qfext07 leipzig 17 sep. 2007 casimir force measurements with quartz tuning fork and afm dr. thorsten...

Qfext07Leipzig 17 Sep. 2007

Casimir force measurements with quartz tuning fork and AFM

Dr. Thorsten LudwigBinnotec e.V.

Bouchéstr. 12, Haus 612435 Berlin

[email protected]


Casimir with tuning fork and AFM

Dr. Thorsten Ludwig

Content

• Force Sensors for sub nano Newton– Light silicon cantilevers– Quartz tuning forks

• Experimental setups in Berlin– With commercial AFM– quartz tuning fork

• Measurements• Outlook



Dr. Thorsten Ludwig

Motivation

• To measure influences of different material and geometries on the Casimir force

4

2

240 L

cFcas

metal plates



Dr. Thorsten Ludwig

Sub pN Force Measurement

• AFM– Light silicon cantilever

• Quartz tuning fork– SNOM– AFM– MFM– Atomic point contact– Gas sensor– Micro gyros



Dr. Thorsten Ludwig

Silicon cantilver



Dr. Thorsten Ludwig

AFM silicon cantilever

• Standard commercial AFM force sensor– Calibrated, good quality, ready made– Direct force measurement

• Disadvantage– Need for laser and optical measuring system– Low k 0,01 N/m, very flexible– Adhesion , catch in– fragile– High cost of AFM



Dr. Thorsten Ludwig

Quartz tuning forks

Each minute, more than 2,000 quartz watch crystals are produced at a cost of less than $0,20 apiece

Vast amount of scientific literature discussing many aspect of quartz tuning forks as force sensors



Dr. Thorsten Ludwig

Atomic resolution with AFM with quartz tuning forks

F Giessibl APL 2000



Dr. Thorsten Ludwig

Measuring principal

• Driven harmonic oscillator• Resonance frequency• External force creates a

frequency shift

• Proportional to force gradient

• Phase shift• Much literature available

x

F

k

ff

2

W. H. J. Rensena APPLIED PHYSICS LETTERSVOL 75, NUM (1999) 1640

Dynamic mode AFM



Dr. Thorsten Ludwig

Casimir force measurments

• Casimir force for flat-sphere geometry

• Frequency shift

3

3

360 x

RcF

4

30

3602

3

x

Rc

k

ff



Dr. Thorsten Ludwig

Spring konstant k

• Spring constant k

• Young module

• Smaller tuning forks• Low k tuning forks

~2000 N/m• Higher frequenzy shift

210 /1087,7 mNE

3

4

L

TW

Ek

L

TW



Dr. Thorsten Ludwig

Cantilever vs. Tuning fork

• Silicon Cantilever– Advantages

• absolute force• Commercial available

– Disadvantages• External Optical

measuring system needed • Very low stiffness• Catch in / sticking • Adhesion• fragile

• Quartz tuning fork– Advantages

• Self sensing• Easy to operate• Low cost• High stiffness• Small amplitude of

oscillation• Robust• Only electrical equipment

needed• Low energy dissipation

– Disadvantages• Proportional to force

derivate• Oscillating sensor



Dr. Thorsten Ludwig

Atomic force microscope



Dr. Thorsten Ludwig

AFM with optical microscope



Dr. Thorsten Ludwig

AFM in vacuum chamber



Dr. Thorsten Ludwig

Full AFM system



Dr. Thorsten Ludwig

Tuning fork set up



Dr. Thorsten Ludwig

Electrical set up

Function

generator

LockIn

amplifier

Quartz tuning fork

Reference signal

Computer

f scan or PLL

Keithley 2000

DMM 6.5 digit



Dr. Thorsten Ludwig

Tuning fork measuring equipment



Dr. Thorsten Ludwig

Tuning fork in vacuum

• Scan 8 Hz

• Width 800 mHz

• At 32764 Hz

• Q=4 105



Dr. Thorsten Ludwig

Frequency plot of tuning fork sensor

32836,0 32836,2 32836,4 32836,6 32836,8 32837,0

2

4

6

8

10

12

Width 410 mHz

Q = 8 * 105

k = 3250

Am

plitu

de [V

olt]

Frequency [Hz]



Dr. Thorsten Ludwig

Long term stability

32765,490 32765,495 32765,500 32765,505 32765,510

6,50

6,52

6,54

6,56

6,58

6 mHz drift in 3 h

Am

plit

ud

e [V

]

frequency [Hz]

15.27 15.02 14.01 13.48 16.44



Dr. Thorsten Ludwig

Casimir force measurement

0,10 0,15 0,20 0,25 0,30 0,35

0,0

0,1

0,2

0,3

0,4

0,5fr

equ

enc

y sh

ift [H

z]

distance [m]

F

4

30

3602

3

x

Rc

k

ff

k = 4680 N/mf = 32756 HzR = 0,6 mmU = 1 mV



Dr. Thorsten Ludwig

Conclusions

• Silicon cantilevers and quartz tuning forks are both capable of measuring the Casimir force– Tuning fork set up is more sensitive and cost is 1/3 rd– But AFM is necessary to control surface roughness

• Great care has to be taken to measure the Casimir force with both systems– Careful and precise sensor preparation to keep

sensitivity up– Smooth and clean surfaces– Alignment of surfaces



Dr. Thorsten Ludwig

Outlook

• Further development of the tuning fork set up– Faster automatic frequency shift detection– More options to built a compact robust sensor– Separate distance masurement

• Conduct Casimir force measurement under several conditions– Material– Geometries



Dr. Thorsten Ludwig

Thank you for your attention

Dr. Thorsten LudwigNew Energy Technologies

Binnotec e. V.

Bouchéstr. 12, Haus 6,12435 BerlinTel : +49 171 6280 357

[email protected]



Dr. Thorsten Ludwig

Casimir force with silicon cantilever

900 950 1000 1050 1100 1150-115

-110

-105

-100

-95

-90

0,9 mV/nmk = 0,03 N/m7,5 mV jump250 pN

T-B

Ph

oto

dio

de

sig

na

l [m

V]

position [nm]

T-B

200 um sphereOn tip less cantileverK = 30pN/nm



Dr. Thorsten Ludwig

Roughness measurments with AFM



Dr. Thorsten Ludwig

Calibration

qfext07 leipzig 17 sep. 2007 casimir force measurements with quartz tuning fork and afm dr. thorsten...

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