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A low-cost AFM setup with an interferometer for undergraduates and secondary-school students
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2013 Eur. J. Phys. 34 901 (http://iopscience.iop.org/0143-0807/34/4/901) View the table of contents for this issue, or go to the journal homepage for more
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IOP PUBLISHING
EUROPEAN JOURNAL OF PHYSICS
Eur. J. Phys. 34 (2013) 901–914
doi:10.1088/0143-0807/34/4/901
A low-cost AFM setup with an interferometer for undergraduates and secondary-school students Antje Bergmann 1 , Daniela Feigl 1 , David Kuhn 1 , Manuel Schaupp 1 , Gunter ¨ Quast 2 , Kurt Busch 3 , 4 Ludwig Eichner and Jens Schumacher 4 1 Institut f¨ ur Theoretische Festk¨orperphysik, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str 1, D-76131 Karlsruhe, Germany 2 Institut f¨ ur Experimentelle Kernphysik, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str 1, D-76131 Karlsruhe, Germany 3 Humboldt-Universit¨ at zu Berlin, Institut f¨ur Physik, AG Theoretische Optik & Photonik, and Max Born Institute, D-12489 Berlin, Germany 4 Thorlabs, 56 Sparta Ave, Newton, NJ 07860, USA
E-mail:
[email protected]
Received 1 February 2013, in final form 7 March 2013 Published 2 May 2013 Online at stacks.iop.org/EJP/34/901 Abstract
Atomic force microscopy (AFM) is an important tool in nanotechnology. This method makes it possible to observe nanoscopic surfaces beyond the resolution of light microscopy. In order to provide undergraduate and secondary-school students with insights into this world, we have developed a very robust lowcost AFM setup with a Fabry–Perot interferometer as a detecting device. This setup is designed to be operated almost completely manually and its simplicity gives access to a profound understanding of the working principle. Our AFM is operated in a constant height mode, i.e. the topography of the sample surface is represented directly by the deflection of the cantilever. Thus, the measuring procedure can be understood even by secondary-school students; furthermore, it is the method with the lowest cost, totalling not more than 10–15 k Euros. Nevertheless, we are able to examine a large variety of sample topographies such as CD and DVD surfaces, IC structures, blood cells, butterfly wings or moth eyes. Furthermore, force–distance curves can be recorded and the tensile moduli of some materials can be evaluated. We present our setup in detail and describe its working principles. In addition, we show various experiments which have already been performed by students. (Some figures may appear in colour only in the online journal) 1. Introduction
Nanotechnology has become more and more important in day-to-day life. Thus, it is a field of research that is worth teaching even to secondary-school students. An important c 2013 IOP Publishing Ltd Printed in the UK & the USA 0143-0807/13/040901+14$33.00
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and often used tool for analysing nanostructures is the AFM, which is used to scan a surface with a probe in the form of a sharp tip, mounted on a soft cantilever spring [1, 2]. A topographical image is obtained by measuring the forces due to the interactions between the tip and the sample surface. The repulsive forces are due to electrostatic interactions and the Pauli exclusion principle; the attractive forces can be attributed to van der Waals forces [3]. Several authors have already presented ideas for university undergraduate experiments and explanatory models for this method. Bonson et al presented a working model of an AFM which explains the principle in a very demonstrative way by using a modified phonograph stylus [4]. A macroscopic model to describe the forces in a tapping mode AFM was developed by Greczylo and Debowska [6]. Shusteff et al demonstrated an undergraduate experiment for measuring Boltzmann’s constant [5] via an interdigitated cantilever. However, the existing AFM setups or models are suited rather for university students or they constitute educational models to only show the principle on a macroscopic scale. With our setup design, we would like to bridge the gap between these possibilities: our setup is simple enough for it to be easily understood and worked with by secondary-school students, but it is sophisticated enough to perform real measurements in nanoscopic dimensions. Our AFM is enormously robust and user friendly so that the maintenance requirements are conveniently low. Furthermore, the cost of about 10–15 k Euros is comparatively low for a properly working AFM setup and, therefore, affordable for science laboratories for school students or university undergraduate courses. Since our experimental programme targets school students, we have chosen a variety of experiments and samples that we consider to be intriguing for them. The topography of biological samples such as a fly’s eye or a moth’s wing, as well as integrated circuits (ICs) or CD and DVD surfaces can be examined. Besides imaging, our AFM allows us to perform force spectroscopy analysis as a more advanced topic for university students. Force–distance curves can be recorded and different materials’ tensile moduli can be determined. In this paper, we present our setup design and show results for the above-named experiments. 2. A simple AFM setup
In order to build a proper AFM, only a few essential components are needed: a positioning stage for the scanning procedure, a unit which can detect the cantilever deflection and convert it into a voltage signal and an interface and some electronics to both control the scanning process and interpret and record the detected cantilever signal. Our setup was designed to contain not more than these essential parts in order to keep it as simple as possible. Furthermore, we wanted the AFM to dispense with automated procedures so that the user needs to perform all procedures manually—for educational reasons. This guarantees that any manipulation requires understanding of the process. For this reason, our contact mode AFM is operated in the simple constant height mode in which the cantilever deflection signal is used directly for the interpretation of the surface topography. 2.1. Working principle: AFM with an interferometer
Figure 1 shows a schematic of the basic working principle. A laser beam is coupled into a fibre coupler; at one end, the fibre is placed closely above the cantilever, so that the beam is directed onto the back of the cantilever where the deflection
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Figure 1. Schematic of the working principle.
can be detected. A standard cantilever for contact mode scanning can be used for this; special coating is not required. Only about 4% of the laser beam intensity is reflected at the cleaved fibre end [7], but most of the intensity is reflected by the cantilever. Thus, the fibre end and the cantilever comprise a Fabry–Perot interferometer, with which very small displacements, i.e. the cantilever deflection, can be measured [8]. The back-reflected light is then coupled into a photo detector, which converts the light intensity into a voltage signal that can be attributed to the respective deflections. This method is very sensitive; very small displacements of the cantilever result in large changes in light intensity. Figure 2 shows a schematic of this interferometer: I0 represents the incoming light intensity, Ires the resulting intensity from the back-reflected interfering light beams and d is the distance between the fibre end and the cantilever, which is a few micrometres. It becomes clear that cantilever displacements of d result in an optical retardation of 2d. Thus, a height difference d between one interference maximum and minimum is d = λ/4, with λ being the wavelength of the used laser. With λ = 635 nm, we obtain d = 158.75 nm as the maximum signal span when operating the AFM in the constant height mode. This means that the obtained signals are ambiguous if the measured sample possesses structures larger than 158.75 nm. However, this can either be avoided by using a feedback loop controller and implementing a constant force mode or this phenomenon can be used for educational purposes. Having this signal ambiguity to be taken into account implies deliberate consideration of the obtained results when measuring samples that exceed a 158 nm surface structure (see section 3). Furthermore, by running the AFM in the constant height mode, the sample topography can be obtained directly by this signal. For this purpose, a certain voltage is represented by a corresponding greyscale value in the computer software, eventually composing a topographical image. The advantage of this method is the low expense and a considerable simplicity of our setup. The positioning unit in the form of a three-axis piezo stage can be controlled to perform the scanning process in the x–y direction. The cantilever is attached to an additional z-piezo, which
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Figure 2. Fabry–Perot interferometer.
is used for engaging the cantilever tip. This component is not essential; however, we found it to be a very helpful tool of high educational value (see section 2.3). The hardware-to-software interface is realized by a customary analogue-to-digital converter. Our experience with visiting secondary-school students has shown that this simple operating principle can easily be understood. Using a constant height mode instead of the more complex constant force mode makes the setup more transparent and less expensive since additional feedback control systems are not needed.
2.2. The AFM setup in detail
Figure 3 shows our AFM setup. The positioning unit consists of a Thorlabs NanoMax-TS piezo stage (1) with additional differential drives for coarse positioning (2). With a homemade stage attachment (3), it is possible to rotate the sample and compensate for sample tilts. This is very useful and convenient, but not essential or necessary for operation. The optical single mode fibre (4) is positioned above the cantilever via a six-axis kinematic mount (5), so that optimal adjustment of the fibre is possible. The fibre is coupled to a diode laser system which provides a single mode 635 nm, 2.5 mW laser beam for the interferometer function. The cantilever is placed on a simple cantilever holder (6) which is attached to an additional one-axis piezo stage (7) that can be oscillated via a conventional frequency generator. In this way, the engaging of the tip can be performed manually (see section 2.3). Both the laser system and the frequency generator are not shown in figure 3. The interference signal, i.e. the light intensity which represents the cantilever deflection, is detected by a Thorlabs PDA100A-EC Si photo diode detector (not shown either). The detector converts the intensity
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Figure 3. AFM setup.
signal into a voltage, which is then interpreted by software. A USB camera is used for coarse sample positioning (8). 2.3. Engaging the tip
In most commercial AFM setups, the engaging process is performed automatically via feedback control. However, for educational purposes, it is much more comprehensible to perform this step manually. As mentioned before, we use an additional piezo stage to which the cantilever is attached. By oscillating the stage up and down with a frequency generator with approximately 2 Hz (sinusoidal), the stage is moved periodically with an amplitude of a few micrometres. The exact values of the used frequency and amplitude are not crucial; one can decide on what seems to be practical. By observing both the voltage versus time signal of
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(a)
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Figure 4. Engaging the tip using the oscilloscope: the cyan curve shows the direct signal from the
frequency generator; the yellow curve represents the photo diode signal from the interferometer. (a) Continuous interference maxima and minima, no contact between tip and sample and (b) contact between tip and sample where the interference signal disappears.
the excitation frequency coming from the generator and the interferometer signal measured with the photodiode on a two-channel oscilloscope, one can obtain the relevant information for the engaging process. Figures 4(a) and (b) show two oscilloscope snapshots, taken whilst engaging the tip. In figure 4(a), the direct signal coming from the frequency generator which excites the additional z-piezo is represented by the cyan curve; the interference maxima and minima can be identified as the yellow curve. In this situation, there is no contact between the tip and the sample, which is clear from the continuous curve shape. The slight variation of the signal amplitude is due to a slightly reduced light intensity when the fibre is farthest from the cantilever, which is at the top dead centre where the oscillating z-piezo is at the topmost vertical position. This is clearly evident in figure 4(a); the cyan excitation signal shows a reversal point at the image centre. The experimenter can then start to manually move the z-axis of the NanoMax stage towards the tip by using the differential screw. It becomes clear that some of the interference maxima and minima start to disappear as soon as the tip gets in contact with the sample surface since the amplitude of the oscillation is limited. The situation is apparent in figure 4(b): the tip is in contact with the sample for a contact time of about 200 ms; the interference maxima and minima disappear during that period and the signal flattens out. Since the length of the cantilever beam is 450 μm and the amplitude of the oscillation is not larger than 2 μm, there is no danger of destroying the tip due to its deflection whilst being in contact with the sample surface. In some measurements, the deflection can become much larger; we have successfully measured structures up to 10 μm. Of course, this procedure needs to be performed with care to avoid the destruction of the tip. Nevertheless, the differential screws allow a fine travel of 50 μm per revolution, so actually no tip has ever been destroyed during the engaging process by a school or university student. Our experience has shown that even school students can perform the above-described procedure without any problems. Doing so helps them to understand the measuring process; they are then able to interpret measurement results very confidently. Thus, this method is both easy to perform and is of great value for students’ understanding of the method. Once they understand this procedure, the whole principle becomes obvious to them.
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Figure 5. Topographical image of a CD surface (3D illustration).
3. Experiments 3.1. Topographical imaging
In a constant height mode, topographical images are obtained by scanning the sample surface and using the cantilever deflection at each scanned position directly as the height information. One disadvantage is that structures which exhibit height variations exceeding 158 nm deliver ambiguous signals (see section 2.1). However, the obtained images demand a very considered interpretation by students. In particular, school students tend to regard AFM images as photographic images, a misinterpretation which often happens when images are too ‘good’ or obvious. Our experience with students is that they get a good understanding of the AFM imaging method and find it very motivating to draw their own conclusions when analysing the results. Figure 5 shows a topographical image of a compact disc (CD) surface. The 3D illustration was created with ‘gwyddion’, free software for editing and analysing images obtained by scanning probe microscopy5. In the scanned area of 5 μm × 5 μm, several CD pits with a depth in a range of about 0.1 μm can be observed. Since the structure depth is below 158 nm, the image is not ambiguous. The figure shown is almost the raw image; some line artefacts were removed by software for this illustration and the greyscale values were replaced by colour coding. Students would also analyse the pit sizes and their distances—in an optical spectrometer experiment in our laboratory, they would have learned that a CD can be used as a diffraction grating due to its surface structure. Figure 6 shows the topography of an IC chip, taken from the AFM sample kit, provided by Nanosurf. The image is composed of 24 single images, each 20 μm × 20 μm. The images are partially overlapped to obtain a closer match. Some artefacts can be noted in this figure: a black–white transition is evident in the left-third of the composed image. This is an example of the above-mentioned ambiguity of the greyscale values when passing an interference maximum or minimum (see section 2.1). In the larger vertical structures, some typical probe artefacts can 5
http://gwyddion.net.
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Figure 6. Topographical image of an IC chip—composition of 24 single images.
(a)
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Figure 7. (a) Topographical image of a human red blood cell (erythrocyte), coloured by software.
(b) Light microscope image of erythrocytes.
be observed. Rectangular structures are rounded off due to the probe’s inherent geometry (the probe slides down sharp edges); some angles are not depicted correctly for the same reason and due to the limited penetration of the probe. These are standard probe artefacts and should not be discussed further. In figure 7(a), a human red blood cell (erythrocyte) can be seen. The experimenter ‘donated’ a drop of his own blood and let it dry out on a microscope glass slide. For comparison, figure 7(b) shows an image of some erythrocytes in our laboratory’s light microscope. The greyscale values of the AFM image were replaced by redscale values using software. Erythrocytes are doughnut-shaped cells. They are known to have a diameter of about 7.5 μm and a thickness of about 2 μm near the rim and 1 μm in the centre. The diameter can be verified
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Figure 8. Topographical image of a moth’s eye with a nanostructured surface.
in our AFM image, as can be seen from the scale bar. Looking more closely at figure 7(a), one can even spot the dent in the centre of the cell. However, the height of 1–2 μm entails the above-mentioned ambiguity: at the margin of the cell, alternating bright and dark red fringes are visible. The fringes are caused by exceeding the 158 nm limits several times, as explained above. Of course, one cannot obtain reliable information on the absolute height dimensions of the cell. In this case, it is even more difficult since the blood cells tend to appear in clusters and it is hardly possible for us to isolate a single erythrocyte. In addition, the cells can be viewed with a light microscope (see figure 7(b)). However, no information on the height of these cells can be obtained from this. Nevertheless, it is very fascinating for students to actually scan a human cell with an AFM and additionally compare this topographical image with an optical image of the object in the light microscope. Again, by analysing the image, students can learn a lot about the characteristics and difficulties of scanning probe imaging. Since erythrocytes are large enough to be observed in a light microscope, the students can directly compare the AFM topography image and the photographic image. A very intriguing sample with a biological background is a moth’s eye. A moth’s eye exhibits hexagonally arranged nanoscopic nodules. This structure causes a gradually changing refractive index and exhibits an anti-reflective surface which is mimicked for technical applications like solar cells or displays, e.g., by using electron beam etching [9]. Figure 8 shows a topographical image of a moth’s eye; a 4 μm × 4 μm area of the eye was scanned. The eye was cut out of a dead moth and glued to a glass slide with an adhesive. In the image, one can clearly see the small nodules; their lateral dimensions were measured with the gwyddion software and were found to be around 250 nm, which is consistent with the literature [9]. According to the software results, the height of the nodules would be around 10 nm; however, we consider this result to be too small since the penetration depth into the nodules is presumably limited by the cone shape of the used standard AFM tip. That is, the tip
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Figure 9. Schematic illustration of a force–distance curve.
cannot get into the crevices between the densely arranged nodules and the obtained height is underestimated, which is a typical probe artefact. In general, biological objects in the form of dead insects can be obtained very easily and make up highly interesting samples for the students. Besides the samples shown above, we have also examined the eyes of flies and wasps, butterfly wings, etc, that can be prepared on a glass slide and used as samples in an AFM laboratory course. It should be noted that, in the contact mode, the forces applied to a sample are of the order of 10–100 nN. If the sample is very soft, it needs to be considered that the tip can influence or change the sample surface. For example, we managed to push polystyrene microbeads across a glass slide with the tip. This can also be discussed with the students and can be regarded as another interesting educational topic, since there are research experiments where this is intended (e.g., [10]). If this effect is unwanted, one has to make sure to use more rigid samples which cannot be altered by the tip. Most sample materials which are used in our experiments, e.g. the above-mentioned samples, are not changed by the scanning procedure. 3.2. Force–distance curves
The force–distance curves obtained by AFMs disclose information on the interaction between the probe and the sample, such as adhesion forces and elastic properties described by the elastic modulus [11]. In general, adhesion forces include several forces, such as van der Waals forces, electrostatic and capillary forces. There are various models describing these forces which can be very complex [12] and they remain rather undetermined. Therefore, these forces do not possess much educational value and we will not discuss them further. However, the elastic modulus is an interesting quantity which is also a meaningful parameter on a macroscopic scale. Furthermore, via the force–distance curve, obtained results can be compared with the literature. In the following, we explain how the force–distance curves are attained. Figure 9 demonstrates how a force–distance curve is recorded: at first, the sample is moved towards the cantilever tip (1). At some specific distance, the tip snaps onto the sample due to attractive forces (snap-in) (2). Now, the tip is in contact with the sample while the sample is still moving
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Figure 10. Recording of a force–distance curve.
upwards (3), repulsive forces acting on it. Then, the sample is retracted (4) and the tip adheres to its surface as long as the adhesion forces are larger than the forces exerted by the cantilever. At this point, the tip is pulled off the sample and back into its equilibrium position (pull-off) (5). The snap-in and pull-off positions differ, as can be seen in figure 9 due to the acting adhesion forces. The recording of these curves with our setup is easy and works via a so-called z-scan function: at first, the tip is not in contact with the sample. The sample stage is oscillated in the z-direction via a piezo actuator which is controlled by the software. In figure 10, a screenshot of our AFM software can be seen. It shows the detector voltage representing the cantilever deflection signal plotted via the sample position in the z-direction, which can be calibrated by the respective piezo voltage. This first step mentioned above is represented by the red curve (1). The described paths and numbers coincide with the descriptions in figure 10. The stage is then moved upwards; in point (2), the snap-in position is reached and the sample gets in contact with the tip. We can see that, now, the tip follows the oscillating movements of the sample. The green path shows the backward direction; the stage is moved downwards (4). The pull-off position is reached at point (5); here, the tip loses contact with the sample and the cantilever is in its equilibrium position again; thus, the tip deflection is represented by a flat line (1). In this example, it can be conceived very clearly how the distance between snap-in and pull-off is obtained. After recording this curve, the data must be analysed. Since we intend to have our force– distance curves discussed by undergraduate students, we have chosen to use Sneddon’s model [13], which is based on continuum mechanics of contacts, to extract the elastic modulus from the data. It is usable for samples with small adhesion forces and it is rather easy to use on the measurements. In this model, the tip is considered to be non-deformable and the sample surface is considered as an infinitely extending elastic half-space [14]. The load force F of the cantilever on the sample surface is described by Hooke’s law: F = k · d,
(1)
where k is the cantilever spring constant and d its deflection. The load force causes a deformation of the sample surface by δ, which can be obtained from the force–distance curve
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Figure 11. Determination of δ via the z-scan function. Black curve: reference sample; blue curve:
sample of interest.
(see below). A calibration is performed via the known piezo voltage. Thus, the cantilever deflection d can be calculated from d = z − δ,
(2)
with z being the measured piezo deflection. δ is obtained as follows: a stiff sample is used as a reference (we use some ferrous alloy) and a z-scan is recorded as in figure 10. After that, the sample which we are interested in is scanned as well. Then, the widths of two peaks of both samples are compared; a peak is defined as the width from one zero crossing to the next in the z-scan curve and we call our sample’s peak z, as mentioned above. Since the stiff reference is less deformable than the sample, its peak is narrower than the sample peak. Then, δ is the difference between both peaks—it represents the sample deformation. Figure 11 demonstrates this: it shows two z-scan curves in one plot: the black curve is the stiff reference; the blue curve depicts an aluminium sample. The deformation δ is indicated by the red arrow. The cantilever tip can be regarded as a cone by approximation. Thus, the load force which depends on the deformation δ is described by E 2 · δ2, (3) Fcone = · tan(α) · π 1 − ν2 where α is the half-cone angle, E is the elastic modulus and ν is Poisson’s ratio [14]. With the above-mentioned relations, we obtain k · d · π · (1 − ν 2 ) . (4) E= 2 · tan(α) · δ 2 The spring constant k and the half-cone angle α can be taken from the cantilever data sheet; Poisson’s ratio is a material constant and must be looked up in the literature. By using these rather simple techniques and relations, undergraduate students are capable of performing these kinds of measurements and evaluations. First of all, it needs to be mentioned that the errors in these measurements are very large. They contain error components in k, d, α, δ and ν. Very large systematic errors arise from the inaccuracy of the spring constant’s absolute value, which can vary by 200% or even more. Even the cantilevers in one batch can possess different values for the spring constants. This is a well-known problem for AFM measurements and there are methods to determine the spring constant of each cantilever (e.g., [15]). However, this would go beyond the scope of our laboratory course sessions. A typical value of 0.2 N m−1 is given in the data sheet of our cantilevers; we used this for our calculations. Thus, it is impossible to obtain results with small errors when using fixed k-values. Since the cantilever was not changed during one
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test series, the corresponding results are comparable within this series, although statements about the absolute values are error-prone. Of course, there are also statistical errors from the measurement: δ can also exhibit errors of 100% or more; this can vary from day to day. We conjecture that air humidity causes unfavourable effects on the measurements (influence of capillary forces), as do slight vibrations of the building or electromagnetic interference from nearby laboratories. Again, one needs to make sure to perform each test series on the same day in order to minimize effects due to environmental disturbances. Our results can be summarized as follows. Our measured values of the modulus of soft matter samples like polymeric material (polyvinyl chloride, polyhydroxybutyrate) were found to be below about 5 GPa. For metallic samples (aluminium, steel, zinc), our obtained values were in the order of 100 GPa. Regarding the dimensions, these results are consistent with the literature. Due to the above-mentioned error sources, it is not possible to obtain accurate values; however, we can distinguish metallic samples from soft organic samples. This suggests that we have arrived at the limits of the method. Further technical extensions and expenditure could, of course, improve the performance of these measurements, e.g., measurement in vacuum could reduce errors due to environmental influences. On the other hand, the didactically advantageous simplicity and the low costs would then be lost. In our laboratory courses, we set a high value on discussing the difficulties of measuring delicate quantities on the nanometre scale. The students need to experience these difficulties and they should be able to evaluate and criticize their measurements. Although the results bear large errors, at least some conclusions on the mere dimensions of the tensile moduli can be drawn. In the end, it is highly fascinating to show the students that physical variables which they know from macroscopic testing (e.g., stress–strain experiments) can—although with certain difficulties—in principle be determined on a nanoscopic scale.
4. Conclusion
We have presented a low-cost atomic force microscope setup for educational purposes. The appeal of the setup lies in its plainness and simplicity, which makes it very easy to understand for secondary-school and undergraduate university students. The many possibilities for user manipulation enable the students to ‘play’ with the setup and gain a substantial understanding of the working principle. Topographical images can easily be recorded from very different samples: CD and DVD surface topographies can be investigated, as well as biological objects like insect eyes or blood cells. The setup is very robust and reliable, which reduces maintenance requirements. In the case of necessary repairs, however, parts can be changed easily and readjustment can be carried out speedily. Force–distance curves can also be recorded and the tensile modulus extracted. However, the errors are rather large and it is recommended to use soft material for these measurements. Nevertheless, the dimensions of the moduli can be determined and students can benefit from detailed discussions on the errors and problems. Although the force–distance measurements are rather suitable for university students, we have made positive experiences with secondary-school students performing topography images and their evaluation.
Acknowledgments
The authors would like to thank Michael Meyer and his staff from the departmental mechanics workshop for the manufacturing of the positioning stage attachment.
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