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When thereproducibility is good, such systematic deviations can be quantified andcorrected for by calibration.Atomic force microscopy7.3.2 Some common artefacts in AFM imagingOne of the reasons that AFMs have not yet fully been integrated into theproduction environment is the presence of numerous ‘artefacts’ in theirimages that are not due to surface topography of the surface being measured.Usually a high level of expertise is required to identify these artefacts. Theavailability of reference substrates and materials will allow industry to useAFMs (and other SPMs) more widely.7.3.2.1 Tip size and shapeMany of the most common artefacts in AFM imaging are related to the finitesize and shape of the tip.
Commonly used AFM probes, such as those manufactured from silicon nitride and silicon, have pyramidal shaped tips [15].These tips can have a radius of curvature as small as 1 nm, but often the radiusis much larger. When imaging vertical features that are several tens of nanometres or more in height, the tip half angle limits the lateral resolution. Whenthe tip moves over a sharp feature, the sides of the tip, rather than just the tipapex, contact the edges of the feature (see Figure 7.4). For features with verticalrelief less than approximately 30 nm, it is the radius of curvature of the tip thatlimits resolution, resulting in tip broadening of the feature of interest.
Theresulting image is a non-linear combination of the sample shape and the tipFIGURE 7.4 Schematic of the imaging mechanism of spherical particle imaging byAFM. The geometry of the AFM tip prevents ‘true’ imaging of the particle as the apex ofthe tip is not in contact with the particle all the time and the final image is a combinationof the tip and particle shape.
Accurate sizing of the nanoparticle can only be obtainedfrom the height measurement.185186C H A P T ER 7 : Scanning probe and particle beam microscopyshape. Various deconvolution (or its non-linear equivalent, erosion) methods,including commercial software packages, are available although such softwaremust be used with caution [16–18]. There are also many physical artefactsthat can be used to measure the shape of an AFM tip [19–21].7.3.2.2 Contaminated tipsAn ideal AFM tip ends in a single point at its apex. However, manufacturinganomalies and/or contamination may lead to double or even multiple tipends.
When this occurs, the tips can map features on the sample surfacemore than once. For example, a double tip will result in a regular doubling offeatures. Such artefacts lead to what are commonly termed double- ormultiple-tip images. Contaminants on a tip can also interact with a samplesurface, leading to repeated patterns of the contaminants scattered across thesurface.
Cleaning of AFM tips and cantilevers is highly recommended [22].7.3.2.3 Other common artefactsWhen the gain parameter of the control loop is too high, rippling artefacts canoccur along the edges of features. These ripples tend to occur along theleading edge of a feature and will generally switch position when the scandirection is changed. Shadow artefacts generally occur along the trailing edgeof a feature, when the feedback loop is unable to compensate for a rapidchange in topography.
Reducing the scan speed often minimises shadowartefacts. Sample damage or deformation during scanning is also a significantartefact, particularly for soft surfaces.Piezoelectric and/or thermal drift can distort images, particularly at thestart of scanning.
Measuring near to the centre of the z axis piezoelectricactuator’s range, and allowing the AFM and the sample to sit for a period toreach thermal equilibration can substantially improve drift-related problems.7.3.3 Determining the coordinate system of an atomic forcemicroscopeThere will always be some imperfections in the coordinate system for a givenAFM. The calibration of the lateral scan axes is usually carried out using 1Dor 2D lateral calibration artefacts. These artefacts are usually formed byequidistant structures with defined features whose mean spacing (the pitch)serves to calibrate the lateral axes.
In Figure 7.5a a set of parallel regressionlines along similar features of the structure is calculated. The mean distancebetween these lines is the pitch, px. In Figure 7.5b a set of parallel regressionlines is calculated, each through a column of centres of similar features; themean distance between these lines is the pitch, px in the x direction of theAtomic force microscopyFIGURE 7.5 Definition of the pitch of lateral artefacts: (a) 1D and (b) 2D.grating. Similarly, another set of parallel regression lines is calculated, eachthrough a series of centres of the grating; the mean distance of these gratinglines is the pitch, py in the y direction of the grating.
The orthogonality of thegrating is the angle formed by the px and py vectors.Local deviations are a measure of the non-linearity of the axes. In addition, the orthogonality deviation and the cross-talk of the lateral scan axescan be determined.For the 2D lateral artefacts it is important not to confuse the pitches, pxand py, and the mean spacings, ax and ay, of the individual grating: px and ax,or py and ay are identical only for perfectly orthogonal gratings. Wherehigh-quality gratings are used, which are almost orthogonal, the differencecan often be ignored in the calibration of the axes.
These differences,however, become significant when a 2D artefact is used to check theorthogonality of the scanner axes.In measurements on lateral artefacts, the selection of the scan range andthe scan speed or rate are important, because the calibration factors arestrongly influenced by dynamic non-linearity and image distortions [23].This is also true for systems with active position control.
In calibration, thescan speed must, therefore, be adjusted to reflect the later measurements thatare to be made.7.3.4 Traceability of atomic force microscopyFrom the metrological point of view, AFMs are generally subdivided into thethree following categories [12]:-reference AFMs with integrated laser interferometers allowing directtraceability of the axis scales via the wavelength of the laser used to the187188C H A P T ER 7 : Scanning probe and particle beam microscopySI unit of length (often referred to as metrological AFMs, see [24–27]for examples developed at NMIs);--AFMs with position measurement using displacement transducers, forexample, capacitive or inductive sensors, strain gauges or opticalencoders. These sensors are calibrated by temporarily mounting laserinterferometers to the device or by measuring high-quality calibrationartefacts.
Two types are to be distinguished here:,active position control AFMs that track to scheduled positions bymeans of a closed loop control system;,AFMs with position measurement but without closed loop forposition control (open loop systems);AFMs in which the position is determined from the electricalvoltage applied to the piezoelectric scanners and, if need be,corrected using a look-up table. Such AFMs need to be calibratedusing a transfer artefact that has itself been calibrated usinga metrological AFM (highest accuracy) or an AFM with positionmeasurement.
These instruments will, however, suffer fromhysteresis in the scanner.Another important aspect of traceability is the uncertainty of measurement (see section 2.8.3). It is very rare to see AFM measurements quotedwith an associated uncertainty as many of the points discussed in section6.11 apply to AFMs (and SPMs in general). Uncertainties are usually onlyquoted for the metrological AFMs or for simple artefacts such as step heights[28] or 1D gratings [29].7.3.4.1 Calibration of AFMsCalibration of AFMs is carried out using certified reference artefacts. Suitablesets of artefacts are available from various manufacturers (see www.nanoscale.de/standards.htm for a comprehensive list of artefacts).
An alternative is to use laser interferometers to calibrate the axes, which offer a moredirect method to traceability if stabilized lasers are used.The aim of the calibration is the determination of the axis scaling factors,Cx, Cy and Cz. Apart from these scaling factors, a total of twenty one degreesof freedom can be identified for the motion process of the SPM similar toa CMM operating in 3D (see section 9.2).A typical calibration for an AFM proceeds in the following manner [12]:-the cross-talk of lateral scan movements to the z axis is investigated bymeasurements on a flatness artefact;Atomic force microscopy-the cross-talk of the lateral scan axes and the orthogonality deviation isdetermined using a 2D lateral artefact. This artefact is usually used tocalibrate Cx and Cy;-deviations from orthogonality can be determined using artefacts withorthogonal structures;-orthogonality deviations are measured using 3D artefacts. Calibrationof the z axis, Cz, and deviations are achieved using 3D artefacts.In most cases, different artefacts are used for these calibration steps (seeTable 7.1).
Alternatively, 3D artefacts can be used – with suitable evaluationsoftware – to calibrate all three factors, Cx, Cy and Cz, and the cross-talkbetween all three axes.7.3.5 Force measurement with AFMsForce measurements with an AFM are carried out by monitoring the cantilever deflection as the sample approaches, makes contact with, and thenretracts from the cantilever. However, the raw cantilever deflectionmeasurement is a measure of the deflection of the cantilever at some point andnot directly of the force.
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