kneuhaus lab3 tip char

BSc (Hons) in Physics & InstrumentationLaboratory Practical

LAB3: AFM Tip Characterisation

Kai NeuhausCo-Worker: Sung Yan

GMITGalway Mayo Institute of Technology

Lecturer: Jim McComb

December 1, 2011

Abstract

The tip of a probe from an atomic force microscope (AFM) is characterisedby different methods. Characterisation of the tip of AFM’s is required to assureshape consistency of the expected topography to be scanned and also to obtainreliable results for measurements and resolution. The first method is the AFM it-self (Burleigh) and the second method uses an scanning electron microscope (SEM)(Leica S340). The material composition is characterised by X-ray refraction flu-orescence spectroscopy and confirms the material of the probe-tip to be Si. Thetip’s geometry is measured with the SEM and the values are used to compare theshapes that are produced by the AFM scan on a calibration grid (grid-spacing16000nm, grid-height 200nm). The probe measured within the SEM was sepa-rately prepared compared to the probe used in the AFM and deviation betweenthe probe geometries were found. The tip radius was found to be 800nm accordingto SEM measurements and about 500nm according to geometrical analysis of thescan images of the scans of the calibration grid with the AFM. Those values do notagree with the value stated in the specification sheet, that claim a tip radius to besmaller than 10nm. It is shown that the tip characteristics determine significantlythe scan image of an AFM scan and must be taken into account.

1


Contents

1 Introduction 3

2 Technical Equipment 42.1 AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Principle Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Controller Adjustments . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 SEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 XRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Sputter Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Discussion Graphical Post Processing and Measuring 6

4 Tip Characterisation 84.1 Geometrical Effects of Tip . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Spring Constant and its Effects . . . . . . . . . . . . . . . . . . . . . . . 94.3 Estimation of Tip Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.4 Material Composition using XRF . . . . . . . . . . . . . . . . . . . . . . 10

5 Conclusion 12

6 Appendix 14

A Correction of bottom length for Spherical Tip 14

B Determination of Spring Constant 15

C Tip Specifications 17C.1 MicroMash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17C.2 Burleigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

D AFM Measurements 19D.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19D.2 Slope Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20D.3 Tip Radius Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

E SEM Measurements 23E.1 Tip Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23E.2 Tip Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24E.3 Lever Geometry, Length and Thickness . . . . . . . . . . . . . . . . . . . 25E.4 Tip Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

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1 Introduction

Tip characterisation of atomic force microscopes (AFM) is essential to assure accuratemeasurements and shape consistency of the features to be scanned. The spring constantof the lever, were the tip is located on, determines the force the tip will exert on thesample as well as the resonance frequency. The resonance frequency may be of interestto determine the maximum scanning speeds and delay times to avoid oscillation of thetip during scanning. Depending on the material of interest, the actual force should beestimated to assure no deformation of the sample due to the tip. The radius of the tipwill restrict the maximum resolution that can be achieved.

This report describes the characterisation of the tip for an atomic force microscope (AFM)from Burleigh Instruments, Inc. and the techniques applied to obtain all importantparameters of the tip and how the tip shape is affecting the image produced by the AFM.

Important parameters for the tip characterisation are the tip shape, height and the tipradius, as well as the material and the properties of the lever the tip is located on. Theproperties of the lever are its geometrical dimensions and its spring constant.

To characterize the tip shape with the AFM a calibration grid (grid spacing 16µm, height0.2µm) is used and the resulting image is evaluated.

The tip shape was further investigated with an scanning electron microscope (SEM)from LEO Electron Microscopy Ltd. and measured. The properties of the material wereevaluated by X-Ray refraction on the same SEM.

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2 Technical Equipment

2.1 AFM

2.1.1 Principle Setup

To obtain scanning images an Burleigh atomic force microscope (AFM) (Burleigh Instru-ments, 1997) was operated in topographic mode together with an calibration grid with aspacing of 1600nm and height of the grid-lines of 200nm.

The scan images were taken at different magnification and image processing was per-formed depending on the requirements until an sufficient picture for post processing wasobtained subsection D.2.

A calibration was performed according to the assumed values of the calibration gridsubsection D.1.

The AFM supplies a scan range of about 70µm in x and y, and in z of about 6µm. For azoom factor of 2 that was used for the final images, the maximum visible range becomes35x35µm. In the pictures this range appears even smaller due to the modified scan limits(590000A) according to the correction factor.

The calibration for the z-values was performed by averaging over all z-values and settingthe average equal to the assumed height of the grid (200nm).

2.1.2 Controller Adjustments

The scans were consistently preformed with an reference force according to 5V. Duringsome trial scans the integral, differential and gain controls were adjusted until an sufficientimage could be obtained.

According to the manual (Burleigh Instruments, 1997) the integral gain determines howthe controller follows the over-all shape of the sample. The differential gain determineshow sensitive the controller reacts on shape changes (z).

Apparently the gain appeared to have the largest effect in improving the image quality.

Some further adjustments were performed according to the scanner delays to even improveimage quality to avoid oscillation of the tip.

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2.2 SEM

Investigating the tip geometry was done with an scanning electron microscope from Leica(Leica S430 Stereoscope).

A second tip was prepared, besides of the tip used in the AFM, by coating it with goldof about a 15nm layer by a sputter process.

As the tip may be different compared to the tip in the AFM, the characterisation maynot produce necessarily conclusive results.

2.3 XRF

The x-ray refraction fluorescence (XRF) scanning was used to determine the materialcomposition of the tip. This investigation was done equally with the SEM and an attachedsolid state detector cooled with liquid nitrogen. The solid state detector was countingthe amount of the x-rays of different energies and the energy values were processed by asoftware plotting the energy spectrum (subsection 4.4).

2.4 Sputter Coating

One AFM tip was prepared with a gold coating of about 15nm thickness by a sputtercoater to be able to use it for the SEM.

The tip was processed for about 1min at a pressure of about 1 · 10−1mbar or 10Pa.

It is to expect that the probe may have assembled a certain amount of dust on its tipthat becomes fixated and may alter the tip radius visible in the SEM.

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3 Discussion Graphical Post Processing and Measur-

ing

The measurements of the calibration grid on the AFM were performed with the systemsoftware and the the pictures of the cross sectional geometry were stored without the useof cursors for measurements.

It was anticipated to preserve a rather pristine picture to be able to do measurements onthe pictures directly.

To assure the accuracy is preserved an estimation of possible errors is discussed in thischapter.

Some graphically measurements were performed in Figure 1.

194.54nm / 50.250mm

abc

d

Figure 1: AFM Cross Section Plot of Calibration Grid. Four distances (a,b,c,d) wheremeasured graphically and compared to the known distance measured by the system soft-ware (Bearing Level = 150.88nm).

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To calibrate the graphical tool (Inkscape., 2011) the total height of the measure box(195.54nm− 53.58nm = 141.96nm was determined and equalled to the measured lengthwith Inkscape. (50.250mm).

factorcal =141.96nm

50.250mm= 2.825nm/mm (1)

To obtain the measuring values for the real heights on the graph

height = factorcal · length + 53.58nm (2)

lengthmm

heightnm

a 34.445 150.89

b 34.463 150.94

c 34.451 150.91

d 34.437 150.87

mean 150.90

std 0.03

Table 1: Measured Values a,b,c,d

The mean value of the heights results in h = 150.90 ± 0.03nm. Comparing this to themeasured height directly measured (150.88nm) this is an percentage deviation of 0.1%.

To support further the precision that can be achieved with post-graphically processingthe subsequent figure Figure 2 is shown here.

Figure 2: High zoom level for accurate positioning of measure bars in Inkscape. Thegreen bar is the lower line at 53.58nm (see Figure 1)

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4 Tip Characterisation

4.1 Geometrical Effects of Tip

h=0.2µm

D = 5µm

16µm

spherical tip on the edgemoving into the groove

image to expect due tothe spherical tip

R R

RR = D

2

Figure 3: Spherical tip shape and expected image produced. The dimensions of the gridheight compared of the tip diameter are distorted and the resulting image would have aneven shallower edge.

The correct size of the bottom should be calculated with Equation 4.

dl =√R2 − (R− h)2 see Appendix A (3)

L = l + 2dl (4)

h=0.2µm

16µm

60◦30◦

asymmetrical pyramidal tip

possible picture to be obtainedby a scan with pyramidal tip

30◦ 60◦

Figure 4: Asymmetric pyramidal tip shape and expected image produced. The dimen-sions of the grid height compared of the tip diameter are distorted and the resultingimage would have an even shallower edge.

The actual size of the bottom should then be calculated with Equation 5.

L = l +h

tan(30◦)+

h

tan(60◦)(5)

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4.2 Spring Constant and its Effects

The spring constant describes the stiffness of the lever where the tip is attached on.During contact mode a certain force is asserted onto the tip and subsequently the lever isdeflected. The deflection creates an angular turning of the tip. This angular displacementwould also be visible within the scan-picture depending on its size.

The spring constant is given according to Appendix C as 0.12Nm−1. No particular forcecalibration was performed but according to Nanoscience Instruments about 10−12N areto expect. Thus a deviation can be estimated according to Equation 8 (Hooke’s Law).

F = kx (6)

x =F

k(7)

x =10−12N

0.12Nm−1= 8.3 · 10−11m = 83.3pm (8)

x

t

l Θ

Figure 5: Displacement of the tip caused by the contact force.

According to Appendix C the lever length l is 290µm ± 5nm (compare with Figure 16295.68µm in Appendix E.3). A deviation of 83.3pm causes by the contact force of 10−12Nwould cause the tip to turn according to Equation 9.

Θ = atan(x

l) = atan

(83.3pm

290µm

)= 0.000016◦ (9)

Though, Rabke suggests possible forces of 10 · 10−9N (Rabke, 1998) then the angulardisplacement would increase to 0.016◦. These angular displacements due to the contactforce appear very small and it is questionable if they are observable within the image atall.

Further estimations according to the spring constant are shown in Appendix B.

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4.3 Estimation of Tip Radius

The tip radius is stated by the specification Appendix C as smaller than 10nm.

An estimation of the tip radius was performed by the use of the scan images subsection D.3and compared with the shape obtained with the SEM subsection E.4.

The values obtained with the AFM are about 525nm for the tip radius and the valueobtained with the SEM is about 800nm for the tip radius.

Though, both values are far too large to be comparable with 10nm as stated in thespecification, they express some indication that the size may be that large as measured.Different effects may cause a larger tip radius, like dust particles accumulating on the tipdue to electrostatic forces and wear and tear breaking off fractions of the tip.

The tips investigated in the SEM and the AFM were actually different tips and largerdifferences between the measured values were to expect.

The source and the use of the tip measured in the SEM was not known but for the tip ofthe AFM it can be assumed it was already heavily used by different students before.

4.4 Material Composition using XRF

The results of the XRF scan are shown in Figure 6.

The largest peak occurs for silicon (Si) as it was to expect, as the the tip was supposedto be composed out of silicon nitride according to the spec-sheet (Figure 10).

A small signal can be found for aluminium (Al) as it was the material of the holder butalso the the material of the reflective coating on the cantilever.

Another signal for gold (Au) can be found besides of niobium (Nb). Though, a signal forgold could be expected due to the gold coating, it is usually not visible as the layer of thegold is to thin and no intearction with the electrons occurs to produce any X-rays. Thesignal for the gold is also not perfectly unique, as the tip of the signal resides betweengold and niobium. However, the existence of niobium itself can only be explained due tosome contamination.

Also the easiest explanation for the peaks for carbon (C), silver (Ag) and cadmium (Cd)are possible contamination effects.

The contamination theory is supported by another scan slightly besides from the top ofthe tip as most of the peculiar peaks disappear (Figure 7).

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Figure 6: XRF scan directly on top of the tip.

Figure 7: XRF scan of the tip’s side.

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5 Conclusion

Though, the preparation were restricted to two different probe samples, one for theAFM and one for the SEM investigations, introducing unknown differences, some basicproperties of the shape of the tip of an AFM could be shown.

The results of the slope obtained from the AFM scans (0.45 and 0.37) and the slopeobtained from the tip’s aspect ratio (3.28) measured do not agree. This can be explainedin accordance with the large tip radius that was estimated with about 800nm (see sub-section E.4). Considering, that the grid height is only 200nm then the tip radius issignificant for creating the slope. An estimation how the slope would occur with an tipradius of 800nm resulted in a value of 0.882. This agrees much better with the obtainedvalues from the AFM (0.45 and 0.37) and may confirm partially the large tip radius.

The difference between the values of the slopes obtain from tha AFM may be explainedby the calibration grid not perfectly leveled within the x-y-plane of the AFM scan range.According to the values in Appendix D.2 the tild angle would be about 4◦.

However, it is also conceivable, that the tip is tilded during scan due to frictional forces.

The large radius of the tip was a bit of an concern, if one assumes the tip prepared forthe SEM was an unused tip. But this assumption may be unfounded. However, the largevalues for the tip radius compared to the radius stated in the spec sheet (10nm) do notconcur at all (Appendix C.1)

Though, the SEM can achieve a theoretical resolution of 0.5nm it can be assumed theresolution is restricted further by the adjustments of the apertures and the spot sizeis much larger than 0.5nm. Also the resolution of the SEM is restricted due to theinteraction volume. The very end of the tip may well not be visible at all if it does notgenerate any secondary electrons.

The tip radius was also estimated by the radius of the upper edge of the grid slope inthe AFM images and resulted in an average value of about 525nm (subsection E.4). Thisappears also to confirm the relative large tip radius against all other expectations.

The spring constant was only compared alone by geometrical means and material proper-ties. Using the measured geometry data of the lever (Appendix E.4) a spring constant kwith a value of 16N/m can be obtained (Appendix B). This value does not agree with thevalues of the specification in Appendix C.1. Though, if adjusting the thickness to 1µma value for the spring constant becomes 0.02N/m - much closer to the expected values,with Equation 16.

As mentioned in Appendix B it appears as if the tip is somehow different to that of thespecification sheet and this would easily explain all kinds of differences between measuredvalues and expected values.

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However, the measured radii occurring in the AFM images compared to the estimatedtip radius of the SEM image appear to concur to some degree.

Further more do the scan images of the AFM show significant shapes that are to expectwith a tip and a large tip radius.

In general can be assumed, that it is possible to compare the tip of an AFM probe withmeasurements of its SEM image, if one uses one and the same probe and can accessreliable specification sheets describing the parameter of the probe.

It is shown that the characteristics of the probe-tip of an AFM contribute significantlyto the resulting scan image and must be taken into account if one wants reliable resultsfrom an AFM scan.

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6 Appendix

A Correction of bottom length for Spherical Tip

hl

R

L

u

R = u+ h (10)

u = R− h (11)

R2 = l2 + u2 (12)

l2 = R2 − u2 (13)

l =√R2 − u2 (14)

substitute u by Equation 11

l =√R2 − (R− h)2 (15)

Figure 8: Deduction for spherical tip

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B Determination of Spring Constant

The spring constant can be determined by applying different forces to the lever and recordits deviation from zero according to such forces. Then the spring constant is the slope ofthe resulting curve.

Such a curve could be obtained with the force calibration curve Figure 9.

However, depending on the start situation one would have to calibrate for force measure-ments for each sample. If the spring constant would be unknown, then it would be fairlyimpossible to calibrate and to measure any force at all.

Another way would be to use the cantilevers geometric parameters and the E modulusto estimate the spring constant before hand (Equation 16).

Figure 9: Force Calibration Curve Example.

According to Ying, Reitsma and Gates the spring constant can be calculated with Equa-tion 16, where k is the spring constant, E the Young’s modulus, t the thickness of thelever, w the width of the lever and L the length.

k =Ewt3

4L3(16)

MikroMasch states the E with 1.69∗1011N/m2 (in 〈110〉 direction). The lever is a structurecomprised by a triangular arrangement of two levers (see Figure 16). The length, width

Kai Neuhaus 15/ 27


and thickness was measured with the SEM as L = 430µm,w = 30µm, t = 8µm. Theuncertainty of the values was estimated as ±0.1µm.

To approximate the triangular arrangement to one single lever the width was taken twiceinto account with w = 60µm.

k =3 · 169 ∗ 109N/m2 · 60µm · (8µm)3

4 · (430µm)3= 16N/m (17)

The spring constant stated in the specification is 0.12 N/m typically (0.30 N/m max).

The estimated value does not concur with the value of the specification (Appendix C.1).

A possible explanation for the large discrepancy may be that the tip is not the tipaccording to the spec-sheet Appendix C.1. Because another specification sheet from themanual of the AFM offers different values (Appendix C.2) for the thickness of the lever(1µm). Otherwise it is indeed difficult to explain the discrepancy alone by errors madeduring the measurement with the SEM.

Other reasons might be, that the E modulus is dependent of the direction of the latticestructure of silicon and the applied calculation do not account for the direction here,because there was no reliable way to determine it.

Using the value for the thickness of the lever from the specification sheet (Appendix C.2)that states a typical thickness with t = 1µm, the subsequent value for the spring constantbecomes 0.02 N/m.

This confirms also the large effect the thickness contributes to the variation of the springconstant.

Deviations of the length of the lever account with an exponent of 3. Though, the effectis not large enough to compensate for the deviation that are caused by the measuredthickness of 8µm.

There is a good reason to believe that the available probe tips are not according thosestated in the specification sheet. The manual supplies a second type of tips subsection C.2with a cantilever thickness of 7µm that would concur much better with the measurementresults of the SEM.

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C Tip Specifications

C.1 MicroMash

Figure 10: Tip Specification Sheet

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C.2 Burleigh

Table 2: Tip Specification according to the Burleigh Manual.

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D AFM Measurements

D.1 Calibration

Figure 11: Calibration for Zoom 2x horizontal

spacing / nm16408.316629.416762.1mean 16603.3std ±146.7 (0.9%)

Table 3: Grid spacing measured for 2x zoom and correction factor

The uncertainty introduced by the correction factor appears insignificant compared tothe expected uncertainty of the slope values. Assuming a grid spacing of 16000nm andthe avearge measured grid spacing of 16603.3nm a correction factor was calculated as16000.016603.3

= 0.963664.

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D.2 Slope Measurements

Figure 12: Measured slopes. Zoom 2X, Plane removal.

dX1/nm dX1(corr)/nm dX2/nm dX2(corr)/nm492.0100 474.1323 481.4300 463.9368227.4900* 219.2239* 544.9100 525.1102454.9700 438.4382 597.8100 576.0880476.1400 458.8390248.6500* 239.6151*mean 457.14 521.71 132.93std 14.62 45.85 12.87

Table 4: Values for dX and dY measured. The values are corrected with 0.963664 as insubsection D.1 The marked (*) values were omitted.

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height 1/nm height 1(corr)/nm height 2/nm height 2(corr)/nm140.24 203.98 115.19 167.55124.58* 138.28 201.13140.24 203.98 145.33 211.39145.72 211.96133.19*

Table 5: The height was measured with inkscape section 3. The correction factor forthe height was obtained by the mean over all height values as 1.45 (marked (*) valuesomitted).

slope 1 slopes 20.43022 0.361160.46525 0.383030.46194 0.36694

mean 0.45247 0.37037std 0.01579 0.00926

Table 6: Slopes and angle of slope for dX and height.

The values for slope1 and slope2, respectively 0.45 ± 0.02µm and 0.37 ± 0.01µm aredifferent by some degree.

The slopes are describing an angle and the difference between these angles is

∆Θ = atan(0.45)− atan(0.37) ≈ 4◦ (18)

This difference could be explained due to the calibration grid not perfectly in level withthe x-y-plane the AFM is scanning and reperesents the angle the calibration grid may betilded.

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D.3 Tip Radius Estimation

R1R2

R3

Figure 13: Radius Estimation. Zoom 2X, plane removal, medium pixel averaging.R1=1898nm; R2=571nm; R3=479nm. The value of R1 appears to be too large andprobably caused by surface defects or dust particles. The mean of R2 and R3 is 525nm.

The tip radius was estimated by constructing circular sections that match best the shapeof the radius on the upper edge of the slope. The radius of the circular sections wascalculated equally like as in section 3.

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E SEM Measurements

E.1 Tip Height

Figure 14: Height of AFM tip measured with SEM. Focus= 50 mm EHT=28.59 kV PhotoNo.=7126 WD= 50 mm Mag= 1.11 K X 5-Dec-2009

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E.2 Tip Slope

Figure 15: Slope of the AFM tip. 18.5◦ + 15.4◦ = 33.9◦ 33.9◦

2= 16.95◦. 90◦ − 16.95◦ =

73.05◦ and slope = tan(73.05◦) = 3.28

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E.3 Lever Geometry, Length and Thickness

Figure 16: The Lever Geometry. The effective distance of the probe tip from the substrateis about 295 ± 1µm. The length of the arms are an average of about 430µm from thesubstrate edge to the tip. The thickness of the lever (not shown) is about 8µm. Theuncertainty is larger than compared to the values shown in the micrograph consideringthe ability to position the cursors onto the exact position.

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E.4 Tip Radius

Figure 17: Tip Radius estimation. The box size is about 1600nm x 1600nm thereforeenclosing a circle of a diameter of 1600nm or about 800nm radius.

Assuming an estimated tip radius of 800nm according to the micrograph (Figure 17) itis possible to estimate an initial slope to expect with an equal tip on the AFM by

slope =

√R2 − (R− h)2

R− h=

√800nm2 − (800nm− 200nm)2

800nm− 200nm= 0.882 (19)

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References

Burleigh Instruments, I. (1997), METRIS-2001,Burleigh Instruments (UK) Ltd.9 Allied Business Center, Coldharbour LaneHarpenden, Herts, AL5 4UT, UK. Webpage. Default. Inaccessible.URL: www. burleigh. com

Inkscape. (2011), Webpage. Accessed: 25 Nov 2011. Draw Freely.URL: http://inkscape.org/

MikroMasch (n.d.), Webpage. Accessed 27 Nov 2011.URL: http: // www. spmtips. com/ faq

Nanoscience Instruments, I. (2011), ‘Atomic force microscopy overview’, Webpage. Ac-cessed 26 Nov 2011.URL: http: // www. nanoscience. com/ education/ afm. html

Rabke, C. (1998), ‘Atomic force microscopy.’, Ceramic Industry 148(13), 52.URL: http: // 0-search. ebscohost. com. library. gmit. ie/ login. aspx?

direct= true&db= buh&AN= 1403996&site= ehost-live

Ying, Z. C., Reitsma, M. G. and Gates, R. S. (2007), ‘Direct measurement of cantileverspring constants and correction for cantilever irregularities using an instrumentedindenter.’, Review of Scientific Instruments 78(6), 063708.URL: http: // 0-search. ebscohost. com. library. gmit. ie/ login. aspx?

direct= true&db= aph&AN= 25684824&site= ehost-live

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www.burleigh.com

http://www.spmtips.com/faq

http://www.nanoscience.com/education/afm.html

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