Modelling of Atomic Force Microscope(AFM)

Deng Wenqi
Supervisors: Guang-Ming Zhang,Dave
Harvey, Francis Lilley
 Background of AFM
 Brief introduction of Comsol Multiphysics
 Simulation and results
 Project plan
How AFM works?
•The x and y-piezos provide lateral scanning(~30nm) ,
while the z-piezo extends and retracts to follow the
surface topography(up to 0.1nm) .
Image mode
 Non-contact mode
•The cantilever is oscillated near its
resonant frequency at a position just
above the sample surface
•Measures the topography by detecting
the vibration amplitude affected by the
attractive forces
•Difficult to use in normal ambient
•Better to use in ultra high vacuum
Image mode
 Contact mode
•Constant force during scanning
•Damage soft sample
Image mode
 Tapping mode
•The cantilever is vibrated at its
resonant frequency
•Intermittent contact with sample
• Reduce sample destruction
Phase imaging
•Measure the phase lag of the
cantilever oscillation (solid
wave) relative to the phase of
the piezo drive (dashed wave).
•The amplitude signal is used
simultaneously by the
controller for Tapping Mode
• Spatial variations in sample
properties cause shifts in the
cantilever phase (bottom)
Why phase image provides more
information of structure?
Topography (left) & phase (right) images of a composite polymer
•Higher spots in the AFM topography images should correspond to the hard
phase polymer?
•Brighter areas correspond to harder materials?
•We don’t have an agreement yet.
First model
•Model consists of a piezo actuator,
a cantilever and the tip.
• A sinusoidal voltage signal is
applied to piezo( purple block)
Free vibration results
•Vibration curve is not smooth
Contact model
•Define contact pair between
the tip and sample
•Omit the inertial effect
•Start with linear
discretization model
Displacement and contact force curves
•Bouncing effect
Quasi-static study
 Bouncing effect disappear
 Smooth curves
•Free vibration
Quasi-static study
 Different materials such as
cooper,GaAs,Ge,Si,andpolymer are tested
Contact force curve of cooper
Phase curve
Light contact
Young’s modulus
Deeper contact
Young’s modulus
Phase curve
Tip sample separation(Polymer)
Tip sample separation(Copper)
Problems of static study
 It omits the inertial effect of the whole model
 Does not reflect the resonant frequency of the
 No matter what frequency you apply, the amplitude is
almost the same.
Problem of resonant frequency
 When using linear discretization model, the resonant
frequency is not right.
 Different mesh lead to different results
1.15e5 Hz
2.69e5 Hz
 This problem will not occur when changing to
quadratic discretization.
82424.8 Hz
82425 Hz
New model
AFM Probe Type: PNP-DB
Manufacturer: NanoWorld
Geometry built in COMSOL
100 µm
Eigenfrequency Study
Resonant frequency is 82424Hz
Time dependent study 1
Fixed boundary
Edge load=sin(2*pi*f*t)*100[nN]
Free vibration
Time dependent study 2
•Apply the contact force on the tip
1.Treat the contact force as
2.Relate the contact force with
Young’s modulus of tip and
Displacement curves of the cantilever
•Phase shift between green and blue is 3.8 degree
•Phase shift between red and blue is is 4 degree
Time dependent study 2
 Load a force on the sample for a short period
 Unload the force, sample almost recovered
Problems of simulation
 Difficult to define the contact force equation
 It’s better to model tip and sample together
 However, it is still difficult to solve contact
modelling in time dependent study.
Contact model
Project Plan
1) Phase interpretation
2) Nano-NDE(non-destructive evaluation) for defect
detection, imaging of internal micro-structures,
measurement of mechanical properties.
Test samples:
1) Single layer samples with surface defects.
2) Multiple layers samples with defects
Project Plan
 Elastic deformation force only
 Elastic deformation force + Van Der Waals
 Curve of phase shift vs height
 Curve of phase shift vs material
 Image restoration using these curves: material
phase image
Project Plan
Future work
 Solve the problem of contact modelling
 Define the relationship between phase shift and
material parameter, such as phase shift vs young’s
modulus, phase shift vs thickness
 Observe how phase change in non-destructive
evaluation, eg. The sample has a defect inside
 Test soft material like cells and compare the results
with real experiment
Thank you!!!
Any Questions?

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