WO2009144613A1

WO2009144613A1 - Reading-out apparatus for reading out a multiple of resonator elements

Info

Publication number: WO2009144613A1
Application number: PCT/IB2009/052051
Authority: WO
Inventors: Warner J. Venstra
Original assignee: Koninklijke Philips Electronics N. V.
Priority date: 2008-05-26
Filing date: 2009-05-18
Publication date: 2009-12-03

Abstract

The invention relates to a reading-out apparatus for reading out a multiple (6) of resonator elements (2, 3, 4, 5), wherein the reading-out apparatus comprises a driving unit (7) for driving the multiple (6) of resonator elements (2, 3, 4, 5) such that at least one of the multiple (6) of resonator elements (2, 3, 4, 5) is operated in a nonlinear regime. The reading-out apparatus further comprises a driving response determination unit (8) for determining a driving response of the driven multiple (6) of resonator elements (2, 3, 4, 5) by modifying a driving parameter and a nonlinearity response determination unit (9) for determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behavior caused by the operation in the nonlinear regime.

Description

READING-OUT APPARATUS FOR READING OUT A MULTIPLE OF RESONATOR ELEMENTS

FIELD OF THE INVENTION

The present invention relates to a reading-out apparatus for reading out a multiple of resonator elements. The invention relates further to a corresponding reading- out method and a corresponding reading-out computer program. BACKGROUND OF THE INVENTION

Resonator elements are generally read out by inducing oscillations in the resonator elements and by measuring the frequency response of the resonator elements. The capability of a reading-out apparatus, which induces the oscillations and which measures the frequency response, to read-out individual resonator elements separately, i.e. to determine the contribution of an individual resonator element to the frequency response, depends on the bandwidth of the individual resonator elements and the frequency distance of the resonance frequencies of individual resonator elements. For example, if the frequency distance of the resonance frequency of two resonator elements is smaller than the bandwidth of the resonator elements, which is for example defined as the full width at half maximum (FWHM) of an amplitude of oscillation in a frequency spectrum of an individual resonator element, these two resonator elements cannot be separated in a frequency response, to which both resonator elements contribute, by known reading-out apparatuses.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a reading-out apparatus for reading out a multiple of resonator elements, wherein a discrimination of individual resonator elements in a driving response of a multiple of a resonator element is improved. It is a further object of the present invention to provide a corresponding reading-out method and a corresponding reading-out computer program.

In an aspect of the present invention a reading-out apparatus for reading out a multiple of resonator elements is presented, wherein the reading-out apparatus comprises: - a multiple of resonator elements,

- a driving unit for driving the multiple of resonator elements such that at least one of the multiple of resonator elements is operated in a nonlinear regime,

- a driving response determination unit for determining a driving response of the driven multiple of resonator elements by modifying a driving parameter,

- a nonlinearity response determination unit for determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime.

The invention is based on the idea that, if a resonator element is operated in a nonlinear regime, this operation in a nonlinear regime yields a behavior in the driving response of the multiple of resonator elements, which can be assigned to an individual resonator element, which is operated in a nonlinear regime. Thus, by operating the resonator elements in a nonlinear regime, individual resonator elements can be discriminated in the driving response of the multiple of resonator elements, in particular, if the resonator elements are damped and/or comprise a low Q factor, which yields a bandwidth having such a broadness that the resonator elements cannot be separated in a driving response, to which both resonator elements contribute, by known reading-out apparatuses, these resonator elements can be discriminated in the driving response by using the reading-out apparatus in accordance with the invention.

A resonator element is an element, which can oscillate. The resonator element can be any element, which can oscillate, for example, an oscillating mechanical element, an oscillating electrical circuit, an oscillating optical element etc. Preferentially, the resonator elements are resonant sensors, wherein the determined nonlinearity driving parameter value of a resonant sensor depends on a property, which has to be sensed by the resonant sensor. The driving response depends preferentially on the oscillation amplitudes and/or oscillation phases of the resonator elements, wherein, if the driving response has been determined by modifying the driving frequency as a driving parameter, the driving response is called frequency response and wherein, if the driving response has been determined by modifying the driving amplitude as a driving parameter, the driving response is called amplitude response. It is also possible that the driving response is determined by modifying several driving parameters, for example, the driving frequency and the driving amplitude. This driving response is called frequency and amplitude response. The driving response has several values depending on the oscillation amplitudes and/or oscillation phases of the resonator elements, wherein the oscillation amplitudes and/or the oscillation phases depend ton the respective driving parameter, in particular, the driving frequency and/or the driving amplitude. In a preferred embodiment, the driving response is an electromotive force signal, which depends on the movement of the resonator elements in a magnetic field, i.e. which depends on the oscillation amplitudes and oscillation phases of the resonator elements, which depend on a driving frequency and/or a driving amplitude.

A resonator element is preferentially operated in a nonlinear regime, if the resonator element responds nonlinearly on the driving by the driving unit. For example, a resonator element is operated in the nonlinear regime when the resonator behavior cannot be described by a simple harmonic oscillator. One of the implementations of such a harmonic oscillator is an oscillator operated at high amplitudes when higher order terms in the equation of motion, which are neglected in the linear approximation which is valid at low amplitudes, become significant. An example in mechanics is the 'spring stiffening' effect: at large displacements the linear relationship between force and displacement is not valid. In a resonator, this may be the case when the vibration amplitude is large enough so that the elongation of an oscillating beam of the resonator cannot be neglected. The linear differential equation of motion is then replaced by the Duffing equation, which inserts a forcing term which is related to the third order of the displacement. In contrast to 'spring stiffening', in which the nonlinear vibration frequency is increasing with increasing amplitude, the vibration frequency may as well decrease at increasing amplitude, such as in an electrostatically actuated resonator. In such a resonator, the driving force is proportional to the inverse square of the displacement amplitude and consequently not linear. At certain amplitudes, in the nonlinear regime, for example if the displacements are large enough, a situation can occur in which the resonator can be in one or two or possibly more states of different vibration amplitudes. The actual state of the resonator depends preferentially on very small changes in the resonator properties, which may be intentionally affected by a measurand. If a resonator element, which is operated in a nonlinear regime, changes from a first state into a second state, this state change can be seen in the driving response as a steep and/or sudden change and/or as a discontinuity and/or as a jump in the driving response. Concerning the position of the steep and/or sudden changes and/or the discontinuities and/or jumps in the driving response, the resonator exhibits extreme sensitivity and low noise. To probe the exact location of the resonator's state change, i.e., for example the discontinuity or discontinuities in the driving response, this state change may be induced by sweeping the driving frequency of the driving unit through or around the point of bistability, or by sweeping the driving amplitude of the driving unit through or around the point at which the resonator is bistable, or by any suitable combination of driving amplitude and frequency. In order to sweep a driving parameter, its value may be modulated by an upwards or downwards ramp, a sine, or any other time varying signal. In an embodiment, if the driving unit is an electrical driving unit, the amplitude is preferentially swept by sweeping the power of the electrical driving unit. An electronic system with comparable characteristics (with spring softening rather than spring stiffening), which can be regarded as resonator element, is for example an RLC circuit with nonlinear elements such as diodes etc..

The driving parameter is, in particular, a parameter, on which the driving of the multiple of resonator elements depends and with which the resonator elements are driven, for example, a driving frequency or a driving amplitude. The driving response determination unit is preferentially adapted for sweeping the driving frequency and/or the driving amplitude, i.e. in preferred embodiments the driving power, of the driving of the resonator elements for determining a driving response of the driven resonator elements. The driving response is, for example, an electromotive force signal measured at the resonator elements, wherein this electromotive force signal depends on the swept driving parameter, for example, on the driving frequency and/or the driving amplitude, i.e. in particular the driving power. The nonlinearity response determination unit is preferentially adapted for determining a sharp and/or steep and/or sudden change and/or discontinuity and/or jump in the determined driving response as a behavior caused by the operation in the nonlinear regime. The at least one nonlinearity driving parameter value is preferentially the value of the driving parameter, for example, a driving frequency and/or driving amplitude value, in particular a driving power value, at which this change and/or discontinuity and/or jump occurs. The reading-out apparatus is preferentially adapted such that, if a certain number of resonator elements is operated in a nonlinear regime, the same number of, for example, jumps and, thus, the same number of driving parameter values can be determined by the nonlinearity response determination unit. The driving unit is a unit for inducing an oscillation or vibration of at least one resonator element, in particular, of all resonator elements.

It is preferred that the resonator elements are resonant sensors and that the reading-out apparatus comprises a property determination unit for determining a property of an object being in contact with the multiple of resonator elements using the determined at least one nonlinearity driving parameter value. The oscillating properties of a resonant sensor are modified by an object, which has to be sensed. Thus, a property, which has to be sensed by a resonant sensor, can be sensed by determining the oscillating behaviour of the respective resonator element, in particular, by determining the nonlinearity driving parameter value of the respective resonant sensor, wherein the property determination unit determines a property of the object from the determined at least one nonlinear driving parameter value, which is, for example, a discontinuity or jump frequency in a frequency response and/or a discontinuity or jump amplitude or discontinuity or jump power in an amplitude or power response, wherein the discontinuity or jump frequency, the discontinuity or jump amplitude or the discontinuity or jump power indicate the position, at which a discontinuity or jump in the respective driving response is determined, which is caused by the nonlinear regime, in which at least one of the resonator elements is operated. For example, the reading-out apparatus can be calibrated by exposing an object having a known property to a resonant sensor and by determining the driving parameter value in the driving response for this resonant sensor, wherein this known property of the object is preferentially assigned to the nonlinearity driving parameter value of the respective resonant sensor and stored in the property determination unit. The object, of which a property can be determined, is, for example, a fluid, in particular, air or water, surrounding the resonant sensors. A property of an object is, for example, the temperature, the viscosity, the number or concentration of certain particles, the presence of certain species of particles among a large variety and/or number of particles, in particular, molecules, within the object etc. It is further preferred that the multiple of resonator elements are connected to each other. The resonator elements can be connected in an arbitrary network. Preferentially, the resonator elements are connected in series, while preferentially care is taken to minimize mutual mechanical and/or electrical coupling between the individual resonators. Other, in particular parallel, configurations are possible as well. Since the resonator elements are connected to each other, it is not necessary to contact each individual resonator element by the driving unit and/or by the driving response determination unit separately, which simplifies the connection of the different elements of the reading-out apparatus and, thus, the manufacturing of the reading-out apparatus. It is further preferred that the multiple of resonator elements are flexural resonator elements, in particular, micro or nanomechanical flexural resonators. The resonator elements are preferentially sensors. The resonator elements are preferentially made of a thin film material such as silicon nitride, which is coated with a layer of a conductor metal, in particular, a layer of gold. If silicon nitride is coated with a layer of a conductor metal, in particular, a layer of gold, an adhesion layer is preferentially arranged between the layer of the conductor metal and silicon nitride. The adhesion layer can comprise chromium or another suitable material, which can be used as an adhesion promoter for gold.

It is further preferred that the resonator elements are double clamped, i.e. preferentially double clamped flexural resonator elements.

In another preferred embodiment an at least partly conducting flexural structure, through which a current can be run, can be used as a resonator element, in particular, if the driving unit uses a magnetomotive drive for driving the resonator elements and if the driving response determination unit is adapted for magnetomotively determining, in particular, detecting, the driving response. Furthermore, any resonator structure with nonlinearity leading to nonlinearity and/or bistability can preferentially be used as resonator element, for example, nanowires, nanostrings etc. Electrostatic arrays could also be used.

It is preferred that the driving unit is connected to the multiple of resonator elements such that at least two resonator elements are drivable simultaneously only and/or that the driving response determination unit, which determines, in particular, a frequency, amplitude or power response, is connected to the multiple of resonator elements such that the driving response of at least two resonator elements is determinable simultaneously only. It is further preferred that the driving unit and the multiple of resonator elements are adapted such that the multiple of resonator elements are simultaneously driveable and that the driving response determination unit and the multiple of resonator elements are adapted such that a driving response of the multiple of resonator elements is simultaneously determinable for the multiple of resonator elements. This means preferentially all resonator elements are driveable simultaneously and the driving response for all resonator elements is determinable simultaneously. This speeds up the reading-out procedure and, since the driving unit is preferentially connected to the multiple of resonator elements such that at least two resonator elements are driveable simultaneously only, in particular, that all resonator elements are driveable simultaneously only, and/or since the driving response determination unit is preferentially connected to the resonator elements such that the driving response of at least two resonator elements is determinable simultaneously only, in particular, such that the driving response of all resonator element is determinable simultaneously only, the connections of the reading-out apparatus are simplified. Preferably, the driving unit and the driving response determination unit are each connected to the multiple of resonator elements at two contact locations.

It is further preferred that the driving unit is adapted for driving the resonator elements electromagnetically. This allows to drive the resonator elements in an easily controllable manner.

In a preferred embodiment, the reading-out apparatus further comprises a magnetic unit for providing a magnetic field, in which the multiple of resonator elements are located, wherein the resonator elements are electrically conductive and wherein the driving unit is adapted for applying an alternating current to the multiple of resonator elements. Since an alternating current flows through the resonator elements, which are located in the magnetic field, the driving unit induces an oscillation in the resonator elements, thereby driving the resonator elements in a controllable manner, wherein the quality of the control of the driving of the resonator elements, i.e. of the inducing of an oscillation, is further improved.

The magnetic unit is preferentially a permanent or an electro magnet. It is further preferred that permanent magnets are configured in a Halbach array to increase the strength of the magnetic field.

It is further preferred that the driving response determination unit is adapted for determining the driving response by measuring a voltage or current at the multiple of with which the resonator elements are driven elements is further improved. It is further preferred that the driving response determination unit is adapted for measuring the voltage or current at a number of contacts, wherein the number of contacts is smaller than the number of contacts needed for measuring the voltage or the current in each of the multiple of resonator elements separately. It is further preferred that the driving response determination unit is connected to the multiple of resonator elements at two contact locations only. This reduces the number of contacts needed in the reading-out apparatus and facilitates therefore the manufacturing and connection process.

It is further preferred that the resonator elements of the multiple of resonator elements comprise different resonance frequencies, in particular, slightly different resonance frequencies, i.e. the frequency distance between the resonance frequencies of the individual resonator elements can be much smaller than the bandwidth of the individual resonator elements. For instance, if the bandwidth of a first resonator element is 5kHz, then the band between the first and a second resonator element, i.e. the band which 'separates' the two resonators, can be for instance 0.5kHz. It is also preferred that the driving unit is adapted such that predetermined resonator elements are operated in the nonlinear regime. Preferentially, the driving unit is adapted such that only at least one predetermined resonator element is operated in the nonlinear regime. This can, for example, be achieved by choosing the driving amplitude of the driving unit, for example, an amplitude of a current flowing through an electrically conductive resonator element located in a magnetic field, such that only the at least one predetermined resonator element is operated in the nonlinear regime.

In a further aspect of the present invention a reading-out method for reading out a multiple of resonator elements is presented, wherein the reading-out method comprises following steps:

- driving the multiple of resonator elements such that at least one of the multiple of resonator elements is operated in a nonlinear regime by a driving unit,

- determining a driving response of the driven multiple of resonator elements by modifying a driving parameter by a driving response determination unit,

- determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime, by a nonlinearity driving determination unit.

In a further aspect of the present invention a computer program for reading out a multiple of resonator elements is presented, wherein the computer program comprises program code means for causing a reading-out apparatus as defined in claim 1 to carry out the steps of the reading-out method as defined in claim 12, when the computer program is run on a computer controlling the reading-out apparatus.

It shall be understood that the reading-out apparatus of claim 1 , the reading-out method of claim 12 and the computer program of claim 13 have similar and/or identical preferred embodiments as defined in the dependent claims.

It shall be understood that a preferred embodiment of the invention can also be any combination of the dependent claims with the respective independent claim. BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. In the following drawings

Fig. 1 shows schematically and exemplarily an embodiment of a reading- out apparatus for reading out a multiple of resonator elements, Fig. 2 shows schematically and exemplarily some units of the reading-out apparatus in more detail, Fig. 3 shows schematically and exemplarily a principal of driving and reading out resonator elements,

Fig. 4 shows schematically and exemplarily some units of another embodiment of a reading-out apparatus,

Figs. 5 and 6 show schematically and exemplarily frequency responses for different amplitudes of a driving current,

Figs. 7 to 10 show schematically and exemplarily frequency responses of individual resonator elements operated in a linear regime, Figs. 11 and 12 show schematically and exemplarily the frequency response of four resonator elements operated in a linear regime, Figs. 13 and 14 show schematically and exemplarily a frequency response of four resonator elements operated in a nonlinear regime, Figs. 15 and 16 show schematically and exemplarily a power response of four resonator elements operated in a linear regime and operated in a nonlinear regime, Figs. 17 and 18 show schematically and exemplarily a driving response depending on a driving power and a driving frequency measured by using a power sweep, and

Fig. 19 shows schematically a flow chart illustrating an embodiment of a reading-out method for reading out a multiple of resonator elements.

DETAILED DESCRIPTION OF EMBODIMENTS

Fig. 1 shows schematically and exemplarily a reading-out apparatus 1 for reading out a multiple of resonator elements. The reading-out apparatus 1 comprises a multiple 6 of resonator elements 2, 3, 4, 5, which are, in this embodiment resonant sensors. The reading-out apparatus 1 further comprises a driving unit 7 for driving the multiple 6 of resonator elements 2, 3, 4, 5 such that a least one of the multiple 6 resonator elements 2, 3, 4, 5 is operated in a nonlinear regime. The driving unit 7 is preferentially adapted such that a predetermined number of resonator elements 2, 3, 4, 5 is operated in a nonlinear regime, wherein it is further preferred that all resonator elements are operated in a nonlinear regime.

The reading-out apparatus 1 further comprises a driving response determination unit 8 for determining a driving response of the driven multiple of resonator elements. The driving response determination unit 8 determines, for example, a frequency response, an amplitude response or a power response. Furthermore, the response determination unit 8 can be adapted for determining a combination of these responses. Thus, the driving unit induces oscillations of the resonator elements 2, 3, 4, 5, wherein a frequency, an amplitude and/or a power of the driving can be swept, wherein the response of the resonator elements 2, 3, 4, 5 depending on the swept frequency, amplitude and/or power is determined by the driving response determination unit 8. The frequency, the amplitude and/or the power, with which the resonator elements are driven, can be regarded as driving parameters. The driving response determination unit 8 determines the driving response preferentially by measuring the response of the resonator elements, for example, by measuring a voltage or current generated in the resonator elements by their movement within a magnetic field, as will be described further below. The reading-out apparatus 1 further comprises a nonlinearity response determination unit 9 for determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime. This behaviour is preferentially a jump in the driving response, wherein the at least one nonlinearity driving parameter value is the value, at which the respective jump occurs. In this case, the nonlinearity driving parameter value can be regarded as a jump value. The nonlinearity driving parameter value, i.e. in this embodiment the jump value, is, for example, the frequency, the amplitude and/or the power value, at which a jump in the driving response occurs. The driving unit 7 and the driving response determination unit 8 are preferentially adapted such that, if a number of resonator elements is operated in a nonlinear regime, the same number of nonlinearity driving parameter values can be determined by the nonlinearity response determination unit 9, wherein each nonlinearity driving parameter value can be assigned to a resonator element.

The reading-out apparatus further comprises, in this embodiment, a property determination unit 10 for determining a property of an object being in contact with the multiple of resonator elements 2, 3, 4, 5 using the determined at least one nonlinearity driving parameter value. The object is, for example, a fluid, in particular water or gas, which is in contact with the multiple elements for determining a property of the object. The object influences the oscillating properties of the resonator elements, for example, because a mass is attached to the resonator elements or the temperature of the resonator elements is modified or the viscosity of an object, which is preferentially a fluid surrounding the resonator elements, influences the oscillation of the resonator elements etc.. Thus, the oscillation of the resonator elements depends on the property of the object, which has to be determined, such that the driving parameter value can be related to a certain property, in particular a property value, of the object. For example, by calibration it can be determined which property value belongs to which driving parameter value and this relationship can be stored in the property determination unit 10 for determining a property of an object depending on the determined at least one driving parameter value.

The multiple 6 of resonator elements 2, 3, 4, 5 form a network of resonator elements, which are, as will be shown further below, in this embodiment, connected in parallel. In other embodiments, the resonator elements can be connected in series or in any other arbitrary configuration.

The resonator elements 2, 3, 4, 5 are, in this embodiment, double clamped flexural resonator element, in particular, resonating sensors. These resonating sensors are preferentially made of LPCVD silicon nitride coated with a conductive layer preferentially of metal, in particular, with a thin conductive layer preferentially of gold. Instead of a resonator made of LPCVD silicon nitride coated with a conductive layer, another conductive resonator can be used, for example, a solid metal wire.

The gold layer is particularly useful, if thiol chemistry is used to functionalize the resonators, in particular, if the resonators are used as biosensors. In other embodiments, silicon nitride may be directly functionalized. If the resonator elements are magnetomotively driven and/or if a response is detected magnetomotively, a conductive layer is preferentially used. The conductive layer comprises preferentially TiN-Al or Au on a SiC, SiN etc. substrate.

To functionalize means in particular to attach a layer of 'probe' molecules to a surface which is able to bind specific molecules within a fluid to be analyzed, i.e. the 'target' molecules. These may be organic or anorganic molecules. One of the ways is to attach thiol groups to the 'probe', which forms a strong bond with Au. If this principle is used, the resonator elements are preferentially coated with a layer of Au. The reading-out apparatus 1 can comprise a resonance frequency determining unit 15 for determining the resonance frequency of at least one of the resonator elements 2, 3, 4, 5 using the at least one nonlinearity driving parameter value, which corresponds to the respective resonator element. The property determination unit 10 can be adapted such that a resonance frequency determined by the resonance frequency determining unit 15 is used for determining a property of an object like a fluid. The relationship between the respective resonance frequency of a resonator element and a property of an object can be determined by calibration.

In this embodiment, a user can chose between using the determined resonance frequency and/or the determined nonlinearity driving parameter value for determining a property of an object. In other embodiments, the resonance frequency determining unit 15 can be omitted, wherein the property of an object is determined by using at least one nonlinearity driving parameter value, without determining the resonance frequency. In this embodiment, the driving unit 7 and the multiple 6 of resonator elements 2, 3, 4, 5 are adapted such the multiple 6 of resonator elements 2, 3, 4, 5 are simultaneously drivable and the driving response determination unit 8 and the multiple 6 of resonator elements 2, 3, 4, 5 are adapted such that a driving response of the multiple 6 of resonator elements 2, 3, 4, 5 is simultaneously determinable. In particular, in this embodiment, the driving unit 7 and the multiple 6 of resonator elements 2, 3, 4, 5 are adapted such that all resonator elements 2, 3, 4, 5 are drivable simultaneously only, wherein not all resonator elements 2, 3, 4, 5 have to be operated in a nonlinear regime, and the driving response determination unit 8 and the multiple 6 of resonator elements 2,

3, 4, 5 are adapted such that a driving response of the multiple 6 of resonator elements 2, 3, 4, 5 is determinable simultaneously only, i.e. preferentially all resonator elements 2, 3,

4, 5 contribute to the driving response. In other embodiments, the driving unit 8 is connected to the multiple of resonator elements such that at least two resonator elements are drivable simultaneously only and/or the driving response determination unit 8 is connected to the multiple of resonator elements such that the frequency response of at least two resonator elements is determinable simultaneously only.

In this embodiment, the driving unit 7 is adapted for driving the resonator elements 2, 3, 4, 5 electromagnetically. This will be explained in the following with reference to Figs. 2 and 3.

Fig. 2 shows some units of the reading-out apparatus 1 schematically and exemplarily in more detail.

In Fig. 2, the resonator elements 2, 3, 4, 5 are double clamped flexural resonator elements, which are connected in parallel. In Fig. 2, the driving unit 7, the driving response determination unit 8, the nonlinearity response determination unit 9, optionally the resonance frequency determination unit 15 and optionally the property determination unit 10 are integrated in a driving and determination unit 11 comprising a network analyzer. The driving and determination unit 11 is connected with the multiple 6 of resonator elements 2, 3, 4, 5 at one or two contact locations only via a converter 12 for converting a voltage generated by the driving unit, in particular, the network analyzer, into an alternating current. Such a connection of the driving and determination unit 11, in particular, of the driving unit integrated in the driving and determination unit 11, allows to drive all resonator elements 2, 3, 4, 5 simultaneously. The driving unit 7, which uses the network analyzer and which is integrated in the driving and determination unit 11, applies an alternating current to the resonator elements 2, 3, 4, 5, in particular in all resonator elements simultaneously.

The reading-out apparatus 1 further comprises a magnetic unit 14 for providing a magnetic field, in which the multiple of resonator elements 2, 3, 4, 5 are located. This magnetic unit 14 is shown schematically and exemplarily in Figs. 1 and 2 and is preferentially a permanent magnet. In other embodiments, the magnetic unit 14 can be a cryogenic superconducting magnet. The magnetic field generated by the magnetic unit 14 is adapted such that it is strong enough at the locations, at which the resonator elements 2, 3, 4, 5 are located, to drive the resonator elements into the nonlinear regime. The multiple 6 of resonator elements 2, 3, 4, 5 is read out by the driving response determination unit 8, which is integrated in the driving and determination unit 11, via a high impedance differential amplifier unit 13. The driving response determination unit 8 uses the network analyzer for determining the driving response of the driven multiple 6 of resonator elements 2, 3, 4, 5. The driving response determination unit 8 is connected via the amplifier unit 13 to the multiple 6 of resonator elements 2, 3, 4, 5 at two contact locations only, which are preferentially identical to the contact locations, at which the driving unit 7 is connected to the multiple 6 of resonator elements 2, 3, 4, 5.

The resonator elements 2, 3, 4, 5 are preferentially contained in a chip, which is placed in the magnetic field, which is generated by the magnetic unit 14 and which is indicated by the arrow marked B. The alternating output voltage of the network analyzer is converted into an alternating current by the converter 12, wherein the alternating current is applied through all resonator elements simultaneously. Meanwhile the voltage generated by the resonators is measured using preferentially the same two connections via the amplifier unit 13. Preferentially a buffered signal is fed back into the driving and determination unit 11, in particular, into the network analyzer.

The number of resonator elements is by no means limited to four. In other embodiments, the multiple of resonator elements can comprise less or more than four resonator elements, wherein also in these embodiments the number of connections for the multiple of resonator elements is preferentially two only. In this embodiment magnetomotive drive and detection is used to drive and detect all resonators, i.e. resonator elements, simultaneously. Fig. 3 shows schematically and exemplarily the principal of operation, wherein above the driving principal and below the detection principal is shown, in particular of magnetomotive detection. An alternating current I through a resonator element, for example, the resonator element 2, moves charge carriers in the resonator element at speed v. In presents of magnetic fields B the carriers experience a Lorentz force F_L. As the resonator element is preferentially a flexible structure, it will bend as a result of this force, i.e. the resonator element 2 is driven such that an oscillation is induced (above in Fig. 3). The movement of the resonator element 2 with the speed Vbeam introduces a force F on the charge carriers resulting in a voltage V across the resonator element, wherein the voltage V can be measured by the driving response determination unit 8 for determining a driving response of the driven multiple of resonator elements using, in this embodiment, the network analyzer (below in Fig. 3). This voltage V is called electromotive force or EMF. The resonator elements 2, 3, 4, 5 of the multiple of the resonator elements comprise different resonance frequencies. In this embodiment, the resonator elements are designed with the same geometry, wherein spacings between resonance frequencies of the resonator elements are "generated" by statistic differences due to imperfect fabrication. The resonant frequency is preferentially slightly different for all resonator elements. In this embodiment, the resonance frequencies of the resonators all lay within 2 kHz, while the bandwidth of the single resonators is about 5.5 KHz. Preferentially, reactive or dissipative coupling between the individual resonator elements is minimized so that the measured voltage is given by the superposition of the voltages generated by the individual resonators. For example, preferentially the resonator elements are placed in series, in order to reduce mutual coupling. A serial placement will be described in the following. Fig. 4 shows some units of another embodiment of a reading-out apparatus schematically and exemplarily in more detail.

In Fig. 4 the resonator elements 31, 32, 33, 34, 35 are double clamped flexural resonator elements, which are connected in series. In Fig. 2, a driving unit, a driving response determination unit, a nonlinear response determination unit, and optionally a resonance frequency determination unit and optionally a property determination unit are integrated in a driving and determination unit 41 comprising a network analyzer. The driving and determination unit 41 is connected with a multiple 36 of resonator elements 31, 32, 33, 34, 35 at one or two contact locations only via a converter 44 for converting a voltage generated by the driving unit, in particular, the network analyzer, into an alternating current. Such a connection of the driving and determination unit 41, in particular, of the driving unit integrated in the driving and determination unit 41, allows to drive all resonator elements 31, 32, 33, 34, 35 simultaneously. The driving unit, which uses the network analyzer, which is integrated in the driving and determination unit 41, applies an alternating current to the resonator elements 31, 32, 33, 34, 35, in particular, in all resonator elements simultaneously.

The reading-out apparatus shown in Fig. 4 further comprises a magnetic unit 44 for proving a magnetic field, in which the multiple of resonator elements 31, 32, 33, 34, 35 are located. The magnetic unit 44 can be, as already mentioned above with respect to the magnetic unit 14, a permanent magnet, a cryogenic superconducting magnet or another magnet. Also the magnetic field generated by this magnetic unit 44 is adapted such that it is strong enough at the locations, at which the resonator elements 31, 32, 33, 34, 35 are located, to drive the resonator elements into the nonlinear regime. The multiple 36 of resonator elements 31, 33, 33, 34, 35 is read out by a driving response determination unit, which is integrated in the driving and determination unit 41, via an amplifier unit 43, which can be a high impedance differential amplifier unit. The driving response determination unit uses the network analyzer for determining the driving response of the driven multiple 36 of resonator elements 31, 32, 33, 34, 35. The driving response determination unit is connected via the amplifier unit 43 to the multiple 36 of resonator elements 31, 32, 33, 34, 35 at one or two contact locations only, which is preferentially identical to the contact location, at which the driving unit is connected to the multiple 36 of resonator elements 31, 32, 33, 34, 35. Also the resonator elements 31, 32, 33, 34, 35 are preferentially contained in a ship, which is placed in the magnetic field, which is generated by the magnetic unit 44 and which is indicated by the arrow B.

The alternating output voltage of the network analyzer is converted into an alternating current by the converter 42, wherein the alternating current is applied through all resonator elements simultaneously. Meanwhile the voltage generated by the resonator elements is measured using preferentially the same connection via the amplifier 43. Preferentially, a buffer signal is feedback into the driving and determination unit 41, in particular, into the network analyzer.

The number of resonator elements is not limited to five. In other embodiments, the multiple of resonator elements can comprise less or more than five resonator elements, wherein also in these embodiments, the number of connections for the multiple of resonator elements is preferentially one or two only.

In Figs. 5 to 11 and 13 the signal amplitude of a signal, which can be detected by a reading-out apparatus, in particular, in accordance with the invention, is shown versus frequency in arbitrary units and in Figs. 12 and 14 the phase of the signal is shown versus frequency in arbitrary units. These dependences can be regarded as driving responses.

Fig. 5 shows schematically and exemplarily a driving response being in this example a frequency response of several resonator elements with increasing amplitude of the driving current. The direction of increasing amplitude is indicated by arrow 16. At low amplitudes all resonances coincide and the individual signals cannot be recovered. At a certain amplitude the resonator elements start to jump from high to low amplitude. If such a jump is visible in the frequency response, the corresponding resonator element is operated in a nonlinear regime, which causes this behaviour, i.e. the jump. The frequency, at which this jump occurs, is the jump frequency and a nonlinearity driving parameter value, at which the response comprise a behavior caused by the operation in the nonlinear regime. Fig. 6 shows schematically and exemplarily jumps of individual resonators indicated by a, b, c and d, which can be discriminated in the frequency response. These dependences can be regarded as driving responses.

The nonlinear regime and the resulting jumps in the driving response will in the following be described in an example.

Fig. 7 shows schematically and exemplarily a measured resonant curve of a single resonator element, which is preferentially a resonating sensor, wherein the amplified amplitude of the electromotive force is shown depending on the driving frequency. The circles show the measured values and the solid line is a Lorentzian fit. Corresponding resonant curves of three other resonator elements is schematically and exemplarily shown in Figs. 8 to 10. The resonance frequency of four resonator elements was measured by driving them at low amplitude. An offset is visible which represents the voltage drop over the ohmic resistance of the resonator elements plus connecting wires. This voltage drop is slightly different for each of the four resonator elements. The bandwidth of these resonance curves is about 5 KHz and the resonance frequencies of the two closest resonator elements shown in Figs. 7 and 9 differ by about 0.5 Hz, which is an order of magnitude less than the bandwidth. Obviously these two resonator elements cannot be resolved by standard techniques. For low amplitudes of the driving current the response of the resonator elements is linear such that they cannot be discriminated in a combined frequency response. But, if the amplitude of the driving current is increased, discrete jumps of the resonator elements become visible, wherein the corresponding jump frequencies can be determined and used for determining properties of an object, if the resonator elements are resonating sensors. This different behaviour of the frequency response in a linear regime and in a nonlinear regime will be further illustrated in the following with respect to Figs. 11 to 14.

Fig. 11 shows the amplitude of the detected signal at large drive amplitude versus frequency and Fig. 12 shows the phase of the detected signal versus frequency. The signal is offset by the ohmic resistance of the resonator. The detected amplitude and phase are the frequency responses and, in this embodiment, the driving response. The frequency response shown in Figs. 11 and 12 correspond to an operation in a linear regime. In this example, four resonating sensors are operated in a linear regime. As can be seen in Figs. 11 and 12, these four resonators cannot be discriminated in the frequency response. Figs. 13 and 14 show the amplitude of the detected signal versus frequency (Fig. 13) and the phase of the detected signal versus frequency (Fig. 14), wherein the four resonator elements are operated in a nonlinear regime. Four jumps are clearly visible, which correspond to the four resonator elements operated in a nonlinear regime. The corresponding jump frequencies, i.e., in this example, the driving parameter values, at which the driving response comprises a behavior caused by an operation in the nonlinear regime, can be determined very accurately, and, for example, be used for determining a property of an object.

Resonance frequencies of the resonator elements are preferentially in a range of 10 kHz up to 100 MHz. The resonator elements, in particular, the resonator elements, are preferentially made by using optical or electron beam lithography.

In the case of a double clamped resonator element, which is preferentially a, in particular nanomechanical, double clamped flexural resonator, which is driven at a large amplitude in a nonlinear regime, the elongation of the beam cannot be neglected. As a result, a cubic term is introduced in the equation of motion, which becomes the form:

wherein in this Duffing equation x denotes the second derivative of the displacement to time, x denotes the first derivative of the displacement to time, x denotes the displacement, γ denotes the proportionality constant and / denotes the driving force.

Depending on the sign of K the resonance frequency shifts up or down when increasing the amplitude. At large enough amplitudes of the driving current the amplitude frequency curve of a single resonator element becomes multi- valued and the slope of the curve becomes infinite. The frequency location of this point depends on the direction of the frequency sweep, i.e. the sweep history, which is, for example, from low to high frequencies or from high to low frequencies, and the vibration amplitude. The location of the amplitude jump can be determined accurately. The driving unit 7 can be adapted for providing a frequency sweep or a power sweep to interrogate the multiple of the resonator elements. The direction of the sweep maybe upward or downward or it can be a combination of a frequency sweep and a power sweep. Preferentially, by using proper power and/or frequency sweep paths and/or times, in particular, in case of a large array of cantilevers, only a selection of the array can be interrogated, i.e. only predetermined resonator elements are operated in a nonlinear regime. In a preferred embodiment, only two wires are needed for connecting the driving unit and the driving response determination unit, which are, in this preferred embodiment, integrated in a driving and detection unit, to the multiple of resonator elements, wherein preferentially different resonator elements can be addressed by using only these two wires.

Although in the above described embodiments the resonator elements are resonant sensors, the reading-out apparatus can be used in other embodiments for reading-out and preferentially for steering electrical or electro -mechanical devices containing a large number of similar units such as displays, ccd's, memories, microarrays, dmd's etc. Due to the nonlinear jumps the units can be closely packed in the frequency domain despite of a possibly low Q factor. Furthermore, as all units can be connected in a network, the wiring on a chip can be reduced resulting in an increased fill factor of such devices. Fig. 15 shows schematically and exemplarily a logarithm of the detected amplitude of the detected signal in arbitrary units depending on the logarithm of the driving power in arbitrary units for two different constant frequencies. The detected amplitude 24 is measured at a frequency of 273 kHz, wherein the resonator elements are operated at low vibration amplitude (in a linear regime). The detected amplitude 25 is measured at a frequency of 276 kHz, wherein the displacements are large such that the resonator elements are operated in a nonlinear regime. The detected amplitude 25 shows clearly four jumps 20 to 23, which can be determined by the nonlinearity response determination unit, which determines the driving power values, i.e. the nonlinearity driving parameter values, at which the determined driving response, which is in Figs. 15 and 16 a power response, comprises a behavior caused by the operation in the nonlinear regime, i.e., in this embodiment, the jumps in the detected amplitude and the corresponding jumps in the detected phase, which are shown in Fig. 16. Fig. 16 shows schematically and exemplarily a dependence of the phase of the detected signal depending on the logarithm of the driving power for a frequency of 273 kHz, in which the resonator elements are operated in a linear regime, and for a frequency of 276 kHz, at which the resonator elements are operated in a nonlinear regime. The operation in the linear regime is indicated by the line 26 and the operation in the nonlinear regime is indicated by the line 27. The line 27 clearly shows the four jumps in the detected phase, wherein the corresponding driving powers can be determined by the nonlinearity response determination unit as driving parameter values, at which the determined driving response comprises a behavior caused by the operation in the nonlinear regime .

Although in Figs. 15 and 16 a result of a power sweep performed at certain frequencies is shown, in other embodiments the power sweep can be performed at other frequencies as long as a frequency is used, at which at least one of the resonator elements is operated in a nonlinear regime. Fig. 17 shows schematically and exemplarily the detected amplitude depending on the power and frequency applied to, in this example, six resonator elements by the driving unit. Fig. 18 shows schematically and exemplarily the phase depending on the driving frequency and the driving current l_άme, i.e. depending on the driving amplitude and the driving power. The amplitude and the phase are larger, if in the Figs. 17 and 18, respectively, a brighter value is shown. In Figs. 17 and 18 a power sweep is performed, i.e. for a constant frequency CW f the driving power is modified, wherein this power sweep is repeated for the different constant frequencies shown in Figs. 17 to 18. Figs. 17 and 18 clearly show six jumps in the detected amplitude and the detected phase, which are caused by operating the six resonator elements in a nonlinear regime. In other embodiments, a frequency sweep can be performed, i.e. the driving power and, thus, the driving amplitude can remain constant, wherein the driving frequency is modified and wherein this frequency sweep is repeated for the different constant driving powers shown in Figs. 17 and 18. In further other embodiments, jumps of the detected amplitude and/or the detected phase caused by operating the resonator elements in a nonlinear regime and, thus, the corresponding driving parameter values, for example, the corresponding driving frequency and/or the corresponding driving power or amplitude, can be determined by performing any path within the driving parameter space, which is, in this embodiment, a two-dimensional space defined by the driving frequency and the driving power or the driving amplitude of the driving current, which is applied to the resonator elements, as long as at least one resonator element is operated in the nonlinear regime along this path. In the following an embodiment of a reading-out method for reading out a multiple of resonator elements will be explained with reference to a flow chart shown in Fig. 19.

In step 101, the driving unit 7 drives the multiple 6 of resonator elements 2, 3, 4, 5 such that at least one of the multiple of resonator elements is operated in a nonlinear regime. In step 102, the driving response determination unit 8 determines a driving response of the driven multiple of resonator elements by modifying a driving parameter. The steps 101 and 102 are preferentially performed simultaneously.

In step 103, the nonlinearity response determination unit 9 determines at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime. In this embodiment, the nonlinearity response determination unit 9 determines for each resonator element, which is operated in a nonlinear regime, a jump frequency and/or a jump power or jump amplitude being a nonlinearity driving parameter value, at which the amplitude and/or the phase of the detected signal performs a jump. In step 104, the property determination unit 10 determines a property of an object, which is in contact with the multiple of resonator elements, like a fluid, using the determined at least one nonlinearity driving parameter value. In other embodiments, the nonlinearity driving parameter value can be used for determining a resonance frequency of the respective resonator element and the resonance frequency can be used for determining a property of an object.

Although in the above mentioned embodiments, which have been described with reference to Figs. 2 and 4, the driving unit 7 and the driving response determination unit 8 are integrated in a driving and determination unit 11 , in other embodiments, these two units do not have to be integrated in one unit. Furthermore, if the frequency, at which the resonator elements are driven, is constant and if the amplitude for driving the resonator elements is modified, for example, by modifying the power and, thus, the amplitude of the current applied to the resonator elements, a network analyzer is not used in an embodiment, because an amplitude sweep or a power sweep is performed at a constant frequency.

Although in the above described embodiment, the reading-out apparatus comprises a driving response determination unit and a property determination unit, in another embodiment, the reading-out apparatus can only comprise the multiple of resonator elements, the driving unit, the driving response determination unit and the nonlinearity response determination unit. Correspondingly, in an embodiment, the reading-out method only comprises the steps of driving the multiple of resonator elements such that at least one the multiple of resonator elements is operated in a nonlinear regime, determining a driving response of the driven multiple of resonator elements and determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime.

Although in the above described embodiment, a network analyzer is preferentially used, instead of a network analyzer other detection apparatuses can be used, for example, a lock-in amplifier. If, for example, the driving amplitude or the driving power is modified as a driving parameter, a fixed driving frequency is preferentially used together with a voltage-controlled amplifier (VCA) as a driving unit, i.e. e.g. an oscillator at fixed frequency connected to a VCA, and a differentiator at the output, i.e. the output of the resonator elements, to detect the discontinuities and/or jumps in the driving response.

The resonator elements are preferentially micro and/or nanoelectro- mechanical (MEMS, NEMS) resonators. A change of the oscillation behavior of the sensor elements due to mass, force and/or stress changes can be measured by determining at least one driving parameter value, for example, a frequency value and/or an amplitude value or a power value, at which the driving response comprises a behavior caused by the operation in the nonlinear regime, for example, at which the driving response, which is, for example, a measured EMF signal, comprises one or several jumps. A shift of this determined driving parameter value, which could be regarded as nonlinearity driving parameter value, which can be determined by the nonlinearity response determination unit and which is caused by mass, force and/or stress changes, is preferentially used for determining a property and/or the physical or chemical content of an object, like a fluid such as air or gas, in particular, in the process industry, or a liquid, which is in contact with the resonator elements. In this way, the resonator elements could be used as a detector. If the resonator elements are used as a detector, the resonator elements, in particular, the cantilevers are preferentially functionalized to make them specific to certain particles or molecules.

Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality.

A single unit or other device may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Determinations, like the determination of a driving response, of a driving parameter value, at which the determined driving response comprises a behavior caused by the operation in the nonlinear regime and which can be regarded as nonlinearity driving parameter value, and/or of a property of an object, and the driving of the multiple of resonator elements performed by one or several units or devices can be performed by any other number of units or devices. For example, the driving of the multiple of resonator elements, the driving response determination and the determination of the nonlinearity driving parameter value can be performed by a single unit or by any other number of units. The driving and the determinations and/or the control of the reading- out apparatus in accordance with the reading-out method can be implemented as program code means of a computer program and/or as dedicated hardware.

A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope.

Claims

CLAIMS:

1. A reading-out apparatus for reading out a multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35), the reading-out apparatus comprising:

- a multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35),

- a driving unit (7) for driving the multiple of resonator elements such that at least one of the multiple of resonator elements is operated in a nonlinear regime,

- a driving response determination unit (8) for determining a driving response of the driven multiple of resonator elements by modifying a driving parameter,

- a nonlinearity response determination unit (9) for determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime.

2. The reading-out apparatus as defined in claim 1, wherein the resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) are resonant sensors and wherein the reading-out apparatus comprises a property determination unit (10) for determining a property of an object being in contact with the multiple of resonator elements (2, 3, 4, 5; 31, 32, 33, 34,

35) using the determined at least one nonlinearity driving parameter value.

3. The reading-out apparatus as defined in claim 1, wherein the multiple (6;

36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) are connected to each other.

4. The reading-out apparatus as defined in claim 1, wherein the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) are flexural resonators.

5. The reading-out apparatus as defined in claim 4, wherein the resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) are double clamped.

6. The reading-out apparatus as defined in claim 1, wherein the driving unit (7) is connected to the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) such that at least two resonator elements are drivable simultaneously only and/or the driving response determination unit is connected to the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) such that the driving response of at least two resonator elements is determinable simultaneously only.

7. The reading-out apparatus as defined in claim 1, wherein the driving unit (7) is adapted for driving the resonator elements electromagnetically.

8. The reading-out apparatus as defined in claim 7, wherein the reading-out apparatus further comprises a magnetic unit (14; 44) for providing a magnetic field, in which the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) are located, wherein the resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) are electrically conductive and wherein the driving unit (7) is adapted for applying an alternating current to the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35).

9. The reading-out apparatus as defined in claim 8, wherein the driving response determination unit (8) is adapted for determining the driving response by measuring a voltage or current at the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35).

10. The reading-out apparatus as defined in claim 1, wherein the resonator elements of the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) comprise different resonance frequencies.

11. The reading-out apparatus as defined in claim 1 , wherein the driving unit (7) is adapted such that predetermined resonator elements are operated in the nonlinear regime.

12. A reading-out method for reading out a multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35), the reading-out method comprising following steps:

- driving the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) such that at least one of the multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) is operated in a nonlinear regime by a driving unit (7),

- determining a driving response of the driven multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35) by modifying a driving parameter by a driving response determination unit (8), - determining at least one nonlinearity driving parameter value, at which the determined driving response comprises a behaviour caused by the operation in the nonlinear regime, by a nonlinearity driving determination unit (9).

13. A computer program for reading out a multiple (6; 36) of resonator elements (2, 3, 4, 5; 31, 32, 33, 34, 35), the computer program comprising program code means for causing a reading-out apparatus as defined in claim 1 to carry out the steps of the reading-out method as defined in claim 12, when the computer program is run on a computer controlling the reading-out apparatus.