Принципы нанометрологии (1027506), страница 41
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When an electronapproaches a potential energy barrier higher than the electron’s energy, theelectron is not completely reflected as one would expect classically, but ratherthe electron’s wavefunction exponentially decays as it travels through thebarrier. With a sufficiently thin barrier, there is a small but non-negligibleprobability that the electron can be found on the other side of the barrier. Inpractice, the STM is realised based on the scanning of an ultra-sharpconductive tip close to a conductive sample.
The electron probabilitydensities of the tip and the substrate can overlap if the distance between thetwo is small enough; in which case the application of a potential differencebetween the tip and the sample will result in a current due to the electronstunnelling through the insulating gap formed by the vacuum layer betweenthe tip and the substrate.
This tunnelling current is exponentially sensitiveto the distance between the tip and the sample. With a barrier height (workfunction) of a few electron volts, a change in distance by an amount equal tothe diameter of a single atom (approximately 0.2 nm) causes the tunnellingcurrent to change by up to three orders of magnitude [1].The key technology that has enabled the STM and subsequent scanningprobe systems to be developed is the ability to move the tip by a controlledamount by such a small distance. This is possible using piezoelectricmaterials, which move the tip over the sample as well as scanning thesubstrate.
Depending on the mode of operation, the feedback will control thepiezoelectric actuator in the z direction in order to maintain a constanttunnelling current by keeping the tip at a constant height relative to thesurface. With this constant current method, a topographical map of a surfaceis obtained. However, this procedure will yield purely topographical information only when used on an electronically homogeneous surface; whenapplied to an electronically inhomogeneous surface, the tunnelling currentwill depend on both the surface topography and the local electronic structure.Atomic force microscopyFor example, if the effective local tunnelling barrier height increases ordecreases at a scan site, then the feedback system must decrease or increasethe tip-sample separation in order to maintain a constant tunnelling current.The final image obtained will thus contain electronic structure informationconvoluted with the topographical information.
A solution to this problem isthe so-called barrier-height imaging mode [5] used to measure varying workfunction (tunnelling barrier height) over inhomogeneous samples. In thismode, the tip is scanned over each measurement site and the distancebetween the tip and the sample is varied while recording dI/dz; the rate oftunnelling current, I, change with respect to tip-sample distance, z. From thisinformation, the work function at each location can be determined and usedto correct constant current measurement.
One of the main limitations ofSTM is that it can be used only with conductive samples.7.3 Atomic force microscopyThe AFM [6,7] was developed to image insulating surfaces with atomicresolution. AFM is the most widely used member of the family of SPMtechniques. Its versatility and the presence of a number of commercialinstruments make it a method of choice for research laboratories, fromacademia to industry.Figure 7.2 is a block diagram of a standard AFM (it is in fact representativeof most SPM types). Its essential components are as follow:-z scanner;-xy scanner;-deflection detector, for example optical beam deflection method (seebelow), piezoresistive sensor [8] or Fabry-Pérot fibre interferometer [9];-cantilever and probe.The sample is scanned continuously in two axes (xy) underneath a forcesensing probe consisting of a tip that is attached to, or part of, a cantilever.
Ascanner is also attached to the z axis (height) and compensates for changes insample height, or forces between the tip and the sample. The presence ofattractive or repulsive forces between the tip and the sample will cause thecantilever to bend and this deflection can be monitored in a number of ways.The most common system to detect the bend of the cantilever is the opticalbeam deflection system, wherein a laser beam reflects off the back of thecantilever onto a photodiode detector.
Such an optical beam deflectionsystem is sensitive to sub-nanometre deflections of the cantilever [10].181182C H A P T ER 7 : Scanning probe and particle beam microscopyFIGURE 7.2 Block diagram of a typical SPM.7.3.1 Noise sources in atomic force microscopyThe limitations of the metrological capabilities of an AFM due to thermalnoise are well documented [11]. However, not only thermal but all noisesources need to be systematically investigated and their particular contributions to the total amount of the noise quantified for metrological purposes[12].
Note that most of the discussions on noise in AFM are also of relevanceto other forms of SPM.Noise source can be either external, including:-variations of temperature and air humidity;-air motion (for example, air-conditioning, air circulation, draughts,exhaust heat);-mechanical vibrations (for example, due to structural vibrations,pumps – see section 3.9);-acoustic (for example, impact sound, ambient noise – see section3.9.6).Atomic force microscopyor internal noise (intrinsic noise), including:-high-voltage amplifiers;-control loops;-detection systems;-digitization.It is also well known that adjustments made by the user (for example, thecontrol loop parameters, scan field size and speed) also have a substantialinfluence on the measurement [13].To reduce the total noise, the subcomponents of noise must be investigated.
The total amount of the z axis noise can be determined by static ordynamic measurements [14] as described in the following section.7.3.1.1 Static noise determinationTo determine the static noise of an SPM, the probe is placed in contactwith the sample, the distance is actively controlled, but the xy scan isdisabled, i.e. the scan size is zero. The z axis signal is recorded and analysed (for example, RMS determination or calculation of the fast Fouriertransform to identify dominant frequencies which then serve to identifycauses of noise). An example of a noise signal for an AFM is shown inFigure 7.3; the RMS noise is 13 pm in this case (represented as an Rqparameter – see section 8.2.7.2).7.3.1.2 Dynamic noise determinationTo determine the dynamic noise of an SPM the probe and sample are displaced in relation to one another (line or area scan).
In this case, scan speed,scan range and measurement rate should be set to values typical of thesubsequent measurements to be carried out. Usually the dynamic noisemeasurement is carried out at least twice with as small a time delay aspossible. The calculation of the difference between the subsequent images isused to correct for surface topography and guidance errors inherent in thescanner.7.3.1.3 Scanner xy noise determinationThe accurate determination of xy noise is extremely difficult for AFM as theyhave small xy position noise and thus require samples with surface roughness substantially smaller than the xy noise [12]. In individual cases, thenoise of subcomponents can be determined.
For xy stage, for example, the xyposition noise can be measured with a laser interferometer.183184C H A P T ER 7 : Scanning probe and particle beam microscopyFIGURE 7.3 Noise results from an AFM. The upper image shows an example ofa static noise investigation on a bare silicon wafer. The noise-equivalent roughness isRq ¼ 0.013 nm. For comparison, the lower image shows the wafer surface: scan size1 mm by 1 mm, Rq ¼ 0.081 nm.For AFM, the following guidance deviations are usually observed:-out-of-plane motions or scanner bow, i.e. any form of cross-talk of xymovements to the z axis;-line skips in the z direction;-distortions within the xy plane (shortening/elongation/rotation) due toorthogonality and/or angular deviations;-orthogonality deviations between the z and the x or y axis.Guidance deviations can be due to the design and/or be caused by deviations in the detection or control loop.
Guidance deviations show a strongdependence on the selected scan field size and speed as well as on the workingpoint in the xy plane and within the z range of the scanner. 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.
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