# Atomic Force Microscopy (AFM)

### Introduction

Atomic force microscope (AFM) is a an extremely versatile and powerful high resolution (typically in nanometer range) microscope, that can provide detailed scans revealing the nanoscale topographical features of sample. The AFM can operate in environments from ultra-high vacuum to fluids, and therefore cuts across all disciplines from physics and chemistry to biology and materials science.

### What kind of things can AFM do?[1]

Atomic force microscopy (AFM) can be used to perform various kinds of operations like imaging, force-distance spectroscopy and surface manipulation (lithography).
Imaging means to perform a 2d or 3d topographical scan of the surface. This can then be used to obtain various  measurements of the surface features.
Force-distance spectroscopy is used to get information like the surface elasticity/stiffness, information about the interaction between the surface and the probe, etc.
AFM probe can also be used to deliberately modify the surface features by pressing the tip/probe aggressively to the sample. It can be used to actually write or manipulate features on the sample.

### Working principle

The most important part of AFM is the cantilever-tip assembly that interacts with the sample. This assembly is also commonly referred to as the probe. The AFM probe raster scans the sample. The cantilever bends up and down depending on the surface features of the sample. The up/down motion of the tip as it scans along the surface is monitored through the beam deflection method. The beam deflection method consists of a laser that is reflected off the back end of the cantilever and directed towards a position sensitive detector that tracks the vertical and lateral motion of the probe.
The detection sensitivity of these detectors has to be calibrated in terms of how many nanometers of motion correspond to a unit of voltage measured on the detector. The atomic interaction between the tip and the surface is shown below.

It is evident that at very small tip-sample distances (a few angstroms) a very strong repulsive force appears between the tip and sample atoms. It’s origin is the so-called exchange interactions due to the overlap of the electronic orbitals at atomic distances. When this repulsive force is predominant, the tip and sample are considered to be in contact. As the distance between the tip and sample increases further we have the attraction (van der Waals)regime. It’s origin is a polarization interaction between atoms: an instantaneous polarization of an atom induces a polarization in nearby atoms and therefore an attractive interaction. The probe can also be mounted into a holder with a shaker piezo. The shaker piezo provides the ability to oscillate the probe at a wide range of frequencies (typically 100 Hz to 2 MHz) enabling dynamic modes of operation in the AFM. The dynamic modes of operation can be performed either in resonant modes (where operation is at or near the resonance frequency of the cantilever) or off-resonance modes (where operation is at a frequency usually far below the cantilevers resonance frequency).

### AFM components

#### Cantilever-Tip Assembly (Probe)[2]

The cantilever is usually of rectangular or triangular geometry of micrometer dimensions. The cantilever consists of a very sharp tip (typical radius of curvature at the end for commercial tips is 5-10 nm) that hangs o the bottom of a long and narrow cantilever. As mentioned previously, the cantilever/tip assembly is also referred to as the probe. AFM cantilevers are typically made of either silicon or silicon nitride, where silicon nitride is used for softer cantilevers with lower spring constants. The spring constant (k) of the cantilever is determined by it’s dimensions using the following formula:

$k=E\frac{wt^3}{4L^3}$

where w=cantilever width; t=cantilever thickness; L=cantilever length and E=Youngs modulus of the cantilever material. Nominal spring constant values are typically provided by the vendor when buying the probes, but there can be significant variation in the actual values.

#### Raster scan[1]

AFM raster scans the sample by either moving the sample below the tip or by moving the tip above the sample. The latter is more popular. The movement is achieved by a piezoelectric material, which expands and contracts proportionally to an applied voltage. Whether they elongate or contract depends upon the polarity of the voltage applied. Traditionally the tip or sample is mounted on a ‘tripod’ of three piezo crystals, with each responsible for scanning in the x,y and z directions. Later tube scanners were incorporated into AFMs. The tube scanner can move the sample in the x, y, and z directions using a single tube piezo with a single interior contact and four external contacts.

#### Cantilever deflection measurement[1][5]

The most common method for cantilever-de ection measurements is the beam-de ection method. In this method a laser light is reflected-off the back of the cantilever, and is collected by a position-sensitive photodiode (PSPD) that consists of two closely spaced photodiodes, whose output signal is collected by a differential amplifier. Deflection of the cantilever results in one photodiode collecting more light than the other photodiode, producing an output signal (the difference between the photodiode signals normalized by their sum), which is proportional to the de ection of the cantilever. The sensitivity of the beam-de ection method is very high. A longer beam path increases the motion of the reflected spot on the photodiodes, but also widens the spot by the same amount due to di raction, so that the same amount of optical power is moved from one photodiode to the other.
Nowadays, quad PSPDs are used that have four photodiode quadrants, and can also measure the lateral de ection of the cantilever.

#### Feedback

A feedback loop is employed to maintain a constant deflection for constant force mode. The Z-controller feedback loops moves the cantilever back to the initial deflection. As the probe scans a feature on the sample, the cantilever gets deflected which changes the position of the laser spot on the PSPD. The Z-controller feedback loop then moves the cantilever along z-axis to bring the spot back to it’s initial position. Similarly for other modes like tapping/ non-contact mode a set amplitude is maintained. The value of deflection/amplitude to be maintained is called the setpoint.

#### Operation modes

AFM typically operates in either Contact mode (static mode), Non-contact mode and Tapping mode(dynamic force mode).
In contact mode[6], the tip is in perpetual contact with the sample. The tip is attached to the end of a cantilever with a low spring constant, lower than the effective spring constant holding the atoms of most solid samples together which is on the order of 1 – 10nN/nm.
Further there are two imaging methods of contact modes: constant force mode and constant height mode.
In constant force mode, the force on the cantillever is kept constant by keeping the de ection of the cantilever constant.
Contact force works in the repulsive region therefore the cantilever bends away from the sample causing it to have some initial deflection. As the scanner gently traces the tip across the sample (or the sample under the tip), the contact force causes the cantilever to bend and the de ection to change. The de ection can be kept constant by employing a feedback loop to bring the cantilever back to the initial deflection.
In constant height mode, the distance between the sample and te cantilever is kept constant. As the scanner gently traces the tip across the sample (or the sample under the tip), the contact force causes the cantilever to bend and the Z-feedback loop works to maintain a constant cantilever deflection.
Constant force mode is more popular than the constant height mode as the forces are controlled in contrast to constant height where forces large enough to break the tip could develop.
Non-contact mode[6] refers to the modes that make use of an oscillating cantilever. A sti cantilever is oscillated in the attractive regime, meaning that the tip is quite close to the sample, but not touching it (hence, non-contact). The forces between the tip and sample are quite low, on the order of pN ($10^-12 N$). The scanning is done by measuring changes to the resonant frequency or amplitude of the cantilever as the interaction between the tip and sample dampens the oscillation.
In Tapping mode[7][8], also known as intermittent-contact mode, the most commonly used of all AFM modes, maps topography by lightly tapping the surface with an oscillating probe tip. The cantilevers oscillation amplitude changes with sample surface topography, and the topography image is obtained by monitoring these changes and closing the z feedback loop to minimize them. Very stiff cantilevers are typically used, as tips can get stuck in the water contamination layer.
Tapping mode imaging is implemented in ambient air by oscillating the cantilever assembly at or near the cantilever’s resonant frequency using a piezoelectric crystal.

Contact mode vs. Non-Contact mode vs. Tapping mode [6] [7]
Contact mode imaging is heavily influenced by frictional and adhesive forces, and can damage samples and distort image data. This also causes the cantilever tips to wear out quickly. Only hard surfaces that won’t get damaged by the tip are can be imaged in this mode.
Non-contact imaging generally provides low resolution and can also be hampered by the contaminant (e.g., water layer which can interfere with oscillation. The cantilever tips don’t wear out quickly in this mode.
Tapping Mode imaging (right) takes advantages of the two above. It eliminates frictional forces by intermittently contacting the surface and oscillating with sucient amplitude to prevent the tip from being trapped by adhesive meniscus forces from the contaminant layer. With the Tapping mode technique, the very soft and fragile samples can be imaged successfully.

### AFM force-distance spectroscopy [1] [2]

Another major application of AFM (besides imaging) as mentioned earlier is force-distance spectroscopy, the direct measurement of tip-sample interaction forces as a function of the gap between the tip and sample (the result of this measurement is called a force-distance curve). In this, the AFM tip is rst made to approach the sample from non-interaction region through the attractive regime all the way to the repulsive regime and the force is measured. Then the probe is retracted and the forces are measured again.
A typical force curve is shown below

The force curve above is divided into different segments where the black line from A-C refers to the tip approaching the surface and D-F (gray line) is for the tip retracting from the surface. The gray line has been given an artificial offset for illustrative purposes.
A. Cantilever is approaching the surface. But is far enough to not feel any force.
B. Snap-in point: the cantilever suddenly snaps into contact with the sample. This snap-in is due to tip-surface interactions.
C. Repulsive portion: the repulsive forces come into play and bend the tip upwards upon further movement of the z-piezo. This section is referred to as the net-repulsive portion. It is interesting to note here that the cantilever deflection and hence the force are proportional to the z-distance. This curve is actually used to convert the volts produces in PSPD to nanometers.
D. Repulsive portion on withdrawal: the tip is now unbending while being withdrawn from the surface.
E. Pull-out: the tip gets stuck in an adhesive dip before it is able to emerge from the adhesion at the interface.
F. The cantilever has returned to its unperturbed state while the z-piezo further increases the tip sample distance. Problems with the technique include no direct measurement of the tip-sample separation and the common need for  low-stiffness cantilevers, which tend to ‘snap’ to the surface.
Force curves can be mined for various mechanical properties of the sample including adhesion, sti ness (modulus), and indentation depth (how much the tip penetrates into the sample at a given load).

### Lithography/ Manipulation[1][2]

AFM tip can be used to perform deliberate damage to the surface to manipulate some features. This process is known as lithography. This is typically done in static mode, the cantilever/probe can carve out patterns or structures on surfaces through an aggressive interaction between the tip and sample configured with a high deflection setpoint. In terms of manipulation, the probe can be used to cut or move around structures.

AFM has several advantages over the scanning electron microscope (SEM). Where SEM provides only a 2d image, AFM provides a 3d surface profile. In addition, samples viewed by AFM do not require any special treatments (such as metal/carbon coatings) that would irreversibly change or damage the sample, and does not typically suffer from charging artifacts in the final image. AFM doesn’t need an expensive vacuum environment for proper operation, and can work in ambient air or even fluids. This is advantageous as this lets one study biological macromolecules and even living organisms. AFM also has a higher resolution than SEM.

Although extremely versatile, AFM does have some limitations.
The scan speed of AFM is pretty slow when compared to SEM.
The scan image size of AFM is also drastically smaller ( 150um x150um) as compared to SEM (order of mm).
As with any other imaging technique, there is the possibility of image artifacts, which could be induced by an unsuitable tip, a poor operating environment, etc. These image artifacts are unavoidable; however, their occurrence and effect on results can be reduced through various methods. Artifacts resulting from a too-coarse tip can be caused for example by inappropriate handling or collisions with the sample by either scanning too fast or having an unreasonably rough surface, causing actual wearing of the tip.
Due to the nature of AFM probes, they cannot normally measure steep wall type features.

### Applications[1]

The AFM has been applied to problems in a wide range of disciplines of the natural sciences, including solid-state physics, semiconductor science and technology, molecular engineering, polymer chemistry and physics, surface  chemistry, molecular biology, cell biology, and medicine.
Applications in the field of solid state physics include (a) the identification of atoms at a surface, (b) the evaluation of interactions between a specific atom and its neighboring atoms, and (c) the study of changes in physical properties arising from changes in an atomic arrangement through atomic manipulation.
In molecular biology, AFM can be used to study the structure and mechanical properties of protein complexes and assemblies. For example, AFM has been used to image microtubules and measure their stiffness.
In cellular biology, AFM can be used to attempt to distinguish cancer cells and normal cells based on a hardness of cells, and to evaluate interactions between a specific cell and its neighboring cells in a competitive culture system. AFM can also be used to indent cells, to study how they regulate the stiffness or shape of the cell membrane or wall.

### Scan rate and Feedback loop optimization [9] [2]

The scan speed also affects the quality of the scanned image. The scan speed should be such that the tip must be able to follow the surface while scanning, which has two preconditions: :
(i) The scan mechanics must be able to position the tip fast enough.
(ii) The sensor must be able to deliver the information from the surface fast enough.
This results in the following rules:
(i) The scan speed of the speed optimized AFM is limited by the response time of the sensor.
(ii)For similar image quality, a higher scan speed requires more information per time unit from the surface and therefore more interaction between tip and sample is needed. This may cause streaks appear on the trailing edge of surface features. Streaks are an indication of the tip not tracking the surface properly.

One should also keep the following points in mind while setting the feeback control gains.
Control of the feedback loop is done through the proportion-integral-derivative control, often referred to as the PID gains. These different gains refer to differences in how the feedback loop adjusts to deviations from the setpoint value, the error signal. For AFM operation, the integral gain is most important and can have a most dramatic effect on the image quality. The proportional gain might provide slight improvement after optimization of the integral gain. The derivative gain is mainly for samples with tall edges. If gains are set too low, the PID loop will not be able to keep the setpoint accurately. If the gains are chosen too high the result will be electrical noise in the image from interference from the feedback. The other parameters that are important in feedback are the scan rate and the setpoint. If the scan rate is too fast, the  PID loop will not have sucient time to adjust the feedback parameter to its setpoint value and the height calculated from the z piezo movement will deviate from the true topography at slopes and near edges. Very slow scan rates are typically not an issue for the PID loop, but result in long acquisition times that can pose their own challenges such as thermal drift. Optimization of the PID gains and the scan rate are necessary in order to optimize feedback loops. The setpoint affects the interaction force or impulse between probe and sample. A setpoint close to the parameter value out of contact feedback is most gentle for the sample, but tends to slow down the feedback.

### References

[1] AFM Wikipedia Article,
https://en.wikipedia.org/wiki/Atomic force microscopy

[2] AFM nanosurf theory,
https://www.nanosurf.com/en/support/afm-modes

[3] CONTR Cantilever specifications,
http://www.nanoworld.com/contact-mode-re ex-coated-pointprobe-afm-tip-contr

[4] HS-100MG Calibration sample specifications,
http://www.tedpella.com/calibration html/AFM SPM Calibration.htm#HS20MG

[5] PSPD and Procedure

[6] Operating modes- Contact, Non-Contact,
http://www.eng.utah.edu/ lzang/images/Lecture 10 AFM.pdf

[7] Dynamic Mode
https://www.nanoscience.com/technology/afm-technology/afm-modes-2/

[8] Contact and Tapping mode
http://www.chembio.uoguelph.ca/educmat/chm729/afm/details.htm

[9] Scan speeds
http://dme-spm.com/geschw.html

[10] Nanosurf manual
Nanosurf FlexAFM Operating instructions

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## One thought on “Atomic Force Microscopy (AFM)”

1. It was interesting when you talked about how piezoelectric material expands and contracts to propel the movement of the sample. My husband is interested in building a scanning tunneling microscope with our son as a fun and education product. Thanks for letting me know that we might need to get a piezo scanner to use in the microscope!