Presentation on theme: "Simulation and Feedback control in Atomic Force Microscope"— Presentation transcript:
1 Simulation and Feedback control in Atomic Force Microscope Michal Hrouzek, Alina Voda, Martin Stark, Joël ChevrierLaboratoire d’Automatique de Grenoble, INP/UJF GrenobleThe European Synchrotron Radiation
2 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
3 Schema of Dynamic Force Microscopy (excitation)Head of the AFMDriving loopHead positioning loopStage with a samplex axis positioning loopy axis positioning loop(set-value of Dw)
4 Detection techniques in dynamic AFM Amplitude Modulation (AM)Original operation technique, Developed by Y. Matin – J. Appl. Phys. 61 (10)Driver is exciting the cantilever with constant driving signal.Interaction forces affect the cantilever and lower the vibration amplitude.Change in amplitude depends directly on interaction force.Frequency Modulation (FM)Newer technique, Developed by T.R. Albrecht – J. Appl. Phys. 69 (2)Driver with controller is exciting the cantilever to constant vibration amplitude.Interaction forces affect the cantilever and change the resonant frequency.Frequency shift depends directly on interaction force. Dw DfMore sensitive compare to AM-techniqueFurther would be treated only FM technique.
5 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
6 Feedback control in AFM Loop controlling position of AFM head in z axisMaintaining constant set-value of frequency shiftLow frequency response (1 – 30 kHz)Cantilever driving loop (cantilever excitation)Exciting the cantilever and ensuring that contact with surface is not lostHigh frequency response (1kHz – 1 MHz)Nonlinear behavior of the driver (due coupling with surface)Directly maintaining cantilever vibration amplitudeCould be used for possible attenuation of thermal noise perturbation and influence of another noises.
7 Position of the head and lever excitation rzd(t), rzp(t) – desired excitation and set-value of frequency shiftmz(t) – measured deflection of the cantileverezd(t), ezp(t) – regulation errors of the bimorph and headzdri(t), zpos(t) – driving signal and head positioning signalz(t) – real deflection of the cantilever
8 Feedback control in AFM Loops controlling position of AFM stage in x-y axesScanningPositioning of the stage with sampleSimple movement in straight lines under the cantilever with tipManipulationParticles manipulation at the surfaceComplex movement with many possible shapesControl of the applied force onto the particle is crucialScanning Manipulation
9 Loops controlling stage position rx,y(t) – desired position piezo-electric stackmx,y(t) – measured (estimated) position of the stageex,y(t) – regulation errorux,y(t) – driving signalyx,y(t) – real position of the stage
10 Loops controlling stage position Accuracy problems with piezo-electric actuatorsPositioning nonlinearities (getting bigger with increasing speed)Usually are used piezo stacks with hysteresis 10% - 15% of max. displacement(Harder stacks have smaller hysteresis but smaller displacement range)Drift due to creep(Could be reduced to curtain level by careful design of the stage)Measurement problems of stage positionHigh level of noise of LVDT detectors get relevant at nano-meter resolutionObserver based regulator can achieve better positioning resolution
11 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
12 Sources of noise in AFM Electronic parts Mechanical parts Photo detectorOptical path noiseThermal gradientLaser intensity noiseShot noiseLaser mode noiseLaser phase noiseElectronic circuitsElectrostatic noisesNoise of amplifiersMechanical partsCantilever and tipThermally induced cantilever noiseMechanical vibrationRelaxationAir turbulences and acoustic wavesMagnetic noisesElectrostatic noisesChemical noisesBimorphThermally induced noise
13 Thermal noise Thermal noise is limiting AFM sensitivity Some noises could be lower by appropriate design and construction of AFM.The minimum detectable interaction force. (dynamic mode)k Spring constant, stiffnessT TemperaturekB Boltzmann constantb Measurement bandwidthA0 Vibration amplitudew0 Resonance frequencyQ Quality factor
14 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
15 Cantilever model Second order differential equation model Q liquid environmentair environmentvacuum environmentL mm lengthw 10-50mm widtht 0.1-5mm thickE GPa for silicon cantileversk N/m stiffness
16 Cantilever model Multimode model of the cantilever E Modulus of elasticityI Area moment of inertiam Mass per unit lengthL Cantilever length
17 Cantilever model Multimode model of the cantilever E Modulus of elasticityI Area moment of inertiam Mass per unit lengthL Cantilever length
18 Computer Simulation The cantilever properties used for multimode model Computed properties of separated harmonic modes
19 Computer SimulationSpectral analysis schema of the multi mode cantilever model
20 Computer Simulation - results Thermal noise was the only excitation of the Cantilever.(displayed spectra is an average over 100 FFT)
21 Measured spectranon-contact silicon cantilever NSC12/50 (cantilever F)(displayed spectra is an average over 1000 FFT)
22 Computer Simulation - results Time response of thermally driven cantilever-Time sequence 0 to 2ms Time sequence 0 to 0.2ms (Zoom)ZoomModelinitializationModeled thermal excitation (blue)(normal distribution)Position of the cantilever (red)
23 Computer Simulation - results Time response of artificially driven cantilever at resonanceblue curve – exciting displacement zdriv(t)=Z0sin(w0t)red curve – displacement of the cantilever at its free end- Time sequence 0 to 10ms - Time sequence 0 to 0.4ms (zoom)Zoom
24 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
25 Computer Simulation with controller Driving with the PID regulator
26 Computer Simulation with controller Driver with phase shiftBand pass filter – selects the frequencies of our interest (10kHz-100kHz)Amplitude detector – gives numerical value of vibration amplitude A(t)Controller – select the gain(t) that is multiplied by filtered cantilever positionLow pass filter – eliminates high frequency noiseGain – amplification of the signalPhase shift – optimal value is p/2
27 Computer Simulation with controller - results Gain of the PID controller gain(t)
28 Computer Simulation with controller - results Displacement of the driving bimorph zbimorph(t) = kbimorph zdrive(t)
29 Computer Simulation with controller - results Displacement of the cantilever (red curve)Displacement of the driving bimorph (blue curve)
30 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
31 Interaction forces Properties Interaction forces They are non-linear Can be long-range or short-range, and attractive or repulsive.Forces are very sensitive to environmental conditions such as temperature, humidity, surface chemistry, and mechanical and electrical noises.Depend on the material, geometry and size of nano entities.Curtain forces are getting dominant in specific environments and some diminish.Interaction forcesvan der Waals (analogous to the gravity at the nano-scale)CasimirThermal motion: Exist for any material and depends only on temperatureCapillary, Hydrogen and Covalent bonding, Steric, Hydropobolic, Double layer, …
32 Interaction forcesIntensity of the van der Waals and repulsive forces.
33 Interaction forces Approach curve of the cantilever. 1) Non-contact 2) “Snap on” point, spring constant is smaller than attractive force.zero) Equilibrium point, lever isn’t deflected in any direction.3) Repulsive interaction is dominant.4) Maximum positive deflection.5) Capillarity holds the tip onto the surface6) “snap off” point, spring constant overcomes the capillarity
34 Interaction forces model Mathematical equations describing interaction forces between the tip and surfaceIntensity of the interaction forces as a function of the separation distance.a0 – intermolecular distanceAH – Hamaker constantRS – Sphere radius (end of the tip)E* – Effective stiffnessNumerical values used from reference: S. I. Lee, Physical Review B, 66(115409), 2002.
35 Interaction forces model - results Approach curve is simulated without any excitation, chip with the cantilever is slowly approaching the surfaceApproach curve with the cantilever, Q=1Approach curve with the cantilever, Q=100This behavior has been observed at the experiment. (Martin Stark, Frederico Martins)
36 Interaction forces model - results Cantilever has been excited with constant driving signal zbimorph(t) = Adrivesin(w0t)Harmonic outputs of separated modes has been recorded.Amplitude of first harmonic mode is decreasing with smaller separation distance.VibrationamplitudeSeparationdistance
37 Interaction forces model - results Amplitude of higher harmonic modes are increasing with smaller separation distance.Time sequences of one period are shown(second mode – red curve, third mode – green curve, fourth mode – blue curve )
38 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controllerInteraction forcesThermal noise in AFMConclusion
39 Outlines of the presentation AFM descriptionFeedback control in AFMSources of noise in AFMCantilever modelDriving loop with controller (model of PLL)Interaction forcesThermal noise in AFMConclusion
40 ConclusionMultimode cantilever model has been developed. Simulations have shown that the model is correct approximation of the dynamic system.Model of the interaction forces have been implemented into Matlab Simulink environment.Dynamic interaction between both models has been simulated and compared with measurements.Driving controller has been employed to control the excitation of the cantilever interacting with the surface.
42 Future workDevelopment of microscope stage controllers that are responsible for the sample positioning under the head with cantilever. This controller has to fulfill new requirements for speed and accuracy due to application of the AFM as a nano-manipulator.Thermal noise is second field of further work. Driving controller has to be redesigned to lower the nose signal ration to achieve better results in weak forces measurements.