Atomic Force Microscope

The scanning tunneling microscope is proposed as a method to measure forces as small as 10 N. As one application for this concept, we introduce a new type of microscope capable of investigating surfaces of insulators on an atomic scale. The atomic force microscope is a combination of the principles of the scanning tunneling microscope and the stylus profilometer. It incorporates a probe that does not damage the surface. Our preliminary results in air demonstrate a lateral resolu0 0 tion of 30 A and a vertical resolution less than 1 A.


Forces between Tip and the Sample
1. van der Waals : ( )*+  " ' " ) Van der Waals interaction is typically from neutral particles.
However, the underlying phenomena is Coulombic interaction between charge fluctuations in neutral particles 2. Electrostatic force: ( ,- % " ' ) If there exists a potential difference U, then there is an attractive force between the tip and the sample 3. Capillary Force: In hydrophilic substrates, moisture from room temperature can form a meniscus with the tip.This causes a capillary force driving the liquid up the tip due to surface tension effects

Repulsive Force
Pauli Exclusion / ionic repulsion: Valence electron wavefunctions can extend few 10's of nm.
Pauli's idea excludes two electrons with same energy and spin in close proximity.
This leads to e repulsive potential  . / ' "% where  is the distance at which the potential is zero.
For the simplest case where in there is only van der Waal's attractive and Pauli's repulsion, the total potential This potential is called as Lennard-Jones potential.
The force due to the potential is then Averaged van der Waal's force on the tip Hamaker's potential Thus the force Its important to note that super short-range potential  !1 leads to a long-range force when averaged over several interacting atoms While the repulsive forces is sharply short-range.

Design of a tip
AFM tip is used to sense tip -sample interaction (Force) Hence a mechanically pliant structure is required and is operated in elastic regime.

Design of commercial AFM tips
Spring constant  =  7 /4 From inches -~ 1 However, for an AFM, there is a need for atomical resolution!Linear translations in Å resolution is required.

Piezoelectricity:
In non-centrosymmetric crystals, strain causes generation of electric dipoles

Typical Block diagram of AFM head
The XY Piezo in addition to linear transducers are used to raster the sample surface.At each point on the surface, the force transducer translates the force sample interaction A feedback loop is used to ensure that the force between the tip and the probe remains the same.'z' transduction need to bring the force to its set value is noted as the sample height Typical expansion coefficient: ~0.1 / Thus, atomic scale movements are possible using Piezoelectric transducers.The cantilever deflection  < = − < ()/ -Hooke's law Where  < is the elastic force on the cantilever.
Say, the cantilever is near a hill with D separation.
There will be tip bending and a restoring force from the cantilever.At equilibrium the cantilever restoring force is same as the sample-tip interaction force.So, the net force on the cantilever is 0. However, the cantilever at 0 force is at a different height (Z) Contact Mode

Force-distance curve
Force on the cantilever and its deflection are just scaled version of the same thing (related by Hooke's law) In contact mode, the tip Z is moved such that the force remains constant.This point is typically in the repulsive region as shown.
The tip is always touching.
At point b, an instability happens and the comes into contact strain and get dipoles; Or force a potential and observe mechanical strain 3-D motion using Piezoelectric transducers When the base of the tube is fixed,  8 voltage along x axis,  9 voltage along Y Δ =  8 2 2 7"  % ℎ Δ =  9 2 2 7"  % ℎ  7" is the piezo strain, L -length of tube, Doutside diameter, h -tube thickness.If a potential V is applied to all four terminals, and -Vx are applied to diametrically opposite sides, one side contracts and other side expands.The tube 'bows' in a fashion to accommodate the differential strain m wide and 0.2 -1 m thick.Either the laser and detector assembly is moved by X-Y stage.Or the cantilever and the detector is moved.Lens focuses the light.Typically the lens focuses the light at an angle to the cantilever to allow for imaging the sample and the cantilever together Position sensitive photo detection Operational Modes of AFM Contact Non-contact mode Typically a Triangular shaped less stiff cantilever is used (K < 1 N/m) Made of Si 3 N 4 like material The tip is brought to contact in a static mode Bending of the cantilever is measured Typically a rectangular stiff material is used.Like Si The cantilever is made to oscillate close to the surface The sample-tip interaction forces the oscillation amplitude and phase to change Generating an AFM Image Steps: 1. Generate scanning signals for X-Y stage movement 2. Take input signal from force sensor and feed to z-piezo 3. Get output control to X-Y-Z motor 4. Generate signal for oscillating probe.Measure phase and amplitude 5. Collect signals and display on computer Generating the X-Y raster The Z potential is set using a feedback setup PID  =  *  :;; +  * ∫  :;;  + ×  :;;   :;;  ) Static Interaction of Tip with Sample A cantilever with the sharp tip is moved close to the surface.At each point, there is sample height determined force () The probe tip is assumed to be much stiffer than the cantilever and the sample Typical inter-atomic force constants in solids -10 -100 N/m In biological samples -~ 0.1 N/m.Hence the cantilever stiffness is typically set at 0.01 -5 N/m