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Atomic force microscopy
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===Configuration=== Fig. 3 shows an AFM, which typically consists of the following features.<ref name="Biningpat">[https://patents.google.com/patent/US4724318 Patent US4724318 β Atomic force microscope and method for imaging surfaces with atomic resolution]</ref> Numbers in parentheses correspond to numbered features in Fig. 3. Coordinate directions are defined by the coordinate system (0). [[File:AFM conf.jpg|thumb|upright=1.15|'''Fig. 3:''' Typical configuration of an AFM.<br /> '''(1)''': Cantilever, '''(2)''': Support for cantilever, '''(3)''': Piezoelectric element (to oscillate cantilever at its eigen frequency), '''(4)''': Tip (Fixed to open end of a cantilever, acts as the probe), '''(5)''': Detector of deflection and motion of the cantilever, '''(6)''': Sample to be measured by AFM, '''(7)''': xyz drive, (moves sample (6) and stage (8) in x, y, and z directions with respect to a tip apex (4)), and '''(8)''': Stage.]] The small spring-like [[cantilever]] (1) is carried by the support (2). Optionally, a piezoelectric element (typically made of a ceramic material) (3) oscillates the cantilever (1). The sharp tip (4) is fixed to the free end of the cantilever (1). The detector (5) records the deflection and motion of the cantilever (1). The sample (6) is mounted on the sample stage (8). An xyz drive (7) permits to displace the sample (6) and the sample stage (8) in x, y, and z directions with respect to the tip apex (4). Although Fig. 3 shows the drive attached to the sample, the drive can also be attached to the tip, or independent drives can be attached to both, since it is the relative displacement of the sample and tip that needs to be controlled. Controllers and plotter are not shown in Fig. 3. According to the configuration described above, the interaction between tip and sample, which can be an atomic-scale phenomenon, is transduced into changes of the motion of cantilever, which is a macro-scale phenomenon. Several different aspects of the cantilever motion can be used to quantify the interaction between the tip and sample, most commonly the value of the deflection, the amplitude of an imposed oscillation of the cantilever, or the shift in resonance frequency of the cantilever (see section Imaging Modes). ====Detector==== The detector (5) of AFM measures the deflection (displacement with respect to the equilibrium position) of the cantilever and converts it into an electrical signal. The intensity of this signal will be proportional to the displacement of the cantilever. Various methods of detection can be used, e.g. interferometry, optical levers, the piezoelectric method, and STM-based detectors (see section "AFM cantilever deflection measurement"). ====Image formation==== ''This section applies specifically to imaging in {{section link||Contact mode}}. For other imaging modes, the process is similar, except that "deflection" should be replaced by the appropriate feedback variable.'' When using the AFM to image a sample, the tip is brought into contact with the sample, and the sample is raster scanned along an xβy grid. Most commonly, an electronic feedback loop is employed to keep the probe-sample force constant during scanning. This feedback loop has the cantilever deflection as input, and its output controls the distance along the z axis between the probe support (2 in fig. 3) and the sample support (8 in fig 3). As long as the tip remains in contact with the sample, and the sample is scanned in the xβy plane, height variations in the sample will change the deflection of the cantilever. The feedback then adjusts the height of the probe support so that the deflection is restored to a user-defined value (the setpoint). A properly adjusted feedback loop adjusts the support-sample separation continuously during the scanning motion, such that the deflection remains approximately constant. In this situation, the feedback output equals the sample surface topography to within a small error. Historically, a different operation method has been used, in which the sample-probe support distance is kept constant and not controlled by a feedback ([[Servomechanism|servo mechanism]]). In this mode, usually referred to as "constant-height mode", the deflection of the cantilever is recorded as a function of the sample xβy position. As long as the tip is in contact with the sample, the deflection then corresponds to surface topography. This method is now less commonly used because the forces between tip and sample are not controlled, which can lead to forces high enough to damage the tip or the sample.{{Citation needed|date=March 2022}} It is, however, common practice to record the deflection even when scanning in constant force mode, with feedback. This reveals the small tracking error of the feedback, and can sometimes reveal features that the feedback was not able to adjust for. The AFM signals, such as sample height or cantilever deflection, are recorded on a computer during the xβy scan. They are plotted in a [[pseudocolor]] image, in which each pixel represents an xβy position on the sample, and the color represents the recorded signal. [[File:Schematics of Topographic image forming.jpg|thumb|upright=1.15|'''Fig. 5:''' Topographic image forming by AFM.<br /> '''(1)''': Tip apex, '''(2)''': Sample surface, '''(3)''': Z-orbit of Tip apex, '''(4)''': Cantilever. ]]
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