate the resonant mechanical element at a non-linear amplitude and at a vibration frequency, the amplitude and the frequency being linked by an initial function, the perturbation generating a measurement function; and detecting and analyzing variations of the amplitude between an amplitude of the initial function and an amplitude of the measurement function; and wherein the initial function exhibits a bifurcation frequency, corresponding to a change of the frequency as a function of amplitude and possessing at least one unstable frequency band having at least two stable amplitudes for the same frequency, and at least one stable frequency band having a single stable amplitude corresponding to a single frequency, wherein the exciting is carried out at a variable vibration frequency within a frequency band defined by a minimum frequency and a maximum frequency, and according to at least one frequency cycle centered on a central frequency .sub.op, and one of the minimum and maximum frequencies being situated in the stable frequency band of the initial function, the other maximum or minimum frequency being situated in the unstable frequency band.

2. The method of claim 1, wherein the vibration frequency varies around the central frequency .sub.op according to (t)=.sub.op+ Cos(t+), with the frequency scan rate, having a value lying between 0 and 2.

3. The method of claim 1, wherein a frequency scan rate of a cycle lies between about 1 Hz and 100 kHz, or with a ratio /.sub.op such that 0</.sub.op<10.sup.1.

4. A device for detecting a perturbation with respect to an initial state, comprising: resonant mechanical element exhibiting a physical parameter sensitive to a perturbation such that the perturbation modifies a resonance frequency of said resonant mechanical element; an excitation source configured to cause the resonant mechanical element to vibrate at a non-linear amplitude and at a vibration frequency, the amplitude and the frequency being linked by an initial function, the perturbation generating a measurement function; and means for detecting variations of amplitude of vibrations of the mechanical element between an amplitude of the initial function, and an amplitude of the measurement function, wherein the initial function, exhibits a bifurcation frequency corresponding to an increase or a decrease of the frequency as a function of amplitude and possesses at least one unstable frequency band in which there exist at least two stable amplitudes for one and the same frequency, and at least one stable frequency band in which a single stable amplitude corresponds to a single frequency, and wherein the excitation source comprises means which vary the vibration frequency in a frequency band defined by a minimum frequency and a maximum frequency and according to at least one frequency cycle centered on a central frequency, one of the minimum or maximum frequencies being situated in the stable frequency band of the initial function, the other maximum or minimum frequency being situated in the unstable frequency band.

5. The device of claim 4, wherein the resonant mechanical element is a resonator beam and the excitation source comprises an actuation electrode facing the resonator.

6. The device of claim 5, wherein the resonator beam has nanometric dimensions, a drive electrode is configured to apply voltages of the order of a few Volts, a gap between the drive electrode and the resonator being of the order of 10 nm and 1 m.

7. A mass sensor comprising a device according to claim 4.

8. A mass spectrometer comprising a device according to claim 4, and being configured to measure a mass of particles deposited on the resonant mechanical element.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be better understood and other advantages will become apparent on reading the nonlimiting description which follows and by virtue of the appended figures among which:

(2) FIG. 1 illustrates an example of setting a vibrating mechanical element into vibration, actuated by a drive electrode according to the known art;

(3) FIG. 2 illustrates the shift in resonance frequency of a vibrating element of the known art, between an initial state and a measurement state after mass variation;

(4) FIG. 3 illustrates the frequency response curve of a vibrating mechanical element, excited in a non-linear and stationary regime;

(5) FIG. 4 illustrates the exploitation of the non-linear regime in terms of amplitude variation, between the response curves corresponding to an initial state and to a measurement state after mass variation, within the framework of a so-called softening resonator;

(6) FIG. 5 illustrates the response curves generated by the excitation source used in the device of the invention making it possible to integrate a process for reinitializing the measurement, within the framework of a so-called softening resonator;

(7) FIGS. 6a, 6b and 6c illustrate the detail of the frequency scan cycles respectively in the absence of particle detection, in the presence of particle detection;

(8) FIGS. 7a and 7b illustrate the cycles used in a device according to the invention, respectively at different instants corresponding to the desorption phenomenon;

(9) FIG. 8 illustrates another example of response curves generated by the excitation source used in the device of the invention making it possible to integrate a process for reinitializing the measurement, within the framework of a so-called stiffening resonator.

(10) FIG. 9 illustrates an exemplary device for detecting a perturbation.

DETAILED DESCRIPTION

(11) According to the present invention, the device comprises at least one resonant mechanical element, also dubbed a resonator, and an excitation source capable of bringing the said resonator into its non-linear operating domain by actuation with an appropriate amplitude, doing so whatever the dimensions and the transduction principle thereof.

(12) This may for example be a device with piezoelectric, thermoelastic, magnetic, electrostatic or else optical actuation, and with piezoresistive, capacitive, piezoelectric, optical or magnetic detection, according to the known art.

(13) Advantageously, the resonator can be a resonator of silicon beam type, of nanometric dimensions, for example a few m long, a few 100 nm thick and wide, resonating at frequencies of the order of some ten MHz.

(14) Advantageously the resonator can be a resonator whose non-linearity coefficient is able to be controlled so as to render it softening: the curve plotting the resonance frequency dependent amplitude being oriented towards the low frequencies with respect to a straight line perpendicular to the abscissa axis, or stiffening: the curve plotting the resonance frequency dependent amplitude being oriented towards the high frequencies with respect to a straight line perpendicular to the abscissa axis. To do this, it is notably possible to use an electrostatic electrode in proximity as described in the reference of Kacem et al, Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors, Nanotechnology, vol. 20, p. 275501, 2009 or in patent application EP 2 365 282, for example with a gap of the order of 100 nm. The voltages used can reach a few Volts, AC or DC.

(15) These are tailored as a function of the device, for example so as to obtain a vibration amplitude between 1 time the critical amplitude and 10 times the latter, as described in the article by N. Kacem, S. Hentz, D. Pinto, B. Reig and V. Nguyen, Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors, Nanotechnology, vol. 20, p. 275501, 2009.

(16) The present invention is described hereinafter within the framework of a perturbation corresponding to a detection of mass, typically of particles, but can be applied more widely to any detection of perturbation engendering a variation of resonance frequency of the vibrating element excited according to the means which are described in the present invention, and which is illustrated hereinafter within the framework of a softening resonator.

(17) Thus, referring to FIG. 4 explained previously, during a detection of a perturbation, in this instance an additional mass shifting the resonance frequency onto the curve F.sub.M, if the response stabilizes in the state B with the added mass, at the start of the latter, the response returns either to the state A.sub.1 or to the state A.sub.2: if this entails the state A.sub.1, the following mass variation can be readily detected; if on the contrary, the passage takes place from the state B to the state A.sub.2, the following added mass to be detected generates a jump of small amplitude, which is difficult to measure precisely.

(18) To alleviate this problem, the present invention proposes a device comprising actuation means integrating a measurement reinitialization phase making it possible not to regain the set position corresponding to the state A2, and allowing or forcing a return to the state A1 in all typical cases.

(19) The means of actuation of the present invention are such that they make it possible to carry out the frequency scan cycle illustrated in FIG. 5, in so-called slow time with respect to the period associated with .sub.op in such a way that 0</.sub.op<10.sup.1, doing so in a range of well defined frequencies between a minimum frequency bound .sub.min and a maximum frequency bound .sub.max, such that the said maximum frequency belongs to the span of unstable frequencies B.sub.INS (two possible stable amplitudes for one and the same frequency), the said minimum frequency belonging to the span of stable frequencies B.sub.s (a single possible amplitude for one and the same frequency), the benefit of the two possible amplitudes respectively lower and higher than the amplitude A.sub.lim allowing, as illustrated in FIGS. 4 and 5, the detection of a significant variation in amplitude, the curve F.sub.M relating to another added mass.

(20) FIG. 6a illustrates more precisely, the cycle followed in the absence of any particle. The curve F.sub.0 is traversed between the points 1 and 2, there is no hysteresis cycle nor any associated jump in amplitude.

(21) During the detection of a first mass variation, by varying the frequency, the cycles described in FIGS. 6b and 6c are described, following the instant of the event.

(22) More precisely, with the detection of a particle:

(23) In the first case, illustrated in FIG. 6b, where the particle falls at an instant (point 2) such that the scan frequency is situated before .sub.lim.sup.M: the hysteresis cycle is then traversed along the paths linked by the succession of the following points: 1-2-3/4-5-6-7-8-9/4-5-6-7-8-9/. . . , one observes a large amplitude jump from 4 to 5 in a cyclic manner.

(24) In the second case, illustrated by FIG. 6c, where the particle falls at an instant (point 2) such that the scan frequency is situated between .sub.lim.sup.M and .sub.lim.sup.0: the hysteresis cycle is then traversed along the paths linked by the succession of the following points: 1-2-3/4-5-6-7-8-9/4-5-6-7-8-9/. . . , one observes a large amplitude jump from 2 to 3 just once and then from 8 to 9 in a cyclic manner.

(25) In the case of a desorption of the molecule detected at the level of the resonator (for example for a gas particle with low binding energy), corresponding to the return to an initial state, it is desired to be able to reposition the situation in a state situated between the points A.sub.1 and A.sub.2 belonging to curve F.sub.0.

(26) During the desorption of the particle, by varying the frequency, the cycles described in FIGS. 7a and 7b are described, following the instant of the event.

(27) In the first case, illustrated in FIG. 7a, where the particle detaches at an instant (point 2) such that the scan frequency is situated in the span of stable frequencies B.sub.S (a single possible stable amplitude for one and the same frequency): one starts from the point 1 or 1 depending on whether one is situated at the top or at the bottom of the curve F.sub.M and the cycle is then traversed along the paths linked by the succession of the following points: 1 or 1-2-3/4-3/4-3/. . . After a jump to the point 2 just once, the curve F.sub.0 is traversed between the points 3 and 4, there is no hysteresis cycle nor any associated amplitude jump.

(28) In the second case, illustrated by FIG. 7b, where the particle detaches at an instant (point 2) such that the scan frequency is situated in the span of unstable frequencies B.sub.INS (two possible stable amplitudes for one and the same frequency): one starts from the point 1 or 1 depending on whether one is situated at the top or at the bottom of the curve F.sub.M and one jumps either to the point 2 at the bottom of the curve F.sub.0 or to the point 2 at the top of the curve F.sub.0. If one jumps to the point 2, the cycle is then traversed along the paths linked by the succession of the following points: 1 or 1-2-3/3-5/3-5/. . . After a jump to the point 2 just once, the curve F.sub.0 is traversed between the points 3 and 5, there is no hysteresis cycle nor any associated amplitude jump. If one jumps to the point 2, the cycle is then traversed along the paths linked by the succession of the following points: 1 or 1-2-3-4-4-5/3-5/3-5/. . . After a jump to the point 2 and a jump to the point 4 just once, the curve F.sub.0 is traversed between the points 3 and 5, there is no hysteresis cycle nor any associated amplitude jump.

(29) In the case where the mass sensor does not desorb, the detected particles remaining present, it is possible advantageously to continue the interrogation process according to the present invention. Indeed, FIG. 5 highlights a dashed third curve F.sub.M, corresponding to the curve obtained during a second measurement, the curve F.sub.M becoming the new reference curve.

(30) FIG. 8 shows the same type of frequency scan, used in the present invention, within the framework of a stiffening resonator, with resonance frequencies which vary in an increasing manner, during the detection of a perturbation.

(31) Advantageously, the actuation frequency varying in the frequency range [.sub.min; .sub.max] can vary periodically around a predetermined central frequency .sub.op, the frequencies .sub.min and .sub.max being adjusted as in the description of FIG. 5.

(32) It is thus considered that the frequency varies according to the following equation:
(t)=.sub.op+ Cos(t+)
with such that 0</.sub.op<10.sup.1 with the frequency scan rate.

(33) The excitation frequency is thus modulated in a harmonic manner around a frequency value .sub.op with a modulation amplitude , in the frequency range [.sub.min; .sub.max].

(34) It is of course possible to vary this frequency according to any type of law, such as for example a square law, that may be described in the form of an infinite series:

(35) $\left(t\right)={}_{\mathrm{op}}+.Math.\frac{4}{}\underset{n=0}{\overset{}{.Math.}}\frac{\sin \left(\left(2n+1\right)\mathrm{.Math.}t\right)}{\left(2n+1\right)}.$

(36) In the case of the resonator before detection of particles, it is possible to define a bifurcation frequency .sub.lim.

(37) The latter can be determined experimentally by observing the frequency response of the device. One then chooses a frequency .sub.max slightly lower than this value, which calibrates the smallest mass that it is possible to detect, for example |.sub.min.sub.max| lying between 0 and 10.sup.1 times the frequency .sub.op, advantageously 10.sup.9 and 10.sup.1 times the frequency .sub.op.

(38) One then defines the modulation amplitude and the value .sub.op with respect to the biggest particle to be detected.

(39) Indeed the minimum frequency .sub.min=.sub.max2 attained by modulation must be situated in a frequency zone where a single vibratory state is possible (quasi-linear).

(40) All the response curves for the beam with or without particle exhibit the same trend (peak deviated towards the low frequencies), shifted all the more to the left the larger the added mass.

(41) Indeed, it may be particularly advantageous to provide for a range of frequencies, such that various types of different mass particles can be detected. Thus within the framework of the detection for example of a set of type of distinct and increasing specific mass particles, there exists a type of particles to be detected having a maximum mass and therefore a specific curve, called the limit curve, maximizing the leftward shift.

(42) Thereafter, the calibration of the scan rates is performed while complying with the following principle: the scan must be fast enough such that during the presence of a particle on the beam, as described in the article by Chaste et al, A nanomechanical mass sensor with yoctogram resolution, Nature Nanotechnology 2012, at least one complete scan cycle of the modulation interval [.sub.max2 , .sub.max] can be carried out.

(43) This scan frequency can lie between for example 1 Hz and 100 kHz or adjusted such that 0</.sub.op<10.sup.1. The principle of frequency modulation is known in the field of RF devices, and can be implanted by many commercial RF voltage sources, and is also used as detection principle for detecting the mechanical motion of an NEMS as described in the article by V. Gouttenoire, T. Barois, S. Perisanu, J.-L. Leclercq, S. T. Purcell, P. Vincent, and A. Ayari, Digital and FM demodulation of a doubly clamped single-walled carbon-nanotube oscillator: towards a nanotube cell phone, Small (Weinheim an der Bergstrasse, Germany), vol. 6, no. 9, pp. 1060-5, May 2010.

(44) It is thus possible to carry out the transduction of the mechanical motion of the device at the same time as applying the detection principle.

(45) In the course of continuous measurements, and with a state of the resonator which does not revert to its initial state, the perturbations accumulating, a curve F.sub.M becomes an initial curve for the following measurement curve F.sub.M and so on. In typical cases of this type, it may be beneficial to verify that the new curve of initial state F.sub.M makes it possible to maintain the conditions required at the level of the frequency bounds in the present invention, namely, that one of these bounds belongs to the unstable frequency band and the other to the stable frequency band, making it possible if appropriate to adjust the central frequency .sub.op.

(46) To ensure this control, the means for detecting and analysing the signal arising from the electrical detection transducer can advantageously be correlated with the excitation source in a servocontrol loop, when it is detected that the frequency .sub.min is no longer low enough and no longer makes it possible to jump from the higher branch to the lower branch (see points 7 to 8 of FIG. 6b), the frequencies .sub.min and .sub.max determining the thresholds of the largest and of the smallest mass to be detected.

(47) FIG. 9 shows a device 1 for detecting a perturbation with respect to an initial state. The device 1 may include at least one resonant mechanical element 10 exhibiting a physical parameter sensitive to a perturbation such that the perturbation modifies the resonance frequency of the resonant mechanical element 10. The device 1 may also include an excitation source 14 of the resonant mechanical element making it possible to cause the resonant mechanical element to vibrate in a domain of non-linear amplitude response at a vibration frequency , the amplitude and the frequency being linked by an initial function f.sub.0(), the perturbation generating a measurement function f.sub.M (). The device 1 may further include detecting and analyzing means 11 for the variations of amplitude of vibrations of the mechanical element 10 between an amplitude of the function f.sub.0(), and an amplitude of the function f.sub.M (). The excitation source 14 may include a piezoelectric, thermoelastic, magnetic, electrostatic, or optical means. The detecting and analyzing means 11 may include at least one of transducer, piezoresistive, capacitive, piezoelectric, optical, and magnetic types.

(48) The invention being generic, it can be applied to a large number of devices, using for example silicon NEMS such as described in the article E. Mile, G. Jourdan, I. Bargatin, S. Labarthe, C. Marcoux, P. Andreucci, S. Hentz, C. Kharrat, E. Colinet, and L. Duraffourg, In-plane nanoelectromechanical resonators based on silicon nanowire piezoresistive detection, Nanotechnology, vol. 21, no. 16, p. 165504, April 2010, or in the patent application filed by the Applicant: PCT/EP2011/065682.