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Micromechanics and measurements of interactions at nanoscale

Joël Chevrier. Micromechanics and measurements of interactions at nanoscale from Gauthier Torricelli PhD thesis. LEPES-CNRS Laboratoire d'Études des Propriétés Électroniques des Solides Université Joseph Fourier Grenoble France ESRF Surface Science Laboratory.

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Micromechanics and measurements of interactions at nanoscale

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  1. Joël Chevrier Micromechanics and measurements of interactions at nanoscale from Gauthier Torricelli PhD thesis LEPES-CNRS Laboratoire d'Études des Propriétés Électroniques des Solides Université Joseph Fourier Grenoble France ESRF Surface Science Laboratory

  2. Vibrating Si microlever at resonance frequency Vacuum, T=300K Atomic Force Microscopy AFM • Casimir interaction: • plasma length lP≈100nm Cf groupe Capasso Cf groupeFischbach

  3. MEMS et NEMS (Micro et Nano electro-mechanical systems) e=160 nm L=2 mm l=200 nm For NEMS: relevant forces? van der Waals/Casimir electrostatic forces chemical bonding hard core repulsion Brownian motion (kBT) Dissipation-Fluctuation dynamical measurement AFM Raphaëlle Dianoux coll. LETI/ESRF/LEPES

  4. R 3 p c R h SP = F R Cas z 3 360 z van der Waals/Casimir interaction : Proximity approximation

  5. A. Lambrecht et al. Eur. Phys. J. D, 8, 309 (2000) van der Waals Hamaker Real mirrors (electronic properties) No characteristic distance Force gradient No characteristic distance Varying Hamaker constant...

  6. Van der Waals Casimir : perfect mirrors lp≈136 nm Casimir/van der Waals force gradient Calculation of Grad F in this geometry performed by Lambrecht et al (dark line) Vacuum gold-gold vibration at resonance

  7. Determination of Force Gradient • Casimir/van der Waals • method: • Static • Dynamic: oscillator at resonance • k, w absolute values • absolute distance (no direct contact allowed) • surface potential • noise-sensibility

  8. Force measurement by AFM Atomic Force Microscopy Expérimental SetupOmicron UHV STM/AFM

  9. Gold film deposition on sphere and cantilever (Nanofab K. Ayadi) Evaporated gold : Ti thin film 2-10nm Au thin film ~200-300nm gold layer thick enough so that it is equivalent to bulk

  10. Measurement Strategy 1-electrostatic calibration 2-DV=0 no average surface potential vdw/Casimir measurement ?

  11. V Z Amplitude phase shift Fréquency shift Dissipation 1-Lock-in 2- PLL (FM modulation) 3-Sx(w)(ADC+calcul) Laser Piezo-excitation Photo détecteur divided in 4 sectors Microlevier (k, w)

  12. Linear régime approximation

  13. sphere surface interaction DV=0 (Casimir) Z≈100nm Linear OK Small amplitude Small amplitude: linear approximation valid

  14. DV=0 (Casimir) Z≈100nm sphere surface interaction Strong non linear effect Large hysteresis Larger amplitude larger amplitude: linear approximation NOT valid Cf Capasso et al work

  15. Measure of the resonance frequency shift in order to investigate the DV=0 régime i.e. van der Waals/Casimir • Three methods: • 1- Direct measure of the resonance curve: amplitude/phase • 2- Frequency Modulation FM-AFM: double feedback loop • Amplitude of oscillation = cte • true w resonance followed real time 3- Lever Excitation: Brownian Motion at T=300K

  16. Method I: Direct measurement of resonance curves Long preliminary work: surface potential, k, z0

  17. 1 Method I: Frequency shift issued from direct measurement of resonance curves DV=0.5V

  18. 1 60nm Vdw limit DV=0V Casimir Casimir limit No ajustable parameter

  19. Constant Vibration Amplitude Frequency modulation Excitation Frequency = Resonance Frequency Method II: FM-AFM measure K determination k=60,5 N/m DV=0.5V DV=0V VDW/Casimir Absolute distance: adjustable parameter

  20. Method III: Excitation: Brownian motion Small amplitude of vibration DV=0V VDW/Casimir as Z decreases

  21. Frequency shift versus distance deduced from the Brownian motion Calculated curve: absolute distance origine is here adjusted

  22. Conclusion: • vdw/Casimir acts as a perturbation on a micro-oscillator • three different methods in the determination of the frequency shift • Dynamical measures on the range 50 to 200 nm : • AFM Dynamical measurements in the linear régime • Clear separation of : • the electrical contribution (DV≠0) • the contribution with voltage compensation(DV=0 ± 0,01 V): • van der Waals/Casimir • Force gradient measured on 3 orders of magnitude (N/m) • Quantitative observation of the intermediate régime • between the 2 limiting régimes: van der Waals and Casimir • in the vicinity of the plasma length lp Problems specially at short distances: important drift roughness lever static deflection non linearity (including in Brownian motion) At distances above 200 nm: insufficient sensibility (higher quality factor, low T,...)

  23. Toward Observation of dissipative processes…. • Increase of the resonance width • increased dissipation • fluctuation

  24. spectral density f : friction coefficient fluctuation - dissipation theorem

  25. Z Z • As Z decreases,changes of Lorentz curve: • the frequency decreases • the witdth increases: dissipation!

  26. 1rst dissipative channel: Johnson Noise large distance short distance Z Z DV ≠0 • DV ≠ 0 dissipation increases • DV=0 NO increase of dissipation  electromechanical coupling

  27. Johnson noise : vJ fluctuating voltage due to resistance R RCw0<<1 fluctuation-dissipation theorem Coupling of oscillator with thermal bath

  28. fluctuation-dissipation theorem

  29. Predicted: DV ≠ 0dissipation increases as z-2 DV = 0 NO increased dissipation!! Result: sphere plan capacity : R: ajusted parameter

  30. 2nd dissipative channel Sphere plane distance around 50nm and in vdw/Casimir regime No external excitation… Brownian motion Sphere radius=40000 nm DV=0 i.e. compensation du potentiel de surface

  31. large distance Z=54nm Z=34nm Z=42nm • As Z decreases: • w0decreases • Dw rapidly increases!!! Rapid increase of dissipation in vdw/Casimir regime

  32. Peak width Distance calibration based on Frequency shift

  33. Origin of this dissipative process? • Surface voltage reduced to zero • vacuum (10-9mbar). • No contact between sphere and surface (sign of frequency shift Dw). • Interaction=Casimir possible origins: - drift of apparatus combined with: -long measurements-strong force gradient - results in drifting resonance frequency... - Brownian motion:sphere/plane coupled through the fluctuating thermal EM field (Dorofeyev, Fuchs et al PRL1999, Stipe, Rugar et al PRL2001) -…?

  34. Conclusion: two dissipative channels observed using the resonance curves

  35. in progress: a new machine 1 2 6 4 3 5 1- Longue distance: Fabry-Pérot interferometer for both dynamic and static measurement Vacuum Low temperature Casimir Radiation pressure: optic, X ray Project See poster Guillaume Jourdan

  36. PhD thesis LSP/LEPES F. Martins Postdoc CNRS M.Stark

  37. Remerciements Guillaume Jourdan (LEPES-LKB) Mario Rodrigues (ESRF) Martin Stark (LEPES-LSP) Serge Huant (LEPES-LSP) Khaled Ayadi (LEPES) Florence Marchi (LEPES-UJF) Astrid Lambrecht (LKB) Irina Snigereva (ESRF) Fabio Comin (ESRF) Joël Chevrier (LEPES-UJF-ESRF) Merci à tous pour votre attention… Static measurement: Torricelli poster Fabry Pérot interferometer: Jourdan poster

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