Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST Finite Element Analysis
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes
Experimental results Data processing Stroboscopic method
´ Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras J.-M Friedt, E. FEMTO-ST
Conclusion
23 mars 2005
1 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes
Why ?
´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST Finite Element Analysis Experimental results Data processing Stroboscopic method Conclusion
• SPM usually use the physical quantity under investigation as
probe-distance indication • this is fine on homogeneous surface (constant physical quantity) • shear-force microscopy uses a resonator for independent probe-distance feedback → usable for a wide range of applications (SNOM, SECM, STM ...)
2 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST Finite Element Analysis
Shear force microscopy Feedback on one property of a quartz resonator (current magnitude or phase) to keep the probe-surface distance constant : the resonator is disturbed by the forces acting on the tip ⇒ modification of the transfer function of the resonator. The feedback signal (probe-distance) is recorded for topography monitoring.
Experimental results Data processing Stroboscopic method Conclusion
Y
Z
X
3 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
But ... Shear force microscopy has not displayed the excellent resolution of other scanning probe microscopies ⇒ requires a good understanding of the behavior of the probe and its interaction with the surface
Finite Element Analysis Experimental results Data processing Stroboscopic method Conclusion
• size of the probe ? • “leakage” of the near field (evanescent) physical property ? • vibration amplitude of the probe ? K. H. Choi, J.-M Friedt, F. Frederix, ... Simultaneous Atomic Force Microscope and Quartz Crystal Microbalance Measurement Applied Physics Letters (Vol 81, No 7, 12 Aug 2002) 4 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
Modulef based dynamic simulation : free tuning fork −4
10.5
Simulated admittance of a tuning fork
x 10
10 Finite Element Analysis
9.5
Experimental results
9
Stroboscopic method Conclusion
real (a.u.)
Data processing
8.5 8 7.5 7 6.5 6 0
50
100 150 frequency (kHz)
200
250
5 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
Modulef based dynamic simulation : loaded free tuning fork −4
10
Simulated admittance of a tuning fork with a silica tip
x 10
0.00024
0.00014
real imaginary
0.00022
0.00012
0.0002
0.0001
0.00018
Finite Element Analysis
8e−05 0.00016 6e−05 0.00014
Experimental results
8
Conclusion
zoom
2e−05
0.0001 8e−05 30
30.5
31 frequency (kHz)
31.5
32
0
real part (a.u.)
Data processing Stroboscopic method
4e−05
0.00012
6
4 0
50
100 150 frequency (kHz)
200
250
6 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes
Interferometric methods
´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
Computer
I
distance
Finite Element Analysis
Stroboscopic method
APD
Lock−in amplifier Ref
Lens X20
Data processing
Impedance magnitude
tuning fork excitation
Ar laser: 488 or 514 nm
Experimental results
Impedance phase
Optic signal
Conclusion
Speckle pattern: vibrating tuning fork
Speckle pattern: static tuning fork
Signal synthesizer
Multimode fiber
Sig
current−voltage converter GND
+
OP 27 −
Focusing lens
Tuning fork
Mirau lens x20 Fiber Beam splitter
7 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes
Raw data
´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
4
x 10 4.8
Finite Element Analysis
1400 mV 1100 mV 800 mV
0.01
|I| (a.u.)
2000 mV 1700 mV
0.012
500 mV 500 mV
Experimental results
φI (a.u.)
0.006
3.274
3.2745
3.275
3.2755
3.276
3.2765
3.277
3.2775
3.278 4
x 10
3.2 3.1 3 2.9
0.004
Conclusion 0.002
0 0
2
4
6
8 10 time (µs)
12
14
16
18
20
vibration amplitude (a.u.)
optic signal(a.u.)
Stroboscopic method
4.4 4.2 3.273 3.2735 4 x 10 3.3
0.008
Data processing
4.6
3.273 3.2735 −3 x 10
3.274
3.2745
3.275
3.2755
3.276
3.2765
3.277
3.2775
3.278 4
x 10
4.2 4 3.8 3.6 3.4 3.2 3.273
3.2735
3.274
3.2745
3.275
3.2755
3.276
frequency (Hz)
3.2765
3.277
3.2775
3.278 4
x 10
8 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes
Linking model and experimental data
´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
1.5
1
Finite Element Analysis
normalized fourier coefficients
0.6
Data processing Stroboscopic method Conclusion
fringe intensity (a.u.)
0.4
Experimental results
fourier coef. 1 (model) fourier coef. 2 (model) fourier coef. 3 (model) fourier coef. 1 (exp.) fourier coef. 2 (exp.) fourier coef. 3 (exp.)
λ/21 λ/5 λ/3 λ/2.1
0.8
0.2 0 −0.2 −0.4
1
0.5
−0.6 −0.8 −1
0
time
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
normalized voltage (exp.) & amplitude (model)
abscissa is graduated in voltage from 400 to 9000 mV (experimental data), which is also equal to (simulated data) a vibration amplitude of λ/21 = 23 nm to λ/1.7 = 290 nm (λ = 488 nm in this experiment).
9 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes
Loaded tuning fork
´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
Experimental results Data processing Stroboscopic method Conclusion
normalized fourier coefficients
Finite Element Analysis
1
0.8 fourier coef. 1 (model) fourier coef. 2 (model) fourier coef. 3 (model) fourier coef. 1 (exp.) fourier coef. 2 (exp.) fourier coef. 3 (exp.)
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
normalized voltage (exp.) & amplitude (model)
abscissa spans from 100 mV to 7600 mV amplitude (experiment) which is also equal to λ/126=4 nm to λ/5=97 nm (here λ = 488 nm). 10 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST
Stroboscopic method acquire images of the moving surface phase-synchronized with the driving voltage oversample each line and intercorrelate images look for the maximum of intercorrelation and find the best sine-wave fit repeat for each line of the image
1
2 3
Finite Element Analysis Experimental results
4
Data processing Stroboscopic method Conclusion 3.5
10
1.295·10
1.25
1.294·10
3
displacement amplitude (µm)
10
1 0.75
10
1.293·10
0.5
10
1.292·10
0.25 10
1.291·10
0 25
50
75
100 125 150 175 200
-0.25
drive voltage: 5 Vpp
2.5
2
1.5
1
drive voltage: 1.8 Vpp
0.5
0
0.000020.000040.000060.000080.00010.00012
0
0
50
100
pixel number x 100 (after interpolation)
150
Results : 0.5 Vpp –1.8 Vpp –5 Vpp → displacement amplitude 350 nm–850 nm–3000 nm (Q = 4500). 11 / 12
Quartz tuning fork vibration amplitude as a limitation of spatial resolution of shear force microscopes ´ J.-M Friedt, E. Carry, Z. Sadani, B. Serio, M. Wilm, S. Ballandras FEMTO-ST Finite Element Analysis Experimental results Data processing Stroboscopic method Conclusion
Conclusion and perspectives • we have developed the basic Finite Element Model of a tip-loaded
tuning fork • we have experimentally measured the vibration amplitude of a
tuning fork Further developments include : • measuring the vibration amplitude as a function of probe-surface distance • adding an external force acting on the tip of the probe to our model • experimentally observe possible spatial resolution loss at high driving-voltage amplitude • is the tuning for usable as a scanner ? (for an N × N pixel image, we must sample at N × 32768 Hz to get a framerate of 32768/N image/s : N = 128 ⇒ 8.5 Msamples/s and 512 fps !)
12 / 12
