AFM
The cantilever holder
l
100 - 200 µm
w
10 - 40 µm
t
0.3 -
2 µm
w
Tip position
l
t
The cantilever dimensions
SEM image of the AFM tip
Typical Features of our AFM
Working environment
Working area
ambient temperature
and pressure
up to 100 x 100 µm2
Resolution per image
64 to 1024 pixels
Lower limit resolution
~0.03 nm
max 3 µm
Sample height
Oblique view
Image information
Chemical composition
no
3D / 2pi
indirectly, from phase
information
Laser diode
mirror
PSPD
probe tip
positioning system
sample
piezo-electric
scanner
z
feedback
system
y
x
computer system
hardware components of the AFM
Force
Intermittentcontact
contact
repulsive
forces
distance
tip to sample separation
Non-contact
attractive
forces
Inter-atomic force vs. distance curve
Modes of operation of an AFM
•
•
Contact mode
Non-contact mode

keff
m
keff  k  f '
ƒ’ = the force gradient between tip and sample
keff= effective spring constant
ω = operational frequency
m = effective mass of cantilever
Theory, inter-molecular forces
Electrostatic, (magnetic) and van der Waals forces
Van der Waals forces:
• Polarisation from permanent dipoles
• Induction-induced dipoles
• Dispersion-fluctuation of electrons as function of
light
•
•
•
•
•
•
Theory, inter-molecular forces
1. Coulombic energy between ions with net charges
leading to a long range attraction with u α r-1
2. Energy interactions between permanent dipole u α r-6
3 energy interactions between an ion and a dipole it
induced in another molecule U α r-4
4 between a permanent dipole and the dipole it induced
in another molecule U α r-6
5 forces between neutral atoms/molecules U α r-6
6. Overlapping energy arising from positive nuclei of one
molecule and the electron cloud of another. This overlap
leads to repulsion at very close intermolecular
separations with α r-9 to α r-12 potential.
Van der waals interactions arise from 2, 4, and 5.
Image processing
• Plane levelling
• Filtering
• Measuring particle sizes
3.535 µm
Source = Topography
Mode = AFM
Fast Scan Direction = X
X scan = left to right
Y scan = bottom to top
# of columns = 256
# of rows = 256
X scan size = 3.535 µm
Y scan size = 3.535 µm
3.535 µm
2D Topography Image – Aerosol Particles
3.78 µm
Particles from stage 6
Tip Characterization
Raised tip t(x-x’,y-y’)
Minimum separation
Tip
image i(x,y)
Sample s(x,y)
(x’,y’)
i ( x' , y ' ) 
max
(u , v)
[ s ( x  u, y  v)  p(u, v)] 
I  S  P  x' x  u, y' y  v