NanoElectro Mechanical Systems (NEMS)

Nano Electro Mechanical Systems (NEMS)

and

interactions at nanoscale

Alessandro Siria:

Institut Néel-CNRS Grenoble

CEA-LETI/MINATEC Grenoble Advisors:

Joel Chevrier, UJF and CNRS Grenoble

Hubert Grange, CEA-LETI/MINATEC Grenoble

Nano Electro Mechanical Systems (NEMS)

NEMS are devices integrating electrical and

mechanical functionalities at the nanoscale.

NEMS are among the best candidates for

measurement of interactions at nanoscale

2

Frequency

NEMS resonators can be assimilated

to harmonic oscillators

( ) ( ) γωωωωχ

im +−=

22

0

1

Am

plit

ude P

hase

Interactions at nanoscale

NEMS standard scheme:

• Mobile part suspended over a fixed substrate;

• Gap from tens nanometers to several microns;

• Plane-Plane geometry.

Gap

3

Interactions between mobile and fixed parts can dominate the NEMS

dynamics

• Chemical forces;

• Van der Waals and Casimir forces

• Electrostatic (residual) forces;

• Optical forces;

• Hydrodynamic forces;

• Near field thermal radiation.

Outlines

• Detection set-up: fibre-based optical interferometry.

• Hydrodynamic forces at micron and submicron scale:

1. Cavity damping of a microlever;

2. Cavity freezing of a microlever.

4

2. Cavity freezing of a microlever.

• Radiative heat transfer at nanoscale:

1. Electromagnetic treatment of thermal radiation;

2. Radiative heat transfer between a sphere and a plane.

• Conclusions and perspectives.

X-ray and Mechanical Systems

OPTICAL FORCES

Interaction between X-ray and Mechanical systems:

1) Mechanical effect of X-ray beam;

2) MEMS based X-ray chopper.

5

European Synchrotron Radiation Facility

@ Surface Science Laboratory (SSL)

In collaboration with

Fabio Comin

Detection set-up: optical interferometry

Fabry Perot cavity formed between the fibre

end and the sample surface

Movement of the surface is translated in

detectable light intensity modulation.

HzmySensibilit1210−<

6

+++= ϕ

λ

πdIIIIdI ph

4sin2)( 2121

HzmySensibilit 10<

Hydrodynamic forces at

7

Hydrodynamic forces at

micron and sub-micron scale

Hydrodynamic forces at short distances

The oscillating behavior of a lever is

studied when an “infinite” wall is gradually

approached.

8

This system mimics a MEMS

oscillating closed to a substrate

Si cantilever:

L = 107 µm

w = 30 µm

t = 0.18 µm

ω0/2π ≈ 50 kHz

No additional damping

Hydrodynamic forces at short distances

The lever is thermally actuated.

With decreasing gap in micrometer range we

observe a broadening and softening of

fundamental resonance.

9

( )( ) γωωω

ωχim +−

=

22

0

1Driven and damped 1D oscillator

Damping of lever studied

recording resonance quality

factorγωω

ω

0

kQ

res

=∆

=

-γγγγV-Kx

Broadening: Softening:

Experimental results

10

Micrometric lenght scale:

mdL µ20≈

Confinement effect

Nanometric lenght scale:

nmdC 400≈

Freeezing of resonance

Cavity damping of the oscillator

γω0

kQ =

Large gap: damping independent on distance

Small gap : damping depending on inverse of distance

11

Theoretical description based on Navier-Stokes equation

Boundary conditions control the agreement theory - experiments

Which boundary conditions??

Reynold’s number:

pvt

v∇−∇=

∂

∂ rr

2ηρ

46 1010Re −− ÷≈⋅⋅

=η

ρdvLAMINAR REGIME

Boundary layer definition:

At lever resonance:

ρω

η2=Ld

mdL µ20≈

Confinement characteristic length

Spatial region surrounding the lever where

12

viscosity dominates the fluid behavior

pv

dd L

∇=∇

⇒<<r2η2

22

2

Ld

dd

v

t

v

≈≈∇

∂

∂

η

ρω

η

ρ

r

r

Inertial << Viscosity

Perfect slip boundary conditions

( )( )xfv

zgv

x

z

=

=

Perfect slip at fluid-solid interface:

13

d

Aηγ

2=

dA

kQ

02 ωη= Linear dependency of the quality factor with the gap size.

Consistent with experimental evidence

2

2

2

2

z

v

z

p

x

v

x

p

z

x

∂

∂=

∂

∂

∂

∂=

∂

∂

η

η

zz Ud

AF

η2−=Navier-Stokes equation

No slip boundary conditions (Couette)

0)(

0)0(

==

==

dzv

zv

x

x

No slip at fluid-solid interface:

14

3

3

d

wLηγ =

3

0

3d

wL

kQ

ωη= NOT Consistent with experiments

2

2

z

v

x

p x

∂

∂=

∂

∂η

zz Ud

wLF

3

3η−=Navier-Stokes equation

• Experimental data

Theoretical model (perfect slip)

Comparison Experiments-Theory

No adjustable parameter

dA

kQ

02 ωη=

15

No adjustable parameter: 80% error at 400 nm

Parallelism adjusted: 5% error at 400 nm

Residual misalignement : 10 mrad

Cavity freezing of the oscillator

In the limit of large damping the oscillator has a

down-shift of the resonance

No adjustable parameter

Parallelism adjusted: 10 mrad

16

02

0

=′⇔= ωω

η A

mGapcrit

If the gap is small enough air confinement can

eventually freeze the mechanical oscillator

Hydrodynamic forces: summary

Cantilever dynamics modified by fluid confinement

according to Navier-Stokes equation;

17

Perfect slip at fluid-solid interface induces a long

range hydrodynamic force: F 1/d

For nanometre size cavity the lever oscillation can

be freezed because of the fluid confinement.

Near – Field radiative

18

Near – Field radiative

heat transfer

Electromagnetic treatment.

Fluctuating dipole

induced by thermal effect

FAR-FIELD: propagative waves

Independent by distance

19

NEAR-FIELD: evanescent waves

Strongly dependent by distance

Dielectric materials: surface Phonon-

Polariton enhancement effect

Surface waves: described by dielectric constant ε(ω)

E

p

20

Infra-red resonance

(SiC, quartz, alumine, silica, Si doped)

Radiative thermal transfer

increased by the resonance effect



Density of energy near a SiC-vacuum interface

Far field: the energy density well

reproduces the Plank black body theory

21

Near field: the energy density exceeds

the Plank black body theory:

Monochromatic thermal emission and

exponential decay with the distance



T2

Plane-Plane geometry

Theoretical model

22

T1

T1 > T2

Plane-plane geometry: experimental issue

d d

23

Plane-Plane

Theory developed

BUT

Experiments very difficult

Plane-sphere

Experimentally possible

BUT

Theory not yet developed

Sphere-Plane geometry: theory

Sphere-Plane geometry

24Proximity force approximation

d

d

Sphere-Plane geometry: theory

d

d

25Proximity force approximation

Far field Far field

Switch to radiative heat transfer measurement…

What we want to measure

26

How we want to measure

Experimental set-up

Optical fiber

27

- Power exchanged = lever deflection : thermal switch effect on the lever

- High vacuum P~10-6 mbar : conduction neglegible

- ∆T = 10-20 K.

Experimental raw data

Calibration ???

28

Contact definition ???

Fluxmeter calibration

29

nmnWH

H

/ 03.2=

⋅= δϕ

δ

Surface roughness

Contact between plate and

sphere asperity

Average surface contact

shifted repect hard contact

30

From SEM image sphere

roughness:

50 nm rms

Comparison Experiments-theory

Glass sphere – glass plane

Sphere diameter 40 µµµµm

31

H and b adjusted:

H = 2,162 nm/nW

b = 31,8 nm

Glass sphere – glass plane

Sphere diameter 40 µµµµm

Comparison Experiments-theory

32

ZOOM ON NEAR-FIELD REGIME

H and b adjusted:

H = 2,162 nm/nW

b = 31,8 nm

Conclusions

Development of experimental set-up for the radiative

thermal transfer

33

Relative comparison theory-experience with

4% indetermination

Precise measurement heat transfer in 50nm-5um range

Perspectives

Interaction forces in plane-plane geometry: Gap

34

Hydrodynamic force (perfect slip):

F 1/d

Electrostatic force:

F 1/d2

Thermal radiation:

Φ 1/d2

Hydrodynamic force (no

slip):

F 1/d3

Casimir force:

F 1/d4

Dependency on distance of the major interaction forces

Set-up

Misalignment correction

Attocube inertial motor goniometer:

10-4 deg

35

Focused Ion Beam sample realization

Alignment

Alignment can controlled using

X-ray diffraction

36

The precision in angle given by the

Bragg peak .

For Silicon Bragg width ~10-4 deg

arc sec

No

rma

lize

d c

ou

nt

What happens at large gap?

Damping of the lever is not depending

on distance:

WHY?

Coming back to NS equation:

v ∂r

37

Boundary layer definition:ρω

η2=Ld v

t

vdd L

rr

2∇>>

∂

∂⇒>> ηρ

Damping should saturate

pvt

v∇−∇=

∂

∂ rr

2ηρ

Theory: electromagnetic treatment.

Green Tensor formalism:

Fluctuation-dissipation theorem:

( ) ( ) ( ) ( ) ( ) ( )'',''2',', ,0*

ωωδδδωωεπ

ωεωω −−Θ= rrTrjrj nm

f

n

f

m

rrrr

( ) ( ) ( ) ( )

( ) ( ) ( )ωωω

ωωωµω

,',',,

,',',, 0

rjrrGrH

rjrrGirE

fH

fE

rrrrtrr

rrrrtrr

⋅=

⋅=

38

Electromagnetic energy density:

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )[ ]( ) ( ) ( )[ ]∫

∫

∞−+

Θ+

+−+−Θ

=

⋅+⋅=

0

0

0

''2

0

3

0

3

22

2

0

22

00

22

2

*0*0

ImIm2

1,

112

1,

4

1,,

,,2

,,2

,,

k

z

ps

k

ps

errk

dKK

c

T

rrk

KdK

c

Ttzu

rHrHrErEtru

γ

γπ

ωω

γπ

ωωω

ωωµ

ωωε

ω

rrrrrrrrr

More about Derjaguin approximation

39


40


41

Spheres radius: 20 µm

42

43

Casimir force and radiative heat transfer:

same origin, same experimental set-up

44

Siria et al, 2009Jourdan et al, 2007

NanoElectro Mechanical Systems (NEMS)

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