Quantitative measurements of

non contact interaction

G. Torricelli, M. Rodrigues, C. Alandi, M.Stark, F. CominJ. Chevrier Université Joseph Fourier GrenobleLEPES CNRS GrenobleSpectro CNRS UJFESRF Grenoble

Coll. S. Huant, F. Martins SpectroColl. G. Jourdan, A Lambrecht, S Reynaud LKB

<<1m

Courtesy of Hubert GRANGE and Marie-Thérèse DELAYE (2004)

CEA LETI

…. forces are acting at the Nanoscale on MEMS and on NEMS

Nature of forces at Nanoscale:

PhotonicRadiation pressurevan der Waals interactionCasimir effect

ElectrostaticBrownian Motion (kBT)Hard core repulsionAdhesion-metallic bondingDissipation

MEMS Parameters:atmosphere-vacuumsurface

roughnesschemical naturenanostructuration

restoring force (mechanical spring constant)surface/bulk elastic stress

L=1000nm=1m

A=50mx50m

FCas= 3pN

Strong gradient: FL5 > K

mechanical instability

When micromechanics and quantum electrodynamics meet:MEMS based on Casimir-Lifschitz forces

Federico Capasso

Radius of interaction R= 50m

no longer local

no microscopy

surface

R

tip

Z

• L >> p retarded régime (Casimir régime) electron coupling to propagating photon modes dominant

• L << p NON retarded régime (Van der Waals)electron coupling to NON propagating photon modes dominant:

surface plasmon-photon coupling

p= 2 c/ p

Characteristic length: plasma length

Aluminum ћp= 14eV

p 100nm

Origin: electron-photon coupling

L=100nm (retarded régime L />p )

F=100 picoN

F =10-3 N/m

Large distance limit and perfect mirror Casimir limit

L>>p

Radiation pressure of virtual photonsi.e. zero point motion of ElectroMagnetic field

x

Hy

EEz

+++ --- +++ --- +++ ---metal (1<0)

+++ --- +++ --- +++ --- metal (2<0)

d

L=10nm (non retarded van der Waals régime L<< p )

F= H R/ L2 H=5x 10-19 Joule

F=500 nanoNewton

F =50 N/m

J.J. Greffet EM2C Ecole Centrale de Paris 2003

polystyrene sphere R= 42 m metal coating (gold) =300 nm

Measure (G. Torricelli PhD thesis LEPES 2001-2004)Omicron VT UHV AFM

100nm < z < 500nmV

Sphere/surface distance determinationCantilever spring constant measurement

Static cantilever deflection F= -kx

Cantilever deflection cannot be neglected at large voltage

zzdef

19200 19300 19400 19500 19600 19700

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0 2,5V 2,0V 0,5V

Am

plit

ud

e (a

.u)

frequency (Hz)

Vdw/ Casimir: Oscillating mode of the sphere at resonance

k

Fd res

VF

res

res

0 50 100 150 200 250 300 350 400-40

-35

-30

-25

-20

-15

-10

-5

0

5

f (

Hz)

Distance (nm)

Casimir/vdw interaction (fit in z-3)

86.4 mK ≈ 88.6N/m

Z ≈ 0.05 - 0.4 m

Electrostatic longrange interaction V=0.5volt (fit in z-2)

fres=52.670 kHz

L=50nmgrad F= 10-1 N/m

p ≈ 130nm

Short distances: D<<p with p plasmon length,

Force machine: sphere-surface distance

10nm

Tuning forkK= 1000 - 10000 N/m

Full scale is 0.3Hz

The distance is again determined using capacitive interaction

Large surface roughness at the origin of our measurementno van der Waals contribution,

instead direct metallic bonding

At nanoscale,At nanoscale,

attractive force attractive force

between 2 metallic plates between 2 metallic plates

in vacuumin vacuum