Diapositive 1

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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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Vibrating Si microlever at resonance frequency
Vacuum, T300K
Atomic Force Microscopy AFM

• Casimir interaction
• plasma length lP100nm

Cf groupe Capasso Cf groupeFischbach
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MEMS et NEMS (Micro et Nano electro-mechanical
systems)
e160 nm L2 mm l200 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
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van der Waals/Casimir interaction
Proximity approximation
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A. Lambrecht et al. Eur. Phys. J. D, 8, 309
(2000)
Real mirrors (electronic properties)
No characteristic distance
Force gradient
No characteristic distance
Varying Hamaker constant...
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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
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• 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

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Force measurement by AFM Atomic Force Microscopy
Expérimental SetupOmicron UHV STM/AFM
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(No Transcript)
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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
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Measurement Strategy
1-electrostatic calibration
2-DV0 no average surface potential vdw/Casimir
measurement ?
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Amplitude phase shift Fréquency shift Dissipation
1-Lock-in 2- PLL (FM modulation) 3-Sx(w)(ADCcalcu
l)
Laser
Piezo-excitation
Photo détecteur divided in 4 sectors
Microlevier (k, w)
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Linear régime approximation
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sphere surface interaction
DV0 (Casimir) Z100nm
Linear OK
Small amplitude
Small amplitude linear approximation valid
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DV0 (Casimir) Z100nm
sphere surface interaction
Strong non linear effect
Large hysteresis
Larger amplitude
larger amplitude linear approximation NOT valid
Cf Capasso et al work
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Measure of the resonance frequency shift in order
to investigate the DV0 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 T300K

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Method I Direct measurement of resonance curves
Long preliminary work surface potential, k, z0
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Method I Frequency shift issued from direct
measurement of resonance curves
DV0.5V
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Vdw limit
DV0V Casimir
Casimir limit
No ajustable parameter
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Method II FM-AFM measure
Constant Vibration Amplitude Frequency modulation
Excitation Frequency Resonance Frequency
K determination
k60,5 N/m
DV0.5V
DV0V VDW/Casimir
Absolute distance adjustable parameter
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Method III Excitation Brownian motion Small
amplitude of vibration
DV0V VDW/Casimir
as Z decreases
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Frequency shift versus distance deduced from the
Brownian motion
Calculated curve absolute distance origine is
here adjusted
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• 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(DV0
  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 importa
nt drift roughness lever static
deflection non linearity (including in
Brownian motion) At distances above 200 nm
insufficient sensibility (higher quality
factor, low T,...)
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Toward Observation of dissipative
processes.

• Increase of the resonance width
• increased dissipation
• fluctuation

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f friction coefficient
fluctuation - dissipation theorem
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• As Z decreases,changes of Lorentz curve
• the frequency decreases
• the witdth increases dissipation!

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1rst dissipative channel Johnson Noise

• DV ? 0 dissipation increases
• DV0 NO increase of dissipation
• ? electromechanical coupling

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fluctuation-dissipation theorem
Coupling of oscillator with thermal bath
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fluctuation-dissipation theorem
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Predicted DV ? 0 dissipation increases as
z-2 DV 0 NO increased dissipation!!
Result
sphere plan capacity
R ajusted parameter
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2nd dissipative channel
Sphere plane distance around 50nm and in
vdw/Casimir regime
No external excitation Brownian motion
Sphere radius40000 nm
DV0 i.e. compensation du potentiel de surface
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large distance
Z54nm
Z34nm
Z42nm

• As Z decreases
• w0 decreases
• Dw rapidly increases!!!

Rapid increase of dissipation in vdw/Casimir
regime
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Distance calibration based on Frequency shift
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• Origin of this dissipative process?
• Surface voltage reduced to zero
• vacuum (10-9mbar).
• No contact between sphere and surface (sign of
  frequency shift Dw).
• InteractionCasimir

possible origins - drift of apparatus combined
with -long measurements-strong force gradient
- results in drifting resonance
frequency... - Brownian motionsphere/plane
coupled through the fluctuating thermal EM
field (Dorofeyev, Fuchs et al PRL1999, Stipe,
Rugar et al PRL2001) -?
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Conclusion two dissipative channels observed
using the resonance curves
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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
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PhD thesis LSP/LEPES F. Martins Postdoc CNRS
M.Stark
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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