why is afm challenging? 1.jump to contact: k>max(- v ts / z (static) ka>max(-f ts ...
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Why is AFM challenging?
1. Jump to contact:k>max(-VTS/z(static)
kA>max(-FTSoscillating mode)
ideal amplitude is A~]
2. Non-monotonic imaging signal
3. Long-range vs. short range forces [F(z)]
4. Noise in the deflection sensor (particularly 1/f noise)
5. FM AFM helps in all cases except 2!
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Thermal limits
Energy in damped driven harmonic oscillator = kBT
This allows one to determine the thermal limit of force gradient sensing in AFM:
{zosc= F’ zo Q/k Is the signal near resonance}
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How does one measure a high Q system?
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Challenge of measuring high Q system
Albrecht, Grutter, Horne Rugar J. Appl. Phys. 69, 668 (1994)
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Better sensitivity with high Q cantilevers
Q=115 slope detection
Q=65,000 FM detection
Q=65,000 slope detection
Albrecht, Grutter, Horne Rugar J. Appl. Phys. 69, 668 (1994)
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P. Grutter, McGill University
AC techniques
Change in resonance curve can be detected by:
• Lock-in (A or ) *
• FM detection (f and Adrive)
Albrecht, Grutter, Horne and RugarJ. Appl. Phys. 69, 668 (1991)
(*) used in Tapping™ mode
f
A
f1 f2 f3
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P. Grutter, McGill University
Some words on Tapping™
Amount of energy dissipated
into sample and tip strongly depends on operation conditions.
Challenging to
determine magnitude or sign of force.
NOT necessarily less
power dissipation than repulsive contact AFM.
Anczykowski et al., Appl. Phys. A 66, S885 (1998)
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P. Grutter, McGill University
Ultimate limits of force sensitivity
1. Brownian motion of cantilever!
thermal limits Martin, Williams, Wickramasinghe JAP 61, 4723 (1987)Albrecht, Grutter, Horne, and Rugar JAP 69, 668 (1991)
D. Sarid ‘Scanning Force Microscopy’
Roseman & Grutter, RSI 71, 3782 (2000)
A2 = kBT/k
A…rms amplitude T=4.5K
2. Other limits:- sensor shot noise- sensor back action- Heisenberg
D.P.E. Smith RSI 66, 3191 (1995)
Bottom line:Under ambient conditions energy resolution ~ 10-24J << 10-21J/molecule
QfkA
TBk
f
f Bo
023
0
2
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Other limitations?
- sensor shot noise
- sensor back action
- Heisenberg
D.P.E. Smith, Rev. Sci. Instr. 66, 3191 (1995)
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Sensor Shot Noise
Effectively, the fluctuations in laser pressure (due to photon statistics) give rise in a fluctuation in the mean position of the cantilever.
P…laser power, f…bandwidth
…wavelength h…Planck’s constant
c…speed of light …interferometer phase
NB: can be used to ‘cool’ high finesse cavities!
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Sensor Back Action
P…laser power, f…bandwidth
…wavelength h…Planck’s constant
c…speed of light
Optical pressure
Off resonance
On resonance
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Optimization
Minimize:
and obtain optimized laser power (for off resonance set Q=1):
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Heisenberg
Minimal detectable energy
with Minimal bandwidth
Quantum limit
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So what?
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How about detecting a single spin?Idea: combine MFM and resonant excitation of the cantilever by combining ultimate AFM techniques and NMR.
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MRFM
D. Rugar, R. Budakian, H. J. Mamin & B. W. Chui, Nature 430, 329 (2004)
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Magnetic Resonance Force Microscopy (MRFM)
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Another cool thing: thermodynamic squeezed state
D. Rugar and P. Grutter, Phys. Rev. Lett. 67, 699 (1993)
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Course Evaluations!