Принципы нанометрологии (1027506), страница 46
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However, depending on the density of thematerial present, some of the electrons in the beam are scattered and areremoved from the beam. At the base of the microscope the unscatteredelectrons hit a fluorescent viewing screen and produce a shadow image of thetest specimen with its different parts displayed in varied darkness according201202C H A P T ER 7 : Scanning probe and particle beam microscopyto their density.
This image can be viewed directly by the operator or photographed with a camera.The limiting resolution of the modern TEM is of the order of 0.05 nmwith aberration-corrected instruments. The resolution of a TEM is normallydefined as the performance obtainable with an ‘ideal’ specimen, i.e. one thinenough to avoid imposing a further limit on the performance due to chromatic effects.
The energy loss suffered by electrons in transit througha specimen will normally be large compared to the energy spread in theelectron beam due to thermal emission velocities, and large also compared tothe instability of the high-voltage supply to the gun and the current suppliesto the electron lenses.In general the specimen itself causes loss of definition in the image due tochromatic aberration of the electrons, which have lost energy in transitthrough it. A ‘thick’ specimen could easily reduce the attainable resolution to1.5 nm to 2 nm [59]. For nanoparticles, this condition could occur ifa particle preparation is very dense; a good preparation of a well-dispersedparticle array on a thin support film would not in general cause a serious lossin resolution.7.5.3 Traceability and calibration of transmission electronmicroscopesAs for SEM, the calibration factor for a TEM is the ratio of the measureddimension in the image plane and the sample dimension in the object plane.Calibration should include the whole system.
This means that a calibrationartefact of known size in the object plane is related to a calibration artefact ofknown size in the image plane. For example, the circles on an eyepiecegraticule, the ruler used to measure photographs and the number of detectedpixels in the image analyser should all be related to an artefact of known sizein the object plane.The final image magnification of a TEM is made up of the magnificationsof all the electron lenses, and it is not feasible to measure the individualstages of magnification. Since the lenses are electromagnetic, the lensstrength is dependent not only on the excitation currents, but also on theprevious magnetic history of each circuit. It is essential, therefore, to cycleeach lens in a reproducible manner if consistent results are to be obtained.Suitable circuitry is now included in many instruments; otherwise, each lenscurrent should be increased to its maximum value before being returned tothe operating value in order to ensure that the magnetic circuits are standardized.
This should be done before each image is recorded. The indicatedElectron microscopymagnification shown on the instrument is a useful guide but should not berelied upon for an accuracy better than 10 %.7.5.3.1 Choice of calibration specimenIt is possible to calibrate the lower part of the magnification range usinga specimen which has been calibrated optically, although this losesaccuracy as the resolution limit of optical instruments is approached. Atthe top end of the scale, it is possible to image crystal planes in suitablesingle crystals of known orientation. These spacings are known to a highdegree of accuracy by x-ray measurements. Unfortunately, there is atpresent no easy way of checking the accuracy of calibration in the centreof the magnification range.
The specimen most often used is a plastic/carbon replica of a cross-ruled diffraction grating. While it is believed thatthese may usually be accurate to about 2 %, it has not so far provedpossible to certify them.7.5.3.2 Linear calibrationLinear calibration is the measurement of the physical distances in the objectplane represented by a distance in the image plane. The image plane is thedigital image inside the computer and so the calibration is expressed inlength per pixel or pixels per unit length.
The procedure for the linear calibration of image analysers varies from machine to machine but usuallyinvolves indicating on the screen both ends of an imaged artefact of knowndimensions in the object plane [61].This calibration artefact may be a grid, grating, micrometer, ruler or otherscale appropriate to the viewing system, and should be arranged to fill thefield of view, as far as possible. The calibration should be measured bothparallel to and orthogonal to the scan direction. Some image analysers can becalibrated in both directions and use both these values. Linear calibration canbe altered by such things as drift in a tube camera, the sagging of zoom lensesand the refocusing of the microscope.7.5.3.3 Localized calibrationThe linear calibration may vary over the field of view.
There may be imagedistortions in the optics or inadequately compensated distortions from a tilted target in the microscope. These distortions can be seen by comparing animage of a square grid with an overlaid software generated pattern. Tubecameras are a source of localized distortion, especially at the edge of thescreen near the start of the scan lines.
The size of these distortions can bedetermined by measuring a graticule with an array of spots all of the samesize that fill the screen, or by measuring one spot or reference particle at203204C H A P T ER 7 : Scanning probe and particle beam microscopydifferent points in the field of view. Some image analysers allow localizedcalibrations to be made [62].7.5.3.4 Reference graticuleMany of the calibrations can be performed easily with a calibrated graticulecontaining arrays of calibrated spots and a square grid.
Such a graticule is thereference stage graticule for image analyser calibration. Periodic patternssuch as grating replicas, super-lattice structures of semiconductors, crystallattice images of carbon, gold or silicon can be used as reference materials.7.5.4 Electron microscopy of nanoparticlesElectron microscopy produces two-dimensional images. The contrast mechanism is based on the scattering of electrons. Figure 7.8a shows a typical TEMimage of gold nanoparticles. Many microscopes still record the images onphotographic film.
In this case, the images have to be scanned into a computerfile to be analysed. However, CCD cameras are becoming increasingly popular.In this case the image is transferred directly onto a computer file.Traditionally size measurements from electron microscope images areachieved by applying threshold intensity uniformly across the image.
Imageintensities above (or below) this level are taken to correspond to areas ofthe particle being measured. This is demonstrated in Figure 7.8b, wherea threshold was applied to identify the particles. Simple analysis allows thearea and radius of the particle to be determined. In the case of non-sphericalparticles the diameter is determined by the fitting of an ellipsoid. A histogramof the sizes can then be easily determined (Figure 7.8c).Although the threshold method described above is a simple, well-definedand recognised method it does suffer from some significant drawbacks. Thefirst is setting the threshold level, which is difficult for poorly contrastingparticles (such as small polymer particles or inhomogeneous particles (seeFigure 7.9)).
The second, more important, drawback occurs when analysingagglomerated particles. With no significant intensity difference between theparticles a simple threshold is insufficient to distinguish between the particles and hence accurately determine size.
It is usually recommended to usea watershed method.7.6 Other particle beam microscopy techniquesIn order to get high-resolution images from any scanning beam microscope one must be able to produce a sufficiently small probe, haveOther particle beam microscopy techniquesFIGURE 7.8 (a) TEM image of nominal 30 nm diameter gold nanoparticles; (b) using threshold to identify theindividual particles; (c) histogram of the measured diameters.a small interaction volume in the substrate and have an abundance ofinformation-rich particles to create the image.
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