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Nano goes to school: a teachingmodel of the atomic forcemicroscopeGorazd Planinsic1 and Janez Kovac2

1 Faculty for Mathematics and Physics, University of Ljubljana and the House of Experiments,Ljubljana, Slovenia2 Institute Josef Stefan, Ljubljana, Slovenia

E-mail: gorazd.planinsic@fmf.uni-lj.si

AbstractThe paper describes a teaching model of the atomic force microscope (AFM),which proved to be successful in the role of an introduction to nanoscience inhigh school. The model can demonstrate the two modes of operation of theAFM (contact mode and oscillating mode) as well as some basic principlesthat limit the resolution of the method. It can be used either as ademonstration experiment, simple laboratory experiment or home experimentthat students can make by themselves.S This article has associated online supplementary files.

IntroductionNanotechnology is going to significantly changeour future. Some prognoses say that its impact onour lives will rival that brought about by the steamengine, electricity, the transistor, and the inter-net [1]. At the nanoscale (i.e. dimensions of atomsand molecules), macroscopic distinctions betweenmaterials, and even between scientific disciplines,cease to exist. As a result, nanoscience offers thepossibility of having diverse technologies and dif-ferent science disciplines which converge with acommon goal. Nanomaterials, with their amazingand unusual properties, are becoming ever morecommon in our everyday lives. For instance, sev-eral anti-ageing cosmetic products, antibacterialcoatings in refrigerators, and different coatings formaking stain-resistant textiles and furniture areproducts of nanotechnology, to name just few. Onthe other hand, it is becoming clear that nanomate-rials represent a great potential hazard to our health

and that our knowledge about how nanoscale par-ticles affect living organisms is very limited. Thisis all the more reason for including nanoscience ineducation at different levels. As reported recentlyby Tibor Gyalog, president of the Swiss Physi-cal Society [2], nanoscience education has becomepart of the curricula in several universities and highschools in Europe, where the major challenge forthe latter is re-education of high-school scienceteachers. Similar changes and activities are takingplace in the USA. For instance, at the Cornell Uni-versity Centre for Nanoscale Systems, the Institutefor Physics Teachers has been formed to upgradehigh-school teachers’ knowledge and understand-ing of recent developments in nanophysics [3].

Introducing nanoscience into schools requiresnew paradigms in education. Since sciencesubjects have a so-called pyramidal structure, wecannot simply remove some ‘older’ topics fromthe curricula and substitute them with the basics

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(a) (b)

Figure 1. AFM images: (a) AFM image of a surface topography of magnetic disk surface sensing the magneticinteraction. The image was acquired over an area of 20 μm × 20 μm with a tip coated with a magnetic thin film.(b) AFM image of the bacteria Staphylococcus aureus sensing van der Waals interaction. The image is shown in athree-dimensional view over an area of 2 μm × 2 μm. Both images were acquired in oscillating mode with theNT-MDT AFM microscope, model Solver PRO.

of nanoscience. Let us focus on physics in highschools. One way to deal with the problem isto identify specific topics from nanophysics (forinstance the description of an apparatus or method,or the characteristics of some special material) thatcan be satisfactorily explained and incorporatedwithin the existing curriculum. Such an examplemay require the students to use their knowledge ina new situation or can serve as an example to showhow in practice one has to apply knowledge fromdifferent topics or even from different scientificdisciplines at the same time. From here one candiscuss nanotechnology from other perspectives(health, social, economic, etc). An alternative isto combine the classes with some other subjects(such as biology, chemistry, philosophy, . . .) andmove the discussion there (several ideas for cross-curricular themes on nanoscience can be foundin [4]).

In the present paper a teaching model ofan atomic force microscope is presented, whichproved to be successful as an introduction tonanophysics for high-school students as well as forin-service physics teachers.

Atomic force microscopeNanoscale particles have existed in our environ-ment for millennia—for instance, as salt crystalsin ocean air or carbon in soot. But the inten-tional manufacture of nanoscale particles and the

exploration of their properties was only possibleafter special tools and methods had been devel-oped that enabled one to ‘see’ and manipulatethese particles. One of these local probe meth-ods, scanning tunnelling microscopy, was devel-oped by Gerd Binning and Heinrich Rohrer in theearly 1980s, for which they were awarded the No-bel Prize in 1986. The interaction probed in thescanning tunnelling microscope (STM) is the tun-nelling current between the probe and the sample,reflecting the strong distance-dependent probabil-ity of electron transport through a gap betweentwo conducting solids. A few years later, anotherscanning instrument was developed by Binning’sgroup, based on the short-range van der Waals in-teraction and called the atomic force microscope(AFM). Since no electron transport is involved inthe AFM method, both insulators and biologicalsamples can be investigated down to atomic res-olution. The information on topography, rough-ness, friction, adhesion, elastic properties, interac-tion between tip and sample surface, distributionsof electric field, magnetic field, resistivity, surfacepotential, etc can be obtained by the AFM withnanometre resolution (see figure 1).

In addition, a manipulation of the samplesurface can be performed by the tip of the AFMvia current or voltage nanolithography. Theability to perform the measurements in air, thereliable performance and the simple construction

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Nano goes to school: a teaching model of the atomic force microscope

of AFM instruments make an AFM standardinstrumentation in many laboratories.

The operation of the AFM is based oninteraction between a sharp tip supported on acantilever and atoms at the surface of the sample.Forces on the tip can be either attractive orrepulsive. The deflection of the tip due to a changeof a force is detected by the reflection of the laserbeam from the back of the cantilever.

There are two basic modes of operation ofthe AFM. In the contact mode, a tip is in closeproximity to the sample surface during scanningin the horizontal plane. This mode is most usefulfor imaging hard surfaces. In the oscillatingmode (also known as non-contact mode), the tipis oscillating along a vertical axis during scanningover a sample surface. The advantage of theoscillating mode is less damage to the surfacedue to the weaker interaction between the tip andthe surface, which makes the oscillating modeparticularly suited for imaging soft biologicalspecimens and carbon nanotubes. In addition, theAFM can probe the interaction between the tip andsurface, giving force–distance curves, obtainedby advancing and retracting the tip towards andaway from the surface at a chosen position.This information yields data on the size of theinteraction potential and its space dependence,that can be useful in research and applicationsof adhesion, wettability, colloidal interactions andmore. For more information on the basics of theSTM and AFM methods see the excellent textbookwritten by Mironov, which is also available on-line [5].

It should be mentioned that in practice theAFM often works in a slightly different way thandescribed above. The holder of the cantilever,while scanning over the surface, is moved up anddown so that the force acting on the tip (andtherefore the deflection of the tip) is kept constant.This is done by correcting the vertical position ofthe holder so that the spot of the reflected laserbeam is kept in a constant position. The shapeof the sample surface is reconstructed from themovements of the holder. Though this approach(known as feedback control) is very importantfrom the technical point of view, it is not essentialfor understanding the basics of the AFM operationat high-school level, and will be ignored in thispaper.

Teaching model of the AFMThe operation of the AFM relies on a few basicphysics principles that make it a suitable topicto be discussed in secondary-school physics or inintroductory physics courses. This also makes theAFM useful for modelling simple experiments thatoffer students hands-on experience and stimulateanalogical transfer. One version of such amodel, which demonstrates the resolution limit ofscanning methods, is available commercially as akit [6].

The model AFM described in this paperdemonstrates the two basic modes used inthe operation of a real AFM: contact modeand oscillation mode. The model combinesthe following topics that are essential forunderstanding the operation of a real AFM andare usually covered in school physics curricula:Hooke’s law, forced oscillation, resonance and thelaw of reflection.

It is important to note a difference betweenour model of an AFM and a real AFM microscope.In our case a magnetic force is the onlysource of interaction between the sample and themicroscope, whereas in the real AFM microscopethe van der Waals force is more often employedthan a magnetic force.

Our main goals in designing this model werethat it can easily be built by teachers or studentsand that it can demonstrate the basics of AFMdetection in a short enough time to be suitable forlecture demonstrations.

Contact mode

In contact mode the sample is systematicallymoved line by line below the cantilever, which(according to Hooke’s law) deflects under theforces that act between the tip and the sample.Deflections of the cantilever reveal the corrugationof the sample surface as well as information aboutthe interactive forces.

To make a model of an AFM that works incontact mode you will need the materials that areshown in figure 2(a). The assembled device isshown in figure 2(b).

Our body of the AFM model is made fromLego blocks. The cantilever is cut from a usedcompact disc (CD), which combines the propertiesof good elasticity and optical reflectivity. Use thepart of the disc that has no printing on the uppersurface and fix it on the Lego block with the data

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surface facing downwards (the reflection from theupper surface of the CD is clearer than from thedata surface, which is protected with a transparentplastic layer). Use a strong neodymium magnet(NIB) for the tip. We used a cylindrical magnetof 14 mm diameter and 5 mm height so that thesize of the magnet (i.e. tip) is comparable with thesize of the ‘atoms’ (see next paragraph). Glue themagnet to the lower surface of the cantilever, asseen in figure 2(b). Use the laser pointer as thelight source. Fix the laser to the Lego blocks withplasticine. Adjust the laser to a position so that thebeam strikes the free end of the cantilever at thereflective part of its surface. The softness of theplasticine allows you to make a fine adjustment ofthe laser.

Now you need to make a sample with asuitable ‘atomic landscape’. In our model onlya single line of ‘atoms’ is used and scanned inorder to make the experiment suitable for lecturedemonstrations. We also believe that at schoollevel all important features of scanning methodscan be shown by observing and studying linescans and that once students understand this theextension to a surface scan can be explainedrelatively quickly, for instance by using computersimulations. The metallic bottle caps provedto be perfect ‘atoms’ that respond to magneticinteraction, and plastic bottle caps are used for the‘atoms’ that do not respond (we also tried othertypes of samples as described briefly in3). Thecompleted sample with an ‘atomic structure’ usedin our experiments is shown in figure 2(c). Beforedesigning your sample, think what characteristicsof the method you would like to demonstrate and

3 In our first attempts to design a suitable atomic landscapewe tested differently oriented permanent magnets glued alongthe line on a plastic ruler. The advantage of this version isthat you can show both the attractive and repulsive interactionbetween the sample and the tip. However, we soon realized thatat an introductory level one character of the force is enoughto show the basic features of the method, and so we decidedto use samples made from iron (ferromagnetic material). Onepossibility is to use an iron strip (we used a 1 mm thick, 2 cmwide strip from soft iron) shaped to mimic the corrugationof the ‘atomic landscape’. Since the magnetic force betweenthe magnet and the iron changes very rapidly with distance,the variations of the sample height and positioning of thesample below the magnet are critical. A metal strip of themeasurements given above can be bent with pliers, but it is notvery easy to shape the strip into a predefined form. In addition,the real atomic surface is rather a discrete structure than acontinuous surface, so the iron strip sample is questionable alsofrom the teaching point of view.

do not forget to take into account the dimensionsof the magnet (see Appendix A. ‘Resolution’). Themodel of an AFM is ready to be tested. Place thedevice in front of a wall or white board, about 2 mfrom the wall, and switch on the laser. Put thesample on the table with one side of the sampleunder the magnet. Use a clothes peg to keep theswitch on the laser in the ON position for a longertime. WARNING: make sure that the laser beam orreflected beam is kept away from students, beforeyou switch on the laser! Fix a piece of paper withprinted parallel lines (about 20 lines with 5 mmseparation is adequate) on the wall so that thereflected laser beam will make a spot at the upperend of the scale. Make a zero mark at the upperline with values increasing downwards. Now, asyou slowly move the sample perpendicularly tothe cantilever the light spot on the screen shouldmove up and down (in our design the maximumshift of the spot on the wall was about 22 cm).Once you are sure that the AFM model works, youcan design a laboratory for students in which theymake systematic measurements of the samples.This is best done in groups of three to four. Thefirst student moves the sample in steps of 5 mm,the second student reads off the positions of thelight spot on the wall and the third student recordsthe data. When all the data are collected, themeasured shape of the surface has to be comparedwith the shape of the sample. This can bedone simply by preparing in advance laboratorysheets with a photograph of the side view of thesample and with a coordinate system plotted overit (leaving an arbitrary vertical scale). Students areasked to plot the measured points in the coordinatesystem and discuss the similarities and differencesbetween the original and the measured shapes (seefigure 3).

Even this very simple representation containsenough to show some basic limitations of themethod (see also Appendix A. ‘Resolution’). Forinstance, it is clearly seen that the gap betweenthe second cap and the third cap appears to beshallower than the gap between the first cap andthe second cap. Note also that the heights ofthe second cap and the third cap appear highercompared to the height of the other metal caps.This is probably because of a small misalignmentof the caps with respect to the line of scanning.

If time permits, one can go further and show,or give as a homework problem, how to calculate

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Nano goes to school: a teaching model of the atomic force microscope

(a) (b)

(c)

Figure 2. (a) Basic material needed to build an AFM model (from top left to bottom right): adhesive tape, Legoblocks, a strip cut from a used CD, plasticine, a strong magnet, a laser pointer and a clothes peg. (b) An AFMmodel during operation in contact mode. (c) Sample of an ‘atomic landscape’ made from bottle caps. Four caps aremade from ferromagnetic metal and one from plastic. Note that the separations between the caps are not equal.

tip movements from the measured positions of thelight spot on the wall, knowing the length of thecantilever and the distance from the tip to the wall.

Oscillating mode

In the oscillating mode the cantilever is driven witha sinusoidal excitation force at constant frequency.The frequency is adjusted to be close to resonantfrequency when no sample is in the vicinity ofthe tip (in our case the resonant frequency was14.6 Hz, and the time in which the amplitudedropped to about one third of the initial value wasabout 1 s). If the sample is now brought near to thetip the interactive forces between the tip and thesample will have the same effect as if the stiffnessof the cantilever had changed. This in turn willchange the resonant frequency of the cantilever,

resulting in a decrease of the oscillating amplitude(note that the excitation frequency is the same allthe time). In this case the changes in amplitude ofthe cantilever (and also its phase with respect to thedriving force) reveal the variation of the interactiveforce gradient (dF/dz) along the sample surface.See Appendix B. ‘Change of the resonance’ for anadditional explanation.

To make your AFM model described in theprevious paragraph work in the oscillating mode,you will need to add a small coil and obtain a sinegenerator (a conventional school sine generatorwith 50 � output impedance and the ability toadjust voltage frequency to within 0.1 Hz or betterwill do). The idea is to place the coil close abovethe magnet and drive the cantilever in resonanceby adjusting the frequency of the current in the

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Figure 3. Laboratory sheet: graphical presentation of the measurements obtained in the contact mode and originalsample. The positions of the light spot on the wall (vertical axes) are measured in arbitrary units. The presenteddata were obtained in less than 5 min.

(a) (b)

Figure 4. AFM model for operation in the oscillating mode: (a) coil for driving the cantilever (windings areprotected with thermo-shrink tube); (b) AFM model during operation in the oscillating mode.

coil. We made our coil by winding 100 turns of0.2 mm thick lacquered copper wire on a rubberstopper (with a diameter of about 15 mm). Theholder for the coil is made from 3 mm copperwire, with its ends inserted into two brass tubesthat are glued onto one of the Lego blocks. Thisdesign allows one to switch easily between thecontact and oscillating mode design. The coil witha holder is shown in figure 4(a), and the assembledmodel during the operation in oscillating mode infigure 4(b).

When working in the oscillating mode youhave to first adjust the frequency and the amplitude

of the current in the coil so that the cantilever(without a sample underneath) is in resonance, butalso so that the trace of the reflected laser light onthe wall is of suitable length (about 40 cm in ourcase). When this is done, place the sample underthe cantilever. The amplitude of the oscillatingspot should decrease (the decrease is also partlydue to higher damping caused by eddy currents inthe caps, but the dominant effect comes from theshift of the resonance). Then move the samplestep by step, as in the previous experiment, andeach time measure with a large ruler the lengthof the trace (i.e. peak-to-peak amplitude) of the

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Nano goes to school: a teaching model of the atomic force microscope

Figure 5. Laboratory sheet: graphical presentation of the measurements obtained in the oscillating mode comparedwith the original sample. The vertical coordinates of the points (given in arbitrary units) correspond to theamplitudes of the oscillating light spot on the wall and were all subtracted from the largest measured value.

oscillating light spot on the wall. As in theprevious case, the measuring procedure is quickerif performed as a group activity.

When all the data are collected, the measuredamplitude variation can be compared with thevariation of the shape of the sample. Again, thiscan be done by plotting the measured values inthe prepared laboratory sheets. Since the largestprotrusions in the sample will produce the smallestamplitudes, the measured shape in this case willappear upside-down. The upright shape can beobtained by subtracting the measured values fromthe largest measured value (figure 5).

Since in this experiment the interactive forceis of the same character all the time (i.e. attractiveforce between the magnet and induced magneticdipole in the ferromagnetic caps), the oscillatingmode measurements give a similar shape to thecontact mode.

The measurements described above andpresented in figures 3 and 5 can also be performedby a single student using a digital camera. For eachmeasured point a photograph of the spot on thewall is taken from a fixed position with a digitalcamera. From the sequence of photographs thecoordinates of the spots (or lengths of the traces)can easily be measured using one of the programsfor analysing digital images (we used freewareImageJ [7]).

An interesting additional experiment can beshown with the model that works in oscillating

mode. Place a permanent magnet below thecantilever, so that you can switch betweenattractive and repulsive forces simply by turningthe magnet around. If you now search forthe resonant frequency of the cantilever in threedifferent situations (without the magnet belowthe tip, with a magnet in repulsion, and withthe magnet in attraction) you will find thatthe measured values agree qualitatively with theprediction given in the Appendix B. ‘Changeof the resonance’. In our case the cantileverresonant frequency was 15.1 Hz; when the magnetin attraction was added the resonant frequencydecreased to 14.3 Hz, and when the magnet inrepulsion was added it increased to 15.7 Hz. Thecantilever when in rest was about 45 mm above theplane of the lower magnets.

Acknowledgment

The authors wish to thank Giacomo Torzo fromthe University of Padua for valuable comments andsuggestions.

Appendix A. ResolutionOne of the most important factors influencingthe resolution of an AFM is the sharpness ofthe scanning tip. In the simplest approximationwe can imagine the tip as a wheel of radius Rrolling over the surface (figure A.1) (in practicethe effective radius is somewhat larger than the tip

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G Planinsic and J Kovac

radius). When the tip moves over the protrusionthe tip centre circumscribes the shape, whichis wider than the protrusion, but when the tipmoves over the depression the shape is narrowerthan the depression. Note also that depressionswith a width smaller than the tip diameter willappear shallower than they are. These effectsare sometimes described as tip convolution. Inpractice the resolution is also determined by thesensitivity of the height detector. The best tipstoday may have a radius of curvature of onlyaround 5 nm.

Appendix B. Change of the resonance

The cantilever and the tip make an oscillator(similar to a mass hanging on a spring), whichhas a characteristic resonance frequency ν0. Forsmall deflections of the cantilever the force–deflection dependence is linear (Hooke’s law) andcan be qualitatively presented with the graph infigure B.1. The slope of the line in the force–deflection graph is equal to the spring constant ofthe system k, which also determines the resonant

frequency if the mass is kept fixed (ν0 = 12π

√km ).

The stiffer the cantilever, the higher the resonantfrequency.

If in addition to the spring force anattractive/repulsive force acts on the tip, this willresult in an apparent change in the cantileverstiffness (i.e. a change in the slope of theforce–deflection graph) and consequently in thedecrease/increase of the resonant frequency. Theeffect of additional forces is shown and explainedin figure B.1, where effective spring constants have

been expressed using a linear approximation forattractive/repulsive forces near x = 0. Notethat no particular forms for the attractive/repulsiveforce have been assumed, only the sign and the factthat both forces have to vanish if we move awayfrom the sample. Note also that the additionalforce changes the equilibrium position of thecantilever (i.e. the position where Ftot = 0).

Using a linear force–distance dependence asdescribed in figure B.1, the change in resonantfrequency can be expressed in the following way:

ν = 1

2π

√keff

m= 1

2π

√k + k ′

m≈ ν0

(1 + k ′

2k

),

where ν0 is the resonant frequency when nosample is present. In the case of a repulsive forcek ′ = kR and ν > ν0, while in the case of anattractive force k ′ = −kA and ν < ν0.

The teaching model of AFM has beentested by the group of 30 physics teachersas one of the activities during the workshop

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Nano goes to school: a teaching model of the atomic force microscope

‘Nano goes to school’ held at the GIREP-EPECconference in Opatija, Croatia in August thisyear. The response from teachers was verypositive. The worksheet for student experimentalactivity based on the AFM model is available atstacks.iop.org/physed/43/37.

Received 13 June 2007, in final form 1 August 2007doi:10.1088/0031-9120/43/01/002

References

[1] Shand H and Wetter K K 2006 Shrinking science:an introduction to nanotechnology State of theWorld 2006, A Worldwatch Institute Report onProgress Toward a Sustainable Society (NewYork: W W Norton) p 78

[2] Gyalog T 2007 Nanoscience education in EuropeEurophys. News 38 13, also available online athttp://www.europhysicsnews.org

[3] Home page of Institute for Physics Teachers,Centre for Nanoscale Systems, CornelUniversity http://www.cns.cornell.edu/cipt/index.html see ‘Resources’ for useful materialfor teachers!

[4] Drexler K E 2005 Productive nanosystems: thephysics of molecular fabrication Phys. Educ.40 339

[5] Mironov V L 2004 Fundamentals of the scanningprobe microscopy, the Russian Academy of

Sciences, Institute of physics of microstructures(Nizhniy Novgorod 2004) also available onlineat http://www.nanotech-america.com/dmdocuments/mironov book en.pdf

[6] West Hill Biological Resources, Inc. www.westhillbio.com (see also [4] for laboratoryexercise with AFM kit)

[7] Program ImageJ for analysing digital images canbe downloaded from http://rsb.info.nih.gov/ij/

Gorazd Planinsic is associate professorat the Faculty for Mathematics andPhysics, University of Ljubljana, wherehe leads the Physics Education course.He also leads the Continuing Educationprogramme for in-servicesecondary-school physics teachers inSlovenia. His fields of interest are thedevelopment of new demonstrations andlaboratory experiments as part of newteaching methods. GP is co-founder andcollaborator of the Slovenian hands-onscience centre, The House ofExperiments.

Dr Janez Kovac is a senior researchassociate at the Jozef Stefan Institute inthe Department of Surface Engineeringand Optoelectronics, Ljubljana, Slovenia.His fields of interest are studies ofphenomena on surfaces at interfaces inthin-film structures of solid materials anddevelopment of new analyticaltechniques.

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