WO2003094173A1 - Procede et dispositif de commande d'un signal d'excitation d'un element oscillatoire mecanique resonant, procede et dispositif de mesure, programme informatique et dispositif de stockage - Google Patents

Procede et dispositif de commande d'un signal d'excitation d'un element oscillatoire mecanique resonant, procede et dispositif de mesure, programme informatique et dispositif de stockage Download PDF

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Publication number
WO2003094173A1
WO2003094173A1 PCT/ES2003/000100 ES0300100W WO03094173A1 WO 2003094173 A1 WO2003094173 A1 WO 2003094173A1 ES 0300100 W ES0300100 W ES 0300100W WO 03094173 A1 WO03094173 A1 WO 03094173A1
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Prior art keywords
oscillation
signal
amplitude
frequency
excitation
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PCT/ES2003/000100
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English (en)
Spanish (es)
Inventor
Francisco Javier Tamayo De Miguel
Laura M. LECHUGA GOMÉZ
M. del Mar ÁLVAREZ SÁNCHEZ
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Consejo Superior De Investigaciones Científicas
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Priority to AU2003214265A priority Critical patent/AU2003214265A1/en
Publication of WO2003094173A1 publication Critical patent/WO2003094173A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
    • G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
    • G01Q60/24—AFM [Atomic Force Microscopy] or apparatus therefor, e.g. AFM probes
    • G01Q60/32—AC mode
    • G01Q60/34—Tapping mode

Definitions

  • the invention falls within the field of mechanical oscillators and measurements based on the dynamic response of said oscillators.
  • the dynamic response of a mechanical oscillator means the relationship between the oscillator movement and an excitation force with a certain frequency.
  • the dynamic response is determined by the resonance frequency, quality factor, damping factor, elastic constant and mass.
  • relevant mechanical oscillators are cantilevers used in atomic force microscopy (AFM), fiber optic probes used in near field optical microscopy (SNOM), and resonant structures of sensors and mechanical biosensors.
  • the basic idea of the atomic force microscope is to measure the force between a very sharp point (radius of curavature of the order of the nanometer) and a surface that you want to characterize, which can be located at a distance between 0.1 and 100 nm.
  • the tip is attached to the end of a cantilever (micro lever) of micrometric dimensions, so that the force is measured from the cantilever deflection.
  • the cantilever is deflected in response to force following approximately Hooke's law, that is, it behaves like a harmonic oscillator.
  • Deflection is usually measured with sub-nanometric resolution by an optical system illustrated schematically in Figure 1: a laser beam 1 emitted by a laser diode 2 strikes the surface of the cantilever or oscillating element 3 (which is provided with the tip 4) and is reflected in a segmented photodetector 5; the object on which the measurement is carried bears the numerical reference 6.
  • Other optical, capacitive, piezoresistive detection methods etc. can also be used.
  • the images are obtained by sweeping the sample with respect to the tip or vice versa, which have an accuracy of 0.01-0.1 nm.
  • the scanning is usually done using piezoelectric crystals.
  • a feedback system can maintain constant force (constant deflection), vertically moving the sample with respect to the tip or vice versa.
  • the vertical displacement with respect to the horizontal provides the topography of the surface of the sample.
  • the AFM it is worth highlighting its high spatial resolution that is determined by the dimensions of the tip and which allows sub-nanometric resolution to be obtained.
  • it allows the topographic visualization of surfaces in different media such as vacuum, air, gases or liquids. It also shows great versatility and allows visualizing magnetic domains, spatial variations of electrical properties or mechanical properties.
  • the AFM has become a fundamental tool in nanotechnology and its use is widespread in the fields of materials physics, physicochemical, biology and biomedicine.
  • the expansion of the atomic forces microscope has led to the commercialization of microfabricated cantilevers with silicon technology.
  • the cantilevers have a length of the order of 100 ⁇ m, a width of the order of 10 ⁇ m and a thickness of less than approximately 1 ⁇ m.
  • the elastic constant (k) is determined by the dimensions of the cantilever, being of the order of 0.1 N / m.
  • static mode To detect and measure the force between the tip and the sample in an AFM there are two modes: static mode and dynamic mode.
  • static mode also called contact mode
  • the tip is usually in contact with the surface of the sample, with a repulsive force appearing.
  • the minimum detectable force that can be applied to the sample is mainly limited by the thermal noise produced by a fluctuation in cantilever deflection. Using the static method, forces below 0.01 nN can hardly be used.
  • the dynamic mode allows lower forces to be measured in the air and vacuum media.
  • the cantilever oscillates with an amplitude of the order of the nanometer, excited by an external sine force with frequency equal to that of the resonance of the Cantilever, or next.
  • the cantilever oscillation changes when the tip is close to the surface of the sample due to the force between the tip and the sample.
  • the oscillation parameters that can be measured are the amplitude and the lag with respect to the exciting force, and its change due to the tip / sample interaction.
  • the change in amplitude or offset is due to the change in the resonant frequency and the change in the damping factor.
  • the forces exerted in the dynamic mode of an AFM can be analyzed by modeling the cantilever as a forced harmonic oscillator whose equation of motion is:
  • m is the effective cantilever mass
  • z is the cantilever deflection
  • ⁇ is the damping factor
  • F 0 cos ( ⁇ t) is the excitation force
  • F ⁇ nt is the interaction force between the tip and the sample.
  • the damping factor ( ⁇ ) depends on the internal friction of the material and the friction of the cantilever with the medium.
  • Q is Another magnitude directly related to the damping factor
  • ⁇ 0 is the angular resonance frequency.
  • the Q varies depending on the viscosity of the medium, so in vacuum it can reach values of the order of 10,000, in air of the order of 100 and in liquids very low values of 1 to 10.
  • One way to obtain complete information on the interaction between the tip and the sample is to measure the frequency spectrum of the cantilever, that is, the amplitude and the lag of the oscillation with respect to the frequency of the exciter signal (see Figure 2) .
  • Two magnitudes are measured from the frequency spectrum, the resonance frequency f 0 and the quality factor Q.
  • the measurement of the offset allows to determine the resonant frequency of the cantilever and its change due to the tip / sample interaction, given that the definition of Resonance frequency is that frequency at which the offset between the cantilever oscillation and the exciter signal is 90 degrees. This frequency is where the maximum amplitude is approximately. However, in the case of low quality factors the Maximum amplitude position differs from the resonant frequency.
  • the quality factor is measured by the width of the amplitude curve as a function of the frequency of the exciter signal by this expression:
  • ⁇ f 0 is the width of the curve at which the amplitude has decayed by half.
  • the cantilever In the dynamic mode of an AFM, the cantilever is excited at a fixed frequency, equal to or close to that of resonance and the interaction between the tip and the sample can be measured by changing the amplitude of the oscillation. Assume that the interaction between the tip and the sample displaces the resonance frequency and that the system can detect amplitude changes above a certain threshold. The amount that the resonance frequency has to be displaced, that is, the amount of interaction between the tip and the sample, so that a change in amplitude can be detected depends on the quality factor (Q) as illustrated in Figure 3. Thus, it is understood why the dynamic mode of AFM in liquids implies high normal forces.
  • Q quality factor
  • a change in detectable amplitude in liquids only occurs when there are high forces between the tip and the sample (high resonance frequency shift), due to the low Q. Similarly, if the interaction between the tip and the sample were measured by changing the oscillation offset the same would happen; The change in offset due to a change in the resonance frequency is proportional to the quality factor.
  • AFM AFM
  • This limitation is fundamental when you want to visualize biological samples (DNA, proteins, cells, etc.). To visualize the native structure of these samples, visualization is required in an aqueous medium. Under these conditions, the biological samples are soft and weakly adhere to the solid support (mica, graphite, silicon, glass, etc.) as a result of the great screening of the attractive forces between the biological samples and the solid support that is produced in solutions aqueous.
  • the tip In the contact mode, the tip displaces and / or destroys the sample during scanning (lateral forces), and visualization of the sample is prevented or made very difficult.
  • the tip usually touches the sample intermittently in each cycle of the oscillation.
  • resonant structures are microfabricated that can be used as sensors and biosensors.
  • Most sensors based on resonant structures have been developed for the detection of chemical compounds in gaseous media demonstrating very high sensitivity. They also allow real-time detection, require a minimum amount of analyte and the tiny size of these devices makes their miniaturization and integration into chips with low cost feasible.
  • An example is bio / sensors based on cantilevers such as those used in AFM, but in which the tip is not used.
  • An important application of this type of sensors is the biosensors and sensors of chemical substances in liquid media. Biosensors detect biological substances instead of chemical substances. For this reason, the detection must be performed in the liquid medium, in which the biological molecules are functional. From now on, cantilever is understood as any resonant mechanical structure.
  • receptor molecules are immobilized on one of the sides of the resonant mechanical structure (EMR), which specifically bind to the substance to be analyzed or detected (analyte).
  • EMR resonant mechanical structure
  • the analyte binds to the receptor molecules.
  • the surface composition has varied and therefore the surface tension. Since the receptor molecules have been immobilized only on one side of the cantilever, the surface tension on this side changes with respect to that on the other side, and a cantilever curvature occurs.
  • This cantilever curvature can be measured by an optical system such as that used in an AFM and described above, or by other optical, capacitive, piezoresistive methods, etc.
  • FIG. 4 An example of cantilevers-based biosensor for detecting DNA hybridization is shown in Figure 4.
  • the device It consists of a cantilevers microarray. Single-stranded DNA with different base sequences has been immobilized on each side of the cantilever. When the microarray is exposed to a liquid solution containing DNA from a chain whose base sequence is complementary to that previously immobilized in one of the cantilevers, this cantilever curves due to the change in surface tension produced by the double strand DNA formation.
  • the receptor molecules are immobilized on one or both sides of the cantilever.
  • the cantilever oscillates with an amplitude of the order of the nanometer and the oscillation is measured in the same way as in a dynamic microscope of forces.
  • the sensitivity to measure changes in cantilever oscillation is proportional to the quality factor.
  • the cantilever resonance frequency is obtained by measuring the oscillation offset with respect to the exciter signal.
  • a change in the resonance frequency produces a offset of the offset with respect to 90 degrees.
  • This deviation is proportional to Q, and therefore, the sensitivity to determine the change in the resonance frequency is proportional to Q.
  • the low sensitivity to measure the dynamic properties of the cantilever in the liquid medium has prevented them from having developed Cantilevers based biosensors using dynamic detection.
  • Cantilever-based biosensors that use the static measurement method have the disadvantage that the signal being measured, the cantilever deflection, has a large drift, making its use impractical. The origin of this drift is due to turbulence of the liquid, slow chemical reactions between the solution and the cantilever surface, and thermal fluctuations. The latter has a dramatic effect on the measurements. Normally to immobilize the receptor molecules on one side of the cantilever, it is necessary to previously evaporate a thin layer of gold (thickness «10-50 nm). As a consequence, the cantilever not only responds to analyte molecules when they bind to receptor molecules, but is very sensitive to very small variations in temperature.
  • WO-A-01/81857 (on which the ActivResonance Controller® product marketed by Infinitésima Ltd. is based, describes an arrangement that allows to increase the low quality factor Q of the cantilever in the liquid medium, by means of a system of electronic feedback
  • the applications of WO-A-01/81857 also They are described in the previous publications.
  • the dynamic response of the cantilever is more sensitive than the static response, as described above.
  • the dynamic response hardly suffers thermal drift, as with the static response, which requires a long stabilization time.
  • the measurement of the dynamic response of the cantilever in a liquid medium is limited by the very low quality factor Q. This makes the AFM in the liquid medium less sensitive and that the biosensors and chemical sensors that detect substances in liquid media traditionally measure The static answer.
  • the method described in WO-A-01/81857 allows to increase the sensitivity of AFM in liquids up to 3 orders of magnitude, which has a strong impact on the application of AFM in biology. Another area of impact is the field of chemical biosensors and sensors based on resonant mechanical microstructures that need to be measured in the liquid medium.
  • WO-A-01/81857 The idea behind the invention described in WO-A-01/81857 is to introduce a cantilever movement control system to increase the quality factor. Let's say that the cantilever reacts to an incident force with frequency ⁇ , F ⁇ ⁇ ) with a transfer function X ( ⁇ ) that corresponds to a damped harmonic oscillator.
  • ⁇ 0 is the angular resonance frequency
  • k is the elastic constant
  • Q is the quality factor of the cantilever.
  • the response of the oscillator can be modified by a feedback system with a transfer function C ( ⁇ ).
  • C transfer function
  • the invention described in WO-A-01/81857 is intended to increase the Q of the cantilever, and this can be done by a controller with a function of transfer:
  • the cantilever oscillated by an alternating magnetic field whose frequency is the one of resonance, or next to her.
  • the oscillating element 3 a thin layer of ferromagnetic material has previously evaporated to respond to the magnetic field.
  • Another excitation method that can be used is the generation of mechanical-acoustic waves in the fluid by means of a piezoelectric crystal.
  • the other important element of this device is the unit that detects the resonance frequency, which is done by means of a phase-locked loop (PLL) 7 comprising a phase detector 8, a Pl 9 controller and a voltage controlled oscillator ( VCO) 10.
  • PLL phase-locked loop
  • VCO voltage controlled oscillator
  • F 0 e ' ⁇ t is the exciting force that makes the cantilever swing.
  • the cantilever is oscillated by the sum of two exciting forces, one is the standard force F 0 e ' ⁇ t , and the other is a force that is proportional to the movement of the cantilever offset 90 degrees, G ze l ⁇ / 2 .
  • the differential equation of this system is:
  • Figure 8 shows the effect of this feedback system on the response of the cantilever immersed in a liquid.
  • the quality factor can be increased up to 3 orders of magnitude, being able to obtain Qs close to 1000. That is a Cantilever in a liquid can present a dynamic response comparable to that found in a vacuum.
  • the resonance frequency signal is compared with the deflection signal of the cantilever immersed in aqueous solution.
  • the deflection signal shows great drift due to the thermal drift of the positions of the laser beam, the photodetector, and the cantilever. There are also slow chemical reactions between the cantilever and the solution. However, the resonance frequency signal is immune to these drifts.
  • the resonance frequency was immune to this alteration.
  • the antigen was introduced, a deflection response similar to when the solution was simply introduced without antigen was introduced. This change in the signal is due to the turbulence produced, the effect of local temperature change and the effect of the reaction of the antigen with the antibodies immobilized in the cantilever.
  • the signal of the resonance frequency that was immune to the introduction of the PBS shows a marked jump when the antigen is introduced into the solution.
  • the feedback system although it does serve to substantially increase the quality factor discussed above, does not always provide optimum sensitivity in the dynamic response of the cantilever or mechanical oscillator element in general.
  • the feedback system described allows obtaining high quality factors.
  • high quality factors involve certain disadvantages due to the presence of transients in the oscillation.
  • the cantilever oscillation is composed of a transitory and a stationary element.
  • the cantilever swing for an excitation force F 0 e l ⁇ t can be expressed as follows :
  • the first adding is the transitory element and the second the steady state of the oscillation.
  • the measurement of the amplitude (A) and the offset of the steady state oscillation ( ⁇ ) requires that the transient oscillation disappears.
  • the magnitude of time that indicates how long it takes for the transient to disappear is the time constant ⁇ ,
  • One aspect of the invention relates to a device for controlling an excitation signal of a resonant mechanical oscillating element excited by said excitation signal.
  • the control device comprises: means for receiving a signal representative of the oscillation of the oscillating element; means for generating a feedback component (F 2 ) of the excitation signal so that said feedback component is a function of at least one characteristic of the signal representative of the oscillation (Z); the excitation signal comprising at least said feedback component (F 2 ) and the excitation signal having an excitation frequency ( ⁇ ).
  • the control device further comprises means of determining a lag.
  • the means of generating a feedback component (F 2 ) are configured so that the feedback component (F 2 ) has an amplitude (GA) that is a function of said offset ( ⁇ ).
  • GA amplitude
  • the control system allows changing the dynamic response of the resonant mechanical oscillator element and increasing its sensitivity to measure forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element, or an object that is located in relation to the mechanical element.
  • the quality factor of a mechanical oscillator is determined by the energy dissipated during its oscillation due to internal friction of the material of the mechanical element and the friction of the mechanical element with the medium during oscillation.
  • a peak located approximately at the resonant frequency is observed. The width of this peak is smaller the greater the quality factor Q, that is, the less energy dissipates in the oscillation.
  • the offset changes more than 90 degrees when the frequency of the exciter signal deviates from the resonant frequency.
  • the oscillator dissipates more or less energy, it is indifferent when what is sought is to see changes in the oscillation of the mechanical element due to external changes that are to be measured (forces acting on the mechanical element or changes in the properties physical and / or chemical means of the medium in which the mechanical element is, or of an object that is located in relation to the mechanical element).
  • the control system of this invention apparently produces a high Q because it provides very narrow amplitude resonance peaks, but does not necessarily affect the energy dissipation of the system, which is the characteristic that determines the quality factor of a mechanical oscillator.
  • the control system of the present invention can cause major phase shifts when the excitation frequency deviates from the resonance frequency.
  • the control system according to the present invention allows a higher "apparent" quality factor to be obtained but, unlike the system set forth in WO-A-01/81857, it is not intended to increase the actual quality factor. It is intended that when measuring the amplitude of the mechanical oscillator with respect to the excitation frequency, a narrower maximum is obtained than that which the mechanical oscillator would have without this control system and was excited by an excitation force with a fixed amplitude. The maximum is at a frequency close to or equal to that of resonance. Similarly, it can be expected that the feedback system will produce a shift change when the excitation frequency deviates from that of the resonance, which is greater than if there was no control system.
  • the offset is not changed if the excitation force is composed only of the feedback component (F 2 ). However, if the excitation force is composed of a base component Fi and the feedback component F 2 in quadrature, the situation is complex, and several feedback loops are required to reach a steady state. This feedback system affects the offset and amplitude.
  • This control system does not change nor does it necessarily change the energy dissipation of the system.
  • the control system intends that the amplitude curve with respect to the frequency of the excitation signal has a narrow maximum around the resonant frequency or a frequency close to it. It can also be intended to increase the change in the oscillation offset when the frequency of the excitation signal deviates from the resonant frequency or a frequency close to it. This occurs when the quality effect is high, but it can also be obtained with a control system that produces these responses without increasing the quality factor, that is, without changing the energy dissipation of the mechanical oscillator.
  • changes in the resonance frequency of the mechanical oscillator can be measured with greater sensitivity as a result of forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element is, or of an object that is located in relation to the mechanical element.
  • changes in the quality factor can also be measured with greater sensitivity as a result of forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element is, or of an object which is located in relation to the mechanical element.
  • the control system increases the sensitivity of mechanical oscillators that have a low quality factor because they are made of a material with high internal friction or because measurements are made in a viscous medium such as a liquid.
  • the invention does not imply certain problems that the control system described in WO-A-01/81857 has, which it pursues increases the quality factor, see what we have commented in the "background of the invention" section.
  • the amplitude (GA) has a maximum at a lag ( ⁇ r ) corresponding to a frequency ( ⁇ r ) close to the resonant frequency of the oscillating element.
  • the excitation force acquires a maximum value at a frequency close to that of resonance and an amplitude curve is obtained with respect to the frequency of the exciter signal, which It has a narrow maximum around that frequency.
  • a change in the resonance frequency when the oscillator is being excited at that frequency causes a change in the amplitude (which may be related to the change in the resonance frequency) greater than the change in amplitude produced if excites the mechanical oscillator with an excitation force with a fixed amplitude (the situation is similar to that illustrated in Figure 3).
  • This allows measuring resonance frequency changes caused by forces acting on the mechanical element or changes in the physical and / or chemical properties of the medium in which the mechanical element is located, or of an object that is located in relation to the element mechanical. This is extremely important in mechanical oscillators with a low quality factor in which a change in the resonance frequency results in a too small change in amplitude or offset.
  • the amplitude has a maximum at a offset ( ⁇ ) corresponding to a frequency substantially equal to the resonant frequency of the oscillating element.
  • ⁇ offset
  • the maximum narrow amplitude appears at the resonant frequency.
  • the amplitude (GA) has a maximum when the offset ( ⁇ ) is a determined offset.
  • the amplitude (GA) has a maximum of a lag that corresponds to the frequency of resonance. Also, if the offset corresponds to a frequency close to that of resonance, the invention works and gives similar results, although not as optimal.
  • the excitation signal (F) is composed of the feedback component (F 2 ), that is, it consists exclusively of said feedback component.
  • the excitation signal (F) comprises the feedback component (F 2 ) and a base component (Fi).
  • the base component can be generated by a substantially fixed oscillator and the feedback component can be generated by the control device according to preset parameters and depending on characteristics determined from the signal representative of the oscillation (Z).
  • the base component (F ⁇ can be a signal with a fixed excitation frequency ( ⁇ ) and with a fixed amplitude and the feedback component (F 2 ) can be a signal with the same excitation frequency ( ⁇ ) and that is out of phase + 90 ° or -90 ° with respect to the base component
  • the control device comprises means of modifying the excitation frequency ( ⁇ ) as a function of the signal representative of the oscillation (Z) so as to maintain a determined offset ( ⁇ ) between the representative signal of the oscillation (Z) and the feedback component (F 2 ).
  • said determined offset is an offset corresponding to the resonance oscillation of the oscillating element. In this way, it can be achieved that the oscillating element is kept oscillating at resonance or substantially at resonance.
  • the control device comprises means of modifying the excitation frequency ( ⁇ ) as a function of the amplitude of the signal representative of the oscillation (Z), in order to maximize the amplitude of the oscillation of the oscillator element.
  • ⁇ excitation frequency
  • Z signal representative of the oscillation
  • the amplitude (GA) of the feedback component (F 2 ) is a function of both the offset ( ⁇ ) between the signal representative of the oscillation (Z) and the feedback component (F 2 ) as of the amplitude of the signal representative of the oscillation (Z).
  • the amplitude GA could have a maximum when the offset is the one that corresponds to the resonance, and in addition the amplitude GA of the feedback component could be greater the greater the amplitude of the signal representative of the oscillation (Z).
  • the means for receiving a signal representative of the oscillation (Z) are associated with a sensor that detects a signal directly related to the oscillation of the oscillating element.
  • the sensor could consist of a laser diode that emits a laser beam that is reflected in the oscillator or cantilever element and that goes to a segmented photodetector. The imbalance between the photocurrents generated in the photodetector segments is due to the deflection and movement of the cantilever.
  • the cantilever is made of a piezoresisitive material, so that when the cantilever bends the resistance of the cantilever changes.
  • the device includes a pass-band filter at the excitation frequency ( ⁇ ) to filter the signal representative of the oscillation (Z).
  • ⁇ excitation frequency
  • Z signal representative of the oscillation
  • the device is constituted by a processing device with a data acquisition card (TAD), so that: the data acquisition card comprises the means of receiving a signal representative of the oscillation (Z) of the oscillating element; the processor device comprises the means of generating the feedback component (F 2 ); and the data acquisition card comprises an output for the component of feedback (F 2 ).
  • TAD data acquisition card
  • the processor device can be a digital processor device, which allows, for example, the amplitude (GA) and / or the excitation frequency ( ⁇ ) to be set in a specific way (digitally manipulable) depending on, for example, the characteristics of the signal representative of the oscillation (Z), for example, using conventional computer applications or specifically designed for a specific use or for a certain type of uses.
  • the amplitude (GA) and / or the excitation frequency ( ⁇ ) can be set in a specific way (digitally manipulable) depending on, for example, the characteristics of the signal representative of the oscillation (Z), for example, using conventional computer applications or specifically designed for a specific use or for a certain type of uses.
  • a measuring device for example, a biosensor device
  • a measuring device comprising: means for generating an excitation signal (F); a resonant mechanical oscillator element; coupling means of the excitation signal to the resonant mechanical oscillator element so that the excitation signal induces an oscillation in said element; a detector device comprising means of generating a signal representative of the oscillation (Z) of the oscillating element; and means for reading and interpreting the signal representative of the oscillation (Z) (for example, of the same type used in the conventional measuring devices discussed in the "background of the invention” section).
  • the means for generating the excitation signal include a control device according to the invention.
  • the oscillating element can be a micro lever (“cantilever”) that can be provided with a tip (for example, as in a microscope of atomic forces).
  • Another aspect of the invention relates to a method for controlling the excitation signal of a resonant mechanical oscillator element excited by said excitation signal (F).
  • the method comprises the steps of: receiving a signal representative of the oscillation (Z) of the oscillating element; generating a feedback component (F 2 ) of the excitation signal so that said feedback component is a function of at least one characteristic of the signal representative of the oscillation (Z), the excitation signal comprising at least , said feedback component (F 2 ) and the excitation signal having an excitation frequency ( ⁇ ); determine a lag ( ⁇ ) between the signal representing the oscillation (Z) of the oscillating element and the feedback component (F 2 ) and generate the feedback component (F 2 ) so that the feedback component (F 2 ) has an amplitude (GA) which is a function of said offset ( ⁇ ).
  • the amplitude has a maximum at a lag ( ⁇ ) corresponding to a frequency close to the resonant frequency of the oscillating element.
  • the amplitude has a maximum at a offset ( ⁇ ) corresponding to a frequency substantially equal to the resonant frequency of the oscillating element.
  • the amplitude (GA) can, for example, have a maximum when the offset ( ⁇ ) is a certain offset.
  • the excitation signal (F) may be composed of the feedback component (F 2 ) (i.e. consist exclusively of said component). There is also the possibility of generating the excitation signal by adding at least the component of feedback (F 2 ) and a base component (F ⁇ ) - As a base component (Fi) a signal with a fixed excitation frequency ( ⁇ ) and with a fixed amplitude can be chosen and as a feedback component (F 2 ) You can choose a signal with the same excitation frequency ( ⁇ ) and that is offset + 90 ° or -90 ° with respect to the base component (Fi).
  • the excitation frequency ( ⁇ ) is modified as a function of the signal representative of the oscillation (Z) so as to maintain a certain offset ( ⁇ ) between the signal representative of the oscillation ( Z) and the feedback component (F 2 ).
  • Said determined offset may be, for example, a offset corresponding to the oscillation of the oscillating element at its resonance frequency, so that the oscillating element is kept oscillating at resonance.
  • the excitation frequency ( ⁇ ) is modified as a function of the amplitude of the signal representative of the oscillation (Z), in order to maximize the amplitude of the oscillation of the oscillating element.
  • the amplitude (GA) of the feedback component (F 2 ) is a function of both the offset ( ⁇ ) between the signal representative of the oscillation (Z) and the feedback component (F 2 ) as of the amplitude of the signal representative of the oscillation (Z).
  • the signal representative of the oscillation (Z) is received through a sensor that detects a signal directly related to the oscillation of the oscillating element.
  • the signal is filtered representative of the oscillation (Z) with a pass-band filter at the excitation frequency ( ⁇ ).
  • the feedback component (F 2 ) is generated with a processor device.
  • Another aspect of the invention relates to a method for carrying out measurements on an object, comprising the steps of: locating the object in relation to the oscillating element of the device described in the foregoing, so that object characteristics affect the oscillation of the object. oscillating element (for example, at the resonant frequency and / or the quality factor of the oscillating element); measure at least one characteristic related to the oscillation of the resonant element; and interpret the result of said measurement.
  • the object can be located in the vicinity of the oscillating element (which may be convenient if the object is a substantially solid surface whose surface structure is to be studied) or in direct contact with the oscillating element (which may be convenient if the object is a liquid and if it is desired to detect the presence of a certain component in the liquid; this is applicable to, for example, biosensors).
  • the oscillating element which may be convenient if the object is a substantially solid surface whose surface structure is to be studied
  • the oscillating element which may be convenient if the object is a liquid and if it is desired to detect the presence of a certain component in the liquid; this is applicable to, for example, biosensors.
  • the object and the oscillating element immersed in a liquid (for example, if the object is a biological structure that must be kept immersed in a liquid).
  • the method may be suitable for studying very diverse objects, for example, liquids, biological substances, chemicals and / or solid surfaces.
  • Another aspect of the invention relates to a computer program, characterized in that it comprises program code means for performing all the steps of the control method described above when the program is executed on a computer.
  • Another aspect of the invention relates to a storage device comprising means for storing at least this computer program.
  • Figure 1 is a schematic representation of the detection of the deflection of a micro lever in an AFM system (according to the state of the art).
  • Figure 2 is a spectrum of cantilever frequencies with and without interaction
  • Figure 3 illustrates the effect of the resonance frequency shift, due to a possible tip-sample interaction, on the change in amplitude of the cantilever when it is excited to resonance or at a nearby frequency, for a high Q value and a low Q ( according to the state of the art).
  • Figure 4 schematically illustrates a cantilever-based biosensor for detecting DNA hybridization (according to the state of the art).
  • Figure 5 illustrates a frequency spectrum of a cantilever in air and in an aqueous medium (according to the state of the art).
  • Figure 6 schematically illustrates a feedback system (according to the state of the art).
  • Figure 7 schematically illustrates, in more detail, a feedback system used in WO-01/81857 (according to the state of the art).
  • Figure 8 shows the effect of the feedback system shown in Figure 7 on the response of a cantilever immersed in a liquid (according to the state of the art).
  • Figure 9 illustrates a comparison of the resonance frequency signal, with the cantilever deflection signal immersed in aqueous solution (according to the state of the art).
  • Figure 10 illustrates results of the feedback system shown in Figure 7 applied to the detection of biological molecules (according to the state of the art).
  • Figure 11 illustrates a general arrangement according to a preferred embodiment of the invention.
  • Figure 12 is a diagram reflecting the result of a practical test according to a preferred embodiment of the invention.
  • Figure 13 reflects the results of computer simulations of a preferred embodiment of the invention.
  • Figure 14 is a diagram reflecting the result of a practical test in accordance with a preferred embodiment of the invention.
  • Fig. 15 is a diagram reflecting the result of a practical test according to a preferred embodiment of the invention.
  • Figure 16 is a diagram reflecting the result of a practical test in accordance with a preferred embodiment of the invention.
  • Figure 17 is a diagram reflecting the result of a practical test in accordance with a preferred embodiment of the invention.
  • Figure 11 illustrates a general arrangement that includes the control device according to a preferred embodiment of the invention.
  • This arrangement includes a conventional configuration according to what has been said in the foregoing, based on an oscillating element 3 or cantilever in which oscillation is induced by an excitation signal F applied to an inductor coil 11.
  • This signal is obtained by measuring the oscillation with a conventional system comprising a laser diode 2 that emits a laser beam 1 that hits the surface of the cantilever or oscillating element 3 and is reflected in a segmented photodetector 5.
  • the difference between the photocurrents generated in the upper and lower segments is proportional to the cantilever deflection.
  • the cantilever is excited by an oscillating magnetic field generated in the inductor coil 11.
  • the cantilever may have been coated with, for example, a thin ferromagnetic layer of cobalt (thickness between 10 and 50 nm).
  • the illustrated arrangement includes the control device according to the invention, schematically illustrated in Figure 11.
  • Said device comprises a personal computer (PC) 13 and a data acquisition card (TAD) 12 (se These are conventional components, which are not illustrated in more detail).
  • PC personal computer
  • TAD data acquisition card
  • a digital control can be applied to increase the "apparent" quality factor of the mechanical oscillator element 3, to increase the sensitivity of the oscillation to forces acting on the mechanical element or changes in the physical properties and / or chemical of the medium in which the mechanical element is, or of an object that is located in relation to the mechanical element.
  • the data acquisition card used has inputs to record the movement of the cantilever, that is to say to record the photocurrents or photovoltaics of each segment of the photodetector 5 as a function of time.
  • amplifier By means of software programmed in, for example, LabView TM, the amplitude and phase of the fundamental harmonic of the oscillation are calculated.
  • the alternating current that excites the coil and oscillates the cantilever is calculated and generated.
  • the excitation signal is calculated by software and generated in a function generating instrument that is controlled by the computer.
  • the amplitude and offset of the oscillation are determined by software.
  • an excitation force (F) is generated, in this case only by the sinusoidal feedback component F 2 , whose amplitude is GA and which has a very high maximum to the offset corresponding to the resonant frequency.
  • GA B exp (-C without 2 ( ⁇ - ⁇ r )) has been chosen that has a maximum at the resonant frequency where the offset measured by the system is ⁇ r .
  • Figure 13 illustrates the result of a simulation of the effect of this GA function on resonance.
  • GA is a function that depends on the offset ( ⁇ ); preferably, GA has a maximum at a lag ( ⁇ ) corresponding to a frequency close to the resonant frequency of the oscillating element.
  • said offset would be 90 °, however, in reality and due to imperfections in the measurement, the offset measured at the resonant frequency will not necessarily be exactly 90 °, but may vary substantially.
  • the offset corresponding to the resonance frequency can be determined by measuring the amplitude and the offset depending on the excitation frequency. Approximately, the maximum amplitude of the oscillation is found at the resonance frequency, and therefore the offset that is measured at said frequency is the offset corresponding to the resonance frequency.
  • GA B exp (-Csin 2 ( ⁇ - ⁇ r )), where ⁇ is the offset measured by the device between the oscillation of the mechanical element and the excitation force, being equal to ⁇ r when the frequency of the excitation force It is the resonance.
  • ⁇ r 90 degrees, as shown in the diagram (a).
  • B 1 and its value determines the height of the curve but not its shape.
  • A is the amplitude of the mechanical oscillator if it were excited by a standard excitation signal with fixed amplitude equal to one
  • ⁇ is the offset if the mechanical oscillator was excited by a standard excitation signal with fixed amplitude.
  • Curves A ( ⁇ ) and ⁇ ( ⁇ ) are represented in Figure 13 (a) in the case of a mechanical oscillator with a low quality factor.
  • the effect of the excitation force F 2 used in this control system can be seen in figure 13 (c). This control system does not change the dependence of the offset.
  • FIG 14 shows the experimental results of the control system represented in Figure 11.
  • the excitation force (F) is composed, in this case, of a sinusoidal feedback component F 2 whose amplitude is GA, which has a maximum accused approximately at the resonant frequency.
  • the chosen GA function is the same as in examples 12 and 13 except a constant component.
  • GA GAo + B exp (-C without 2 (( ⁇ - ⁇ r )).
  • GA has a maximum at approximately the resonant frequency, for which the measured offset is ⁇ r .
  • the constant component of the amplitude, GA 0 provides a sinusoidal excitation signal of constant amplitude that allows to measure the oscillation offset with low noise.
  • This component is particularly important in cases in which the mechanical oscillator oscillates little with the generated excitation signals.
  • the mechanical oscillator can be oscillated with an amplitude that allows the correct measurement of l offset of the swing.
  • the values of GA 0 and B are 0.05 and 3 V respectively.
  • the resonance frequency and the elastic constant of the cantilever are approximately 18.93 kHz and 0.06 N / m respectively.
  • Figure 15 shows other experimental results of the amplitude with respect to the excitation frequency, obtained with the experimental system represented in Figure 11, and in which the GA function is the same as that presented in Figure 14.
  • the amplitude is calibrated in angstroms (A °).
  • the mechanical oscillator is a microcantilever for microscopy of atomic forces, which has been coated on both sides with a thin layer of 25 nm thick cobalt by thermal evaporation. This allows it to be excited by a sinusoidal magnetic field over time, which is produced by a coil placed next to the microcantilever.
  • This control system allows to reduce the width of the resonance peak without necessarily increasing the amplitude of the oscillation, and therefore it is possible to work with systems in which the amplitude of the oscillator is of the order of 0.1 nm as shown here.
  • the effect of C on bandwidth can be analyzed in a simple way if some simplifications are made.
  • X (f) is approximately X (f 0 ), where f 0 is approximately the resonant frequency. This is because the variation of X as a function of f is approximately negligible with respect to the exponential variation of GA for frequencies close to that of resonance. If we assume that the cosine of the offset is approximately 2Q (ff 0 ) / fo, for frequencies close to that of resonance, we obtain that the bandwidth is 0.42 f 0 / (G 1/2 Q), approximately.
  • Figure 16 shows the average value and the mean square deviation of the amplitude as a function of the excitation frequency, without active control (a) and with control active (b), using the same experimental system of Figure 15 and described in the previous paragraph, for C values equal to zero (without control), 10 and 300.
  • the mean square deviation of the cantilever amplitude has been calculated at from 50 measurements for each frequency value.
  • the application of the control entails an increase in the noise of the cantilever movement signal, since it is fed back as an excitation force.
  • the amplified noise may come from the device for measuring the cantilever movement, and the Brownian movement due to the thermal coupling between the cantilever and the surrounding environment.
  • Figure 15a shows the amplitude and its noise as a function of the frequency without the active control of the excitation.
  • the noise is mainly distributed around the resonance frequency, indicating that the predominant source of the noise is the Brownian movement of the cantilever.
  • the cantilever behaves like a harmonic oscillator, which responds to the exciting force and also to the thermal forces of random collision whose spectral density is uniform.
  • the average value and the average quadratic value of the amplitude are the product of the oscillator transfer function module (X) and the excitation force and ⁇ F t respectively.
  • the amplitude noise shows a more complex behavior when the control system is applied (fig. 15b). The noise is not significantly increased near the resonance frequency and exhibits two maximums when the amplitude drops around 40% of its maximum value, which reaches an excitation frequency close to that of the resonance.
  • the excitation force (when the control system is applied) depends on the offset of the cantilever's oscillation with respect to the excitation force, there are two sources of noise in the amplitude, one is due to the thermal forces (which produced the Brownian movement of the Cantilever without control system), and the other comes from the noise of the oscillation phase.
  • ⁇ is approximately equal to the quotient between ⁇ F th and the amplitude of the excitation force. Therefore, amplification of amplitude noise can be approximated as:
  • ⁇ A on off is the amplitude noise with and without oscillation control, respectively. It has been plunged that the resonance offset is 90 degrees.
  • the numerator of this equation is zero at resonance and increases approximately linearly with (ff 0 ) / foy C near the resonance. However, the denominator shows a minimum in resonance, and grows approximately exponentially with the square of (ff o ) / fo and C near the resonance. The combination of these dependencies give rise to two symmetrical maximums on both sides of the resonance peak. More interesting, the increase in noise due to feedback of the excitation force is a function of C and GA 0 / B. Thus, the signal-to-noise ratio can be modified by adjusting GA 0 and B (for a given value of C that first determines the bandwidth of the response amplitude).
  • Figure 17 shows the amplitude (a) and its noise (b) as a function of frequency.
  • the experimental system is the same as described for Figures 16 and 17 in the last two paragraphs.
  • the results in Figure 17 are for GA 0 / B equal to 0.25 and 2.5, keeping the total excitation force constant (GA 0 + B).
  • GA 0 + B the total excitation force constant
  • the amplitude noise approximately does not change for different values of F 0 and Fn, keeping the ratio between them constant. This is in accordance with the noise model produced with this control system described in the last paragraph.
  • the noise can be reduced by increasing the GA 0 / B ratio, and the signal-to-noise ratio can be improved by increasing the amount of feedback (B) while maintaining constant the relationship between the two excitation forces.
  • the materials, size, shape and arrangement of the elements will be subject to variation, provided that this does not imply an alteration of the basic concept of the invention.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
  • Radiology & Medical Imaging (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
  • Measurement Of Resistance Or Impedance (AREA)

Abstract

Selon un aspect, l'invention concerne un dispositif de commande d'un signal d'excitation d'un élément oscillatoire mécanique (3) résonant excité par ce signal d'excitation (F). Ce dispositif de commande comprend des moyens permettant de déterminer un déphasage (f) entre un signal représentant l'oscillation (Z) de l'élément oscillatoire et entre une composante de réalimentation (F2) et des moyens générateurs de la composante de réalimentation (F2) configurés de sorte que la composante de réalimentation (F2) présente une amplitude (GA) qui est une fonction du déphasage (f). Selon d'autres aspects, l'invention concerne un dispositif et un procédé de mesure, un procédé de commande du signal d'excitation et un programme informatique et un dispositif de stockage.
PCT/ES2003/000100 2002-05-03 2003-03-07 Procede et dispositif de commande d'un signal d'excitation d'un element oscillatoire mecanique resonant, procede et dispositif de mesure, programme informatique et dispositif de stockage WO2003094173A1 (fr)

Priority Applications (1)

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AU2003214265A AU2003214265A1 (en) 2002-05-03 2003-03-07 Device for controlling an excitation signal from a resonant mechanical oscillating element, measuring device, method of controlling the excitation signal, method of taking measurements, computer program and storage device

Applications Claiming Priority (2)

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ESP200201021 2002-05-03
ES200201021A ES2194607B1 (es) 2002-05-03 2002-05-03 Un dispositivo de control de una señal de excitacion de un elemento oscilador mecanico resonante, un dispositivo de medicion, un metodo para controlar la señal de excitacion, un metodo para realizar mediciones, un programa de ordenador y un dispositivo de almacenamiento.

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WO2006040025A1 (fr) * 2004-10-07 2006-04-20 Nambition Gmbh Dispositif et procede de microscopie en champ proche

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WO1996028706A1 (fr) * 1995-03-10 1996-09-19 Molecular Imaging Corporation Modulation magnetique d'un detecteur de force en vue de la detection c.a. dans microscope a forces atomiques
WO1996032623A1 (fr) * 1995-04-10 1996-10-17 International Business Machines Corporation Procede et appareil de commande d'un oscillateur mecanique
US5955660A (en) * 1995-12-08 1999-09-21 Seiko Instruments Inc. Method of controlling probe microscope
US6079254A (en) * 1998-05-04 2000-06-27 International Business Machines Corporation Scanning force microscope with automatic surface engagement and improved amplitude demodulation
EP1037058A1 (fr) * 1999-03-18 2000-09-20 Nanosurf AG Dispositif électronique de mesure de la fréquence et son utilisation
WO2000058759A2 (fr) * 1999-03-29 2000-10-05 Nanodevices, Inc. Sonde active pour microscope a forces atomiques et son procede d'utilisation

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WO1996028706A1 (fr) * 1995-03-10 1996-09-19 Molecular Imaging Corporation Modulation magnetique d'un detecteur de force en vue de la detection c.a. dans microscope a forces atomiques
WO1996032623A1 (fr) * 1995-04-10 1996-10-17 International Business Machines Corporation Procede et appareil de commande d'un oscillateur mecanique
US5955660A (en) * 1995-12-08 1999-09-21 Seiko Instruments Inc. Method of controlling probe microscope
US6079254A (en) * 1998-05-04 2000-06-27 International Business Machines Corporation Scanning force microscope with automatic surface engagement and improved amplitude demodulation
EP1037058A1 (fr) * 1999-03-18 2000-09-20 Nanosurf AG Dispositif électronique de mesure de la fréquence et son utilisation
WO2000058759A2 (fr) * 1999-03-29 2000-10-05 Nanodevices, Inc. Sonde active pour microscope a forces atomiques et son procede d'utilisation

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Publication number Priority date Publication date Assignee Title
WO2006040025A1 (fr) * 2004-10-07 2006-04-20 Nambition Gmbh Dispositif et procede de microscopie en champ proche
JP2008516207A (ja) * 2004-10-07 2008-05-15 エヌアンビション・ゲーエムベーハー 走査型プローブ顕微鏡検査のための装置及び方法
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