Post on 30-Mar-2015
Qfext07Leipzig 17 Sep. 2007
Casimir force measurements with quartz tuning fork and AFM
Dr. Thorsten LudwigBinnotec e.V.
Bouchéstr. 12, Haus 612435 Berlin
DrLudwig@thorstenludwig.de
Qfext07Leipzig 17 Sep. 2007
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Motivation
• To measure influences of different material and geometries on the Casimir force
4
2
240 L
cFcas
metal plates
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Sub pN Force Measurement
• AFM– Light silicon cantilever
• Quartz tuning fork– SNOM– AFM– MFM– Atomic point contact– Gas sensor– Micro gyros
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Silicon cantilver
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and 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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Atomic resolution with AFM with quartz tuning forks
F Giessibl APL 2000
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and 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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Atomic force microscope
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
AFM with optical microscope
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
AFM in vacuum chamber
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Full AFM system
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Tuning fork set up
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Tuning fork measuring equipment
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Tuning fork in vacuum
• Scan 8 Hz
• Width 800 mHz
• At 32764 Hz
• Q=4 105
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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]
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
DrLudwig@thorstenludwig.dewww.thorstenludwig.de
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
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
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Roughness measurments with AFM
Qfext07Leipzig 17 Sep. 2007
Casimir with tuning fork and AFM
Dr. Thorsten Ludwig
Calibration