Through the years imaging surfaces and analyzing the morphology of various samples on a micro scale was a dominant and demanding challenge which scientists had to handle. Scanning probe microscopy can produce a highly magnified image of the surface or the bulk of the sample by scanning the specimen using a physical probe. Atomic Force microscope (AFM) was originally developed in order to overcome the limitations of the scanning tunnelling microscope (STM).
In order to analyse and characterize a sample different techniques have to be carried into effect. Due to the fact that human eye as well as optical microscope cannot be used to see dimensions at nano level, other imaging techniques have to be obtained. Scanning probe techniques brought a revolution in this field providing a better image for a variety of surfaces. Initially, scanning probe microscopy (SPM) was introduced, but due to reasons that will be explained later, atomic force microscopy (AFM) was also founded. In this report the principles of operation of the atomic force microscopy, the methods, the advantages, the limitations and the applications of this technique are presented.
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More specific, the specimen is scanned using a physical probe and images of the surfaces are being formed. This surface image is being produced due to mechanically moving the probe in a scan of the specimen and recording the interaction between the probe and the surface as a function of position. The impressive and interesting factor of this technique is that it can reach atomic resolution.
Atomic force microscopy (AFM) provides us with the ability to analyze other materials, like polymers, ceramic materials, proteins, biological samples creating the image of non-conducting surfaces. In addition, the inter-atomic forces between the sample and the tip can be measured while creating digitally a topographical surface of the sample. Furthermore, atomic force microscopy is used to measure the thickness of a crystal growth layer or even to determine the roughness of a surface sample. In general, AFM can analyze and characterize samples at the atomic level, with resolution ranging from 0.1 nm to 1 nm.
Scanning Probe Microscopy (SPM) was founded in 1981 by Gerd Binnig and Heinrich Rohrer (at IBM Zürich) . Moreover, few years later, in 1986 Nobel Prize in Physics was awarded to them for the invention of the scanning tunnelling microscope (STM). Unfortunately, STM can only image materials that can conduct a tunnelling current. In order to overcome this limitation Atomic Force Microscope was invented by G. Binnig, Ch. Gerber and C. Quate at Stanford University. They attempted to glue a tiny sharp of diamond onto one end of a tiny strip of gold oil.
How does it work?
Atomic force microscopy's principle of operation is based on the measurement of the force between the probe and the sample, which depends on their distance. A cantilever with a sharp tip at one end (probe) is used to scan the sample. Recording the vertical position of the tip while is rastered across the sample a topographic image is build up by the computer. Cantilevers are usually made from silicon (Si) or silicon nitride (Si3N4) and range from 100 to 200 Î¼m in length, 10 to 40 Î¼m in width and 0.3 to 2 Î¼m in thickness. 
Figure 1. Illustration of a tip scanning a sample surface. The picture is reproduced from Rubens Bernardes-Filho & Odilio Benedito Garrido de Assis
How are forces measured?
The cantilever acts as a spring and the amount of forces between the probe and the sample is depended on the stiffness of the cantilever (spring constant) and the distance between the probe and the sample surface. These forces lead to a deflection of the cantilever according to Hooke's law.
F = - kx
k = spring constant
x= cantilever deflection
Figure 2. A) Spring depiction of cantilever B) SEM image of a triangular SPM cantilever with probe. Images are from MikroMasch.
Forces versus distance curve
The dominant interactions at short distances between the probe and the sample in the AFM are Van der Waals interactions. However, there are also other interactions such as capillary, electrostatic and magnetic, which are significant in a further distance from the surface. In methods like SPM (Scanning Probe Microscopy) these interactions play an important role. 
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When the probe physical touches the surface (contact mode), the probe predominately experiences repulsive Van der Waals forces. This has as a result the tip deflection which was mentioned earlier. While the probe moves away from the surface (non-contact mode) attractive Van der Waals forces are dominant. The dependence of the van dew Waals regarding the distance between the tip and the sample is shown in Figure 3.
Figure 3. Plot of force as a function of probe-sample separation. Images are from Robert A. Wilson and Heather A. Bullen, Department of Chemistry, Northern Kentucky University, Highland Heights
Modes of operation
The basic concept of operation is shown at Figure 4. There are three primary modes of operation: contact mode, non-contact mode and tapping mode.
Figure 4. Principle of AFM
I. Contact mode is the first and more widely used mode of operation. It operates in the repulsive regime of the Van der Waals curve. The cantilever bends (as shown in the picture) when the spring constant of the cantilever is less than the surface of the sample. The force between the probe and the sample is extremely low (âˆ¼10-9N) and remains constant by using the feedback loops to maintain a constant cantilever deflection. A few instruments operate in UHV but the majority operate in ambient atmosphere, or in liquids. Moreover, the stiffness of the cantilever should be less than the effective spring constant holding atoms together due to the fact that the tip is in hard contact with the surface. Most contact mode cantilevers have a spring constant of < 1 N/m.  
The advantages of the contact mode is that it is a fast scanning technique which can operate well for rough samples and can also be used in friction analysis. In addition, it is the only mode where "atomic resolution" is possible.  However, because in this mode the probe is in contact with the surface there is the possibility to damage or deform samples, especially soft samples like biological tissues or polymers.
II. The non-contact mode uses attractive forces to interact the surface with the tip. A stiff cantilever is oscillated in the attractive regime, meaning that the tip is quite close to the sample but does not touch it (as shown in the picture). It oscillates above the liquid absorbed layer on the surface during scanning.  The force between the probe and the sample is extremely low (âˆ¼10-12N). Measuring the changes to the resonant frequency or the amplitude of the cantilever the surface topography can be measured. 
Figure 5. In the non-contact mode of operation a frequency shift in the resonance peak of the cantilever is induced. Picture is from the book, Atomic force microscopy: biomedical methods and applications. By Pier Carlo Braga and Davide Ricci
The non-contact mode has the benefit that it is a non-destructive mode of operation. Furthermore, the force exerted to the sample is very low (âˆ¼10-12N) and there no lateral forces. The mainly drawback is that it has generally low resolution and in order to have best imaging an ultra high vacuum (UHN) is needed. Moreover, the scan speed is lower than contact mode in order to avoid contact with the water layer. 
III. In the tapping mode or intermittent contact mode, the probe lightly "taps" on the surface of the sample during scanning and only touches the sample at the bottom of each oscillation. In most cases, the cantilever oscillates near its resonant frequency (âˆ¼200 k Hz) in order to improve sensitivity.  The cantilever oscillates closer to the sample in comparison to the non-contact mode. Stiff cantilevers and silicon probes are mainly used for this mode because of the strong forces by the interactions with the thin water layer.
The most important advantage of the tapping mode is that it allows high resolution of soft samples. It can be performed on both wet and dry sample surfaces. Also, it eliminates lateral forces such as drag. However, when imaging in liquids a slower speed is needed in order to scan the sample.
Different operation modes should be chosen according to the characteristics of the sample, since each mode has different advantages.
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Today most AFMs use a laser beam deflection system, introduced by Meyer and Amer in order to produce a topographic image. In an AFM contact mode first the AFM tip is brought manually close to the sample surface. Then the scanner makes a final adjustment in the distance between the tip and the sample according to a set-point determined by the user. Under ambient conditions, sample surfaces are covered by a layer of adsorbed gases consisting primarily of water vapor and nitrogen which is 10-30 monolayers thick.
Figure 6. Schematic diagram showing the operation principles of the AFM in the contact mode. The picture is from Cheryl R. Blanchard, Southwest Research Institute San Antonio
Now, the tip is in contact with the water layer and is scanned the sample under the action of the piezoelectric actuator (either by moving the tip relative to the sample or the other way around). As shown in Figure 6, a laser beam aimed at the back of the cantilever-tip reflects from the cantilever surface to a split photodiode. This detector measures the bending of the cantilever during the scanning across the sample. A feedback loop maintains constant the separation between the tip and the sample by moving the scanner in the z direction to maintain the set-point deflection. Finally, the variation in the x-y plane and the distance the scanner moves in the z direction are used to generate a topographic image of the sample surface.
As I mentioned before the photodiode is divided into four parts, as shown in Figure 7. If the laser is displaced vertically along the positions (B-A, D-C) a bending due to topography is produced, while if the movement is horizontal (B-D, A-C) a torsion because of the "friction" (lateral force) is produced.
Figure 7. The scanned cantilever system. The picture is reproduced from Prof. Nikos Frangis, Aristotle University, Thessaloniki, Greece
Tip and Cantilever
In the early years of AFM operation, the tips were made from crushed diamond particles, which were manually glued on the cantilevers. Nowadays, probes (cantilevers with a sharp tip at one end) are made from Silicon (Si) or Silicon nitride (Si3N4) and are available commercially. In addition, researchers consider carbon nanotubes as the next probe material. Differentiations in cantilever's length, material and shape allow various spring constants and resonant frequencies. V- shaped cantilevers are more popular because they can provide a low mechanical resistance to vertical deflection and high resistance to lateral torsion. However, there are also rectangular cantilevers (Figure 8.) A typical tip radius is around 10 nm, the spring constant is between 0.1 to 100 N/m and the resonance frequency 5-500 kHz. 
Figure 8. Different probes. Optical microscopy images of V-shaped cantilevers and rectangular cantilevers. Pictures are reproduced from DoITPoMS, Department of Materials Science and Metallurgy, University of Cambridge
Phase Imaging, also referred to as phase detection microscopy (PDM) is a powerful extension of Tapping Mode Atomic Force Microscopy (AFM) that provides nanometer-scale information about surface structure which is often not revealed by other SPM techniques. In the phase mode imaging the phase lag between the signal that drives the cantilever oscillation and the cantilever oscillation output signal are measured (see Figure 8). Changes in the phase lag can be correlated with specific material properties (mainly mechanical properties) that effect the interaction between the tip and the sample. The phase lag can be used to detect different material properties such as friction, adhesion and viscoelasticity. Phase imaging is very useful for polymer research and for investigating the magnetic and electrical properties as in Electric Force Microscopy (EFM) and Magnetic Force Microscopy (MFM).
Figure 8. Phase imaging. Picture is reproduced from K.L. Badcock and C.B. Prater
The tip of the AFM is used for measuring forces, imaging surfaces and as a nanoscale tool for cutting or extracting soft materials such as polymers and DNA.
AFM is a useful, interesting and revealing imaging technique. In this point, images are presented in order to understand better and view some samples. To realize the magnitude of this method dimensions are also mentioned.
Figure 9. Tetraphenylporphyrin molecules deposited on quartz, AFM image at ambient conditions (MFP 3D, Asylum Research, CA). Contact mode, image size 20*20 Âµm2. Picture is reproduced from the Surface & Plasma Technology. Research Group of the Institut für Allgemeine Physik
Figure 10. Picture is reproduced from Colorado Advanced Photonics Technology Centre.
Figure 11. Some images that were obtained at EMTERC. Picture is reproduced from lecture notes.
Advantages of AFM over other imaging techniques.
AFM vs. STM
AFM was developed in order to overcome the limitations of STM. While STM is generally applicable only to conducting samples, AFM is applicable to both conductors and insulators. However, in some cases, the resolution of STM is better than AFM due to the exponential dependence of the tunnelling current on the distance. 
AFM vs. SEM
SEM (Scanning Electron Microscope).
Compare to SEM, AFM make measurements in three dimensions, x, y, and z providing it with the advantage to obtain a three-dimensional image of the surface without any preparation and with low cost. In addition, AFM does not require a vacuum environment or any sample preparation; it can operate in an ambient or liquid environment. Although the resolution of AFM is higher than SEM, the scan speed is lower than SEM.
AFM vs. TEM
TEM (Transmission Electron Microscopy)
AFM has the advantage that presents three-dimensional images of a sample surface without any expensive sample preparation. That is also another benefit in comparison to TEM because more information about the structure is available.
AFM vs. optical microscope
AFM seems to have a huge amount of advantages over the optical microscope. However, the only limitation is by the radius of the tip.
Limitations of AFM
Although AFM can operate in various environments (air, liquid, vacuum) and can be used to study a wide variety of samples (conductors, insulators, semiconductors), there are some limitations regarding the atomic resolution. The radius of the tip and the sharpness of it can have a great impact on the resolution.
Figure 12. Diagram of AFM cantilever tip interaction with a surface. Images are from Robert A. Wilson and Heather A. Bullen, Department of Chemistry, Northern Kentucky University, Highland Heights
As shown in Figure 12, while the tip scans across the sample, the sides of the tip make contact before the apex and from that contact the feedback mechanism responds to the feature. This mainly occurs when the feature is sharper than the tip. The phenomenon is known as tip convolution or tip imaging.
Another possible limitation of this technique is compression of features. Researchers are investigated the pressure of the tip over the sample. This compression has a significant impact in the case where the samples are soft biological polymers such as DNA. Last but not least, the strong interaction with the sample, especially when contact mode is performed, is another point that limits AFM possibilities and applications.
With the numerous advantages that were discussed earlier AFM has significantly impacted the fields of physics, chemistry, biology and materials science.
Potential applications of AFM:
Substrate roughness analysis, measuring the surface forces and the adhesion of thin-film and bulk materials
Measures the elastic and plastic behaviour and hardness via nanoindentation
Measures the area and the volume of the defect at a surface of different types of materials such as metals, crystals and ceramics
Ideal for studying crack propagation in surfaces due to the fact that AFM gives great contrast on flat samples
Measures images of composite polymers with little or no sample preparation
Visualises easily nanoparticles; the size, the volume and the surface area of them
High resolution images of carbon nanotubes
Images integrated circuit chips
Data storage media. Creates structures with nanometer-sized dimensions
Measures bio-molecules such as DNA (as long as they are directly attached to a surface)
Accurate metrological measurements on optically transparent materials
Visualizes and characterizes paper coatings (in the case where paper coatings are comprised of nanoparticles)
Atomic force microscopy was introduced in 1986 as a method to examine the surface of insulating samples. For constructing the sample's topography the force that is present between the probe and the sample has to be measured. This force depends on the distance between the probe and the sample, the nature of the sample, the sample surface contamination and the probe geometry. In order to detect the displacement of the cantilever a laser beam deflection system is used. A laser is reflected from the back of the cantilever and collected in a detector. There are different modes of operation. At close contact the force is repulsive while at a larger separation the force is attractive. According to the characteristics of the sample different operation modes should be chosen. AFM leads us to the detection of the atomic scale characteristics on various insulating surfaces such as ceramic materials, polymers and biological samples. Moreover, through the years AFM evolved into a promising and significant instrument providing new insights in the field of material science, biology and electrochemistry. Although there is a limit regarding the operation of AFM, researcher try to overcome it mainly by fabricating tips from different materials. The next step is the use of carbon nanotubes as tips.
 "Scanning tunneling microscopy". G. Binnig, H. Rohrer (1986). IBM Journal of Research and Development 30: 4.
 Park Scientific Instruments. A practical guide to scanning probe microscopy (1997)
 Atomic Force Microscopy, Basic Theory. Robert A. Wilson and Heather A. Bullen, Department of Chemistry, Northern Kentucky University, Highland Heights, KY 41099
 Lecture's notes of the module: ENGT5129 Physical & Electrical Measurements
 Atomic Force Microscopy. Cheryl R. Blanchard, Southwest Research Institute San Antonio