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

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

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

4 Proximity approximation R z R van der Waals/Casimir interaction : z Rc F SP Cas   

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

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

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

8 Expérimental Setup Omicron UHV STM/AFM Force measurement by AFM Atomic Force Microscopy

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

11 Measurement Strategy 1-electrostatic calibration 2-  V=0 no average surface potential vdw/Casimir measurement ?

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

13 Linear régime approximation

14 sphere surface interaction Small amplitude: linear approximation valid  V=0 (Casimir) Z≈100nm Linear OK Small amplitude

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

16 Measure of the resonance frequency shift in order to investigate the  V=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  resonance followed real time 3-Lever Excitation: Brownian Motion at T=300K

17 Method I: Direct measurement of resonance curves Long preliminary work: surface potential, k, z 0

18 1 Method I: Frequency shift issued from direct measurement of resonance curves  V=0.5V

19 1  V=0V Casimir Vdw limit Casimir limit 60nm No ajustable parameter

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

21 Method III: Excitation: Brownian motion Small amplitude of vibration  V=0V VDW/Casimir as Z decreases

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

23 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 (  V≠0) the contribution with voltage compensation(  V=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 p 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,...)

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

25 fluctuation - dissipation theorem spectral density f : friction coefficient

26 As Z decreases,changes of Lorentz curve: the frequency decreases the witdth increases: dissipation! Z Z

27 1 rst dissipative channel: Johnson Noise Z  V ≠0 large distanceshort distance Z   V ≠ 0 dissipation increases   V=0 NO increase of dissipation  electromechanical coupling

28 Coupling of oscillator with thermal bath Johnson noise : v J fluctuating voltage due to resistance R RC   <<1 fluctuation-dissipation theorem

29 fluctuation-dissipation theorem

30 Predicted:  V ≠ 0 dissipation increases as z -2  V = 0 NO increased dissipation!! sphere plan capacity : Result: R: ajusted parameter

31 2 nd dissipative channel Sphere plane distance around 50nm and in vdw/Casimir regime  V=0 i.e. compensation du potentiel de surface Sphere radius=40000 nm No external excitation… Brownian motion

32 As Z decreases:     decreases   rapidly increases!!! large distance Z=54nm Z=42nm Z=34nm Rapid increase of dissipation in vdw/Casimir regime

33 Distance calibration based on Frequency shift Peak width

34 Origin of this dissipative process?  Surface voltage reduced to zero  vacuum (10 -9 mbar).  No contact between sphere and surface (sign of frequency shift  ).  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) -…?

35 Conclusion: two dissipative channels observed using the resonance curves

36 in progress: a new machine 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

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

38 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