1. Modelling of Atomic Force Microscope(AFM)
Deng Wenqi
Supervisors: Guang-Ming Zhang,Dave Harvey, Francis Lilley

2. Outline Background of AFM Brief introduction of Comsol Multiphysics
Simulation and results
Project plan

3. 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) .

4. 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 conditions
Better to use in ultra high vacuum conditions

5. Image mode Contact mode Constant force during scanning
Damage soft sample

6. Image mode Tapping mode
The cantilever is vibrated at its resonant frequency
Intermittent contact with sample
Reduce sample destruction

7. 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 feedback.
Spatial variations in sample properties cause shifts in the cantilever phase (bottom)

8. 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.

9. First model
Model consists of a piezo actuator, a cantilever and the tip.
A sinusoidal voltage signal is applied to piezo( purple block)

10. Free vibration results
Vibration curve is not smooth

11. Contact model Define contact pair between the tip and sample
Omit the inertial effect
Start with linear discretization model

12. Displacement and contact force curves
Bouncing effect

13. Quasi-static study Bouncing effect disappear Smooth curves
Free vibration

14. Quasi-static study
Different materials such as cooper,GaAs,Ge,Si,andpolymer are tested
Contact force curve of cooper

15. Phase curve Phase shift Phase shift Light contact Deeper contact
Young’s modulus
Young’s modulus

16. Phase curve Phase shift Phase shift Tip sample separation(Polymer)
Tip sample separation(Copper)

17. Problems of static study
It omits the inertial effect of the whole model
Does not reflect the resonant frequency of the cantilever
No matter what frequency you apply, the amplitude is almost the same.

18. 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

19. This problem will not occur when changing to quadratic discretization.Hz
82425 Hz

20. New model Geometry built in COMSOL AFM Probe Type: PNP-DB
Manufacturer: NanoWorld
Geometry built in COMSOL
lLength
Width
Thickness
Resonant Frequency
100 µm
13.5um
0.6um
67kHz

21. Eigenfrequency Study
Resonant frequency is 82424Hz

22. Edge load=sin(2*pi*f*t)*100[nN]
Time dependent study 1
Fixed boundary
Edge load=sin(2*pi*f*t)*100[nN]
Mesh
Free vibration

23. Displacement curves of the cantilever
Time dependent study 2
Apply the contact force on the tip
1.Treat the contact force as spring
2.Relate the contact force with Young’s modulus of tip and sample
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

24. Time dependent study 2 Load a force on the sample for a short period
Unload the force, sample almost recovered

25. 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

26. Project Plan
Aim: 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

27. Project Plan Methodologies 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

28. 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

29. Thank you!!!
Any Questions?