Instrumentation

Colliex, C.

doi:10.1107/97809553602060000593

International
Tables for
Crystallography
Volume C
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International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 394-397

Section 4.3.4.2. Instrumentation

C. Colliex^a

4.3.4.2. Instrumentation

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4.3.4.2.1. General instrumental considerations

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In a dedicated instrument for electron inelastic scattering studies, one aims at the best momentum and energy resolution with a well collimated and monochromatized primary beam. This is achieved at the cost of poor spatial localization of the incident electrons and one assumes the specimens to be homogeneous over the whole irradiated volume. In a sophisticated instrument such as that built by Fink & Kisker (1980), the energy resolution can be varied from 0.08 to 0.7 eV, and the momentum transfer resolution between 0.03 and 0.2 Å⁻¹, but typical values for the electron-beam diameter are about 0.2 to 1 mm. Nowadays, many energy-analysing devices are coupled with an electron microscope: consequently, an inelastic scattering study involves recording for a primary intensity [I_0] , the current I(r, $[\boldtheta]$ , ΔE) scattered or transmitted at the position r on the specimen, in the direction $[\boldtheta]$ with respect to the primary beam, and with an energy loss ΔE. Spatial resolution is achieved either with a focused probe or by a selected area method, angular acceptance is defined by an aperture, and energy width is controlled by a detector function after the spectrometer. It is not possible from signal-to-noise considerations to reduce simultaneously all instrumental widths to very small values. One of the parameters (r, $[\boldtheta]$ or ΔE) is chosen for signal integration, another for selection, and the last is the variable. Table 4.3.4.1 classifies these different possibilities for inelastic scattering studies.

Table 4.3.4.1| top | pdf |
Different possibilities for using EELS information as a function of the different accessible parameters (r, $[\boldtheta]$ , ΔE)

	Integration parameter	Selection parameter	Results	Working mode of the spectrometer
1	$[\boldtheta]$	r	Spectrum I_r (ΔE)	Analyser
2	r	$[\boldtheta]$	Spectrum $[I_\boldtheta]$ (ΔE)	Analyser
3	$[\boldtheta]$	ΔE	Energy-filtered image $[I_{\Delta E}(\bf r)]$	Filter
4	r	ΔE	Energy-filtered diffraction pattern $[I_{\Delta E}({\boldtheta})]$	Filter

Because of the great variety of possible EELS experiments, it is impossible to build an optimum spectrometer for all applications. For instance, the design of a spectrometer for low-energy incident electrons and surface studies is different from that for high-energy incident electrons and transmission work. In the latter category, instruments built for dedicated EELS studies (Killat, 1974; Gibbons, Ritsko & Schnatterly, 1975; Fink & Kisker, 1980; etc.) are different from those inserted within an electron-microscope environment, in which case it is possible to investigate the excitation spectrum from a specimen area well characterized in image and diffraction [see the reviews by Colliex (1984) and Egerton (1986)].

The literature on dispersive electron–optical systems (equivalent to optical prisms) is very large. For example, the theory of uniform field magnets, which constitute an important family of analysing devices, has been extensively developed for the components in high-energy particle accelerators (Enge, 1967; Livingood, 1969). As for EELS spectrometers , they can be classified as:

(a) Monochromators, which filter the incident beam to obtain the smallest primary energy width. The natural width for a heated W filament is about 1 eV, possibly rising to about a few eV as a consequence of stochastic interactions [Boersch (1954) effect, analysed for instance by Rose & Spehr (1980)]. For a low-temperature field-emission source, this energy spread is only ∼0.3 eV. This constitutes a clear gain but remains insufficient for meV studies. In this case, one has to introduce a filter lens such as the three-electrode design developed by Hartl (1966) or a cylindrical electrostatic deflector before the accelerator [Kuyatt & Simpson (1967) or Gibbons et al. (1975)]. In both cases, an energy resolution of 50 meV has been achieved for electron beams of 50–300 keV at the specimen.
(b) Analysers, which measure the energy distribution of the beam scattered from the specimen. They can be used either strictly as analysers displaying the energy loss from a given specimen volume, or as filters (or selecting devices) that provide 2D images or diffraction patterns with a given energy loss.

4.3.4.2.2. Spectrometers

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Fig. 4.3.4.7 defines the basic parameters of a `general' energy-loss spectrometer: a region of electrostatic E and/or magnetic B fields transforms a distribution of electrons [I_0] $[(x_0,y_0,t_0,u_0,\rho)]$ in the object plane of coordinate [z_0] along the principal trajectory, into a distribution of electrons [I_1] $[(x_1,y_1,t_1,u_1,\rho)]$ in the object plane of coordinate [z_1] , coincident with the detector plane (or optically conjugate to it). The transverse coordinates are labelled as (x, y), the angular ones as (t, u), and ρ = Δp/p = ΔE/2E is the relative change in absolute momentum value associated with the energy loss.

Figure 4.3.4.7| top | pdf |

Schematic drawing of a uniform magnetic sector spectrometer with induction B normal to the plane of the figure. Definition of the coordinates used in the text (the object plane at coordinate z₀ along the mean trajectory coincides with the specimen, and the image plane at z₁ coincides with the dispersion plane and the detector level).

Common properties of such systems are:

(a) first-order imaging properties or stigmatism, i.e. all electrons leaving are focused at the same point, independently of their inclination on the optical axis;
(b) strong chromatic aberration in order to realize an efficient discrimination between electrons of different ρ.

The spectrometer performance can be evaluated with the following parameters:

D = dispersion = beam displacement in the spectrometer image plane for a given momentum change ρ; it is generally expressed in cm/eV. The higher the dispersion, the easier it is to resolve small energy losses. For a straight-edge 90° magnetic sector, $[D\propto 2R/E_0]$ , where R is the curvature radius of the mean trajectory and is the primary energy.
$[\delta E_{\rm min}]$ = energy resolution. This corresponds to the minimum-energy variation that can be resolved by the instrument. It takes into account the width of the image $[\Delta x_{\rm image}=Mr]$ , where M is the spectrometer magnification and r the radius of the spectrometer source, as well as the second- and higher-order angular aberrations. These are responsible for the imperfect focusing of the electrons that enter the spectrometer within a cone of angular acceptance $[\beta_0]$ and contribute through a term $[\Delta x_{\rm aber}=C\beta^2_0]$ . Moreover, one must convolute these terms with the natural width $[\delta E_0]$ of the primary beam, including AC fields, and with the detection slit width $[\Delta x_{\rm slit}]$ . Combining all these effects, as shown schematically in Fig. 4.3.4.8 , one obtains approximately: $[\Delta x_{\rm tot}=[(\Delta x_{\rm slit})^2+(\Delta x_{\rm image})^2+(\Delta x_{\rm aber})^2+ D\delta E^2_0]^{1/2} \eqno (4.3.4.7)]$ and the corresponding energy resolution is defined as $[\delta E_{\min}=(\Delta x_{\rm tot})_{\min}/D]$ . In many situations, the dominant factor is the second-order aberration term $[C\beta^2_0]$ so that the figure of merit F, defined as $[F=\pi\beta_0 E_0/\delta E_{\rm min}]$ , is of the order of unity for an uncorrected magnetic spectrometer.

Figure 4.3.4.8| top | pdf |
Different factors contributing to the energy resolution in the dispersion plane [courtesy of Johnson (1979)].

From this simplified discussion, one deduces that there is generally competition between large angular acceptance for the inelastic signal, which is very important for obtaining a high signal-to-noise ratio (SNR) for core-level excitations, and good energy resolution. Two solutions have been used to remedy this limitation. The first is to improve spectrometer design, for example by correcting second-order aberrations in a homogeneous magnetic prism (Crewe, 1977a; Parker, Utlaut & Isaacson, 1978; Egerton, 1980b; Krivanek & Swann, 1981; etc). This can enhance the figure of merit by at least a factor of 100. The second possibility is to transform the distribution of electrons to be analysed at the exit surface of the specimen into a more convenient distribution at the spectrometer entrance. This can be done by introducing versatile transfer optics (see Crewe, 1977b; Egerton, 1980a; Johnson, 1980; Craven & Buggy, 1981; etc.). As a final remark on the energy resolution of a spectrometer, it is meaningless to define it without reference to the size and the angular aperture of the analysed beam.

Historically, many types of spectrometer have been used since the first suggestion by Wien (1897) that an energy analyser could be designed by employing crossed electric and magnetic fields. Reviews have been published by Klemperer (1965), Metherell (1971), Pearce-Percy (1978), and Egerton (1986). Nowadays, two configurations are mostly used and have become commercially available on modern electron microscopes: these are spectrometers on TEM/STEM instruments and filters on CTEM ones. In the first case, homogeneous magnetic sectors are the simplest and most widely used devices. Recent instrumental developments by Shuman (1980), Krivanek & Swann (1981), and Scheinfein & Isaacson (1984) have given birth to a generation of spectrometers with the following major characteristics: double focusing, correction for second-order aberrations, dispersion plane perpendicular to the trajectory. This has been made possible by a suitable choice of several parameters, such as the tilt angles and the radius of curvature for the entrance and exit faces and the correct choice of the object source position. As an example, for a 100 keV STEM equipped with a field emission gun, the coupling illustrated in Fig. 4.3.4.9 leads to an energy resolution of 0.35 eV for β₀ = 7.5 mrad on the specimen as visible on the elastic peak, and 0.6 eV for α₀ = 25 mrad as checked on the fine structures on core losses. Krivanek, Manoubi & Colliex (1985) demonstrated a sub-eV energy resolution over the whole range of energy losses up to 1 or 2 keV.

Figure 4.3.4.9| top | pdf |

Optical coupling of a magnetic sector spectrometer on a STEM column.

A very competitive solution is the Wien filter, which consists of uniform electric and magnetic fields crossed perpendicularly, see Fig. 4.3.4.10 . An electron travelling along the axis with a velocity $[{\bf v}_0]$ such that $[|{\bf v}_0|=E/B]$ is not deflected, the net force on it being null. All electrons with different velocities, or at some angle with respect to the optical axis, are deflected. The dispersion of the system is greatly enhanced by decelerating the electrons to about 100 eV within the filter, in which case $[D\simeq]$ a few 100 µm/eV. A presently achievable energy resolution of 150 meV at a spectrometer collection half-angle of 12.5 mrad has been demonstrated by Batson (1986, 1989). It allows the study of the detailed shape of the energy distribution of the electrons emitted from a field emission source and the taking of it into account in the investigation of band-gap states in semiconductors (Batson, 1987).

Figure 4.3.4.10| top | pdf |

Principle of the Wien filter used as an EELS spectrometer : the trajectories are shown in the two principal (dispersive and focusing) sections.

Filtering devices have been designed to form an energy-filtered image or diffraction pattern in a CTEM. The first solution, reproduced in Fig. 4.3.4.11 , is due to Castaing & Henry (1962). It consists of a double magnetic prism and a concave electrostatic mirror biased at the potential of the microscope cathode. The system possesses two pairs of stigmatic points that may coincide with a diffraction plane and an image plane of the electron-microscope column. One of these sets of points is achromatic and can be used for image filtering. The other is strongly chromatic and is used for spectrum analysis. Zanchi, Sevely & Jouffrey (1977) and Rose & Plies (1974) have proposed replacing this system, which requires an extra source of high voltage for the mirror, by a purely magnetic equivalent device. Several solutions, known as the α and $[\omega]$ filters, with three or four magnets, have thus been built, both on very high voltage microscopes (Zanchi, Perez & Sevely, 1975) and on more conventional ones (Krahl & Herrmann, 1980), the latest version now being available from one EM manufacturer (Zeiss EM S12).

Figure 4.3.4.11| top | pdf |

Principle of the Castaing & Henry filter made from a magnetic prism and an electrostatic mirror. (R₁, R₂, and R₃ are the real conjugate stigmatic points, and V₁, V₂, and V₃ the virtual ones: the dispersion plane coincides with the R₃ level and achromatic one with the V₃ level.)

4.3.4.2.3. Detection systems

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The final important component in EELS is the detector that measures the electron flux in the dispersion plane of the spectrometer and transfers it through a suitable interface to the data storage device for further computer processing. Until about 1990, all systems were operated in a sequential acquisition mode. The dispersed beam was scanned in front of a narrow slit located in the spectrometer dispersion plane. Electrons were then generally recorded by a combination of scintillator and photomultiplier capable of single electron counting.

This process is, however, highly inefficient: while the counts are measured in one channel, all information concerning the other channels is lost. These requirements for improved detection efficiency have led to the consideration of possible solutions for parallel detection of the EELS spectrum. They use a multiarray of detectors, the position, the size and the number of which have to be adapted to the spectral distribution delivered by the spectrometer. In most cases with magnetic type devices, auxiliary electron optics has to be introduced between the spectrometer and the detector so that the dispersion matches the size of the individual detection cells. Different systems have been proposed and tested for recording media, the most widely used solutions at present being the photodiode and the charge-coupled diode arrays described by Shuman & Kruit (1985), Krivanek, Ahn & Keeney (1987), Strauss, Naday, Sherman & Zaluzec (1987), Egerton & Crozier (1987), Berger & McMullan (1989), etc. Fig. 4.3.4.12 shows a device, now commercially available from Gatan, that is made of a convenient combination of these different components. This progress in detection has led to significant improvements in many areas of EELS: enhanced detection limits, reduced beam damage in sensitive materials, data of improved quality in terms of both SNR and resolution, and access to time-resolved spectroscopy at the ms time scale (chronospectra). Several of these important consequences are illustrated in the following sections.

Figure 4.3.4.12| top | pdf |

A commercial EELS spectrometer designed for parallel detection on a photodiode array. The family of quadrupoles controls the dispersion on the detector level [courtesy of Krivanek et al. (1987)].

References

Batson, P. E. (1986). High energy resolution electron spectrometer for a 1 nm spatial analysis. Rev. Sci. Instrum. 57, 43–48.Google Scholar

Batson, P. E. (1987). Spatially resolved interband spectroscopy. Physical aspects of microscopic characterization of materials, edited by J. Kirschner, K. Murata & J. A. Venables, pp. 189–195. Scanning Microscopy, Suppl. I.Google Scholar

Batson, P. E. (1989). High resolution energy-loss spectroscopy. Ultramicroscopy, 28, 32–39.Google Scholar

Berger, S. D. & McMullan, D. (1989). Parallel recording for an electron spectrometer on a scanning transmission electron microscope. Ultramicroscopy, 28, 122–125.Google Scholar

Boersch, H. (1954). Experimentelle Bestimmung der Energieverteilung in thermisch ausgelosten Elektronenstrahlen. Z. Phys. 139, 115–146.Google Scholar

Castaing, R. & Henry, L. (1962). Filtrage magnétique des vitesses en microscopie électronique. C. R. Acad. Sci. Paris Sér. B, 255, 76–78.Google Scholar

Colliex, C. (1984). Electron energy loss spectroscopy in the electron microscope. Advances in optical and electron microscopy, Vol. 9, edited by V. E. Cosslett & R. Barer, pp. 65–177. London: Academic Press.Google Scholar

Craven, A. J. & Buggy, T. W. (1981). Design considerations and performance of an analytical STEM. Ultramicroscopy, 7, 27–37.Google Scholar

Crewe, A. V. (1977a). Post specimen optics in the STEM. I. General information. Optik (Stuttgart), 47, 299–312.Google Scholar

Crewe, A. V. (1977b). Post specimen optics in the STEM. II. Optik (Stuttgart), 47, 371–380.Google Scholar

Egerton, R. F. (1980a). The use of electron lenses between a TEM specimen and an electron spectrometer. Optik (Stuttgart), 56, 363–376.Google Scholar

Egerton, R. F. (1980b). Design of an aberration-corrected electron spectrometer for the TEM. Optik (Stuttgart), 57, 229–242.Google Scholar

Egerton, R. F. (1986). Electron energy loss spectroscopy in the electron microscope. New York/London: Plenum.Google Scholar

Egerton, R. F. & Crozier, P. A. (1987). A compact parallel recording. J. Microsc. 148, 157.Google Scholar

Enge, H. A. (1967). Deflecting magnets. Focusing of charged particles, Vol. 2, edited by A. Septier, pp. 203–264. New York: Academic Press.Google Scholar

Fink, J. & Kisker, E. (1980). A method for rapid calculation of electron trajectories in multielement electrostatic cylinder lenses. Rev. Sci. Instrum. 51, 918–920.Google Scholar

Gibbons, P. C., Ritsko, J. J. & Schnatterly, S. E. (1975). Inelastic electron scattering spectrometer. Rev. Sci. Instrum. 46, 1546–1554.Google Scholar

Hartl, W. A. M. (1966). Die Filterlinse als Monochromator für schnelle Elektronen. Z. Phys. 191, 487–502.Google Scholar

Johnson, D. E. (1979). Basic aspects of energy-loss spectrometer systems. Ultramicroscopy, 3, 361–365.Google Scholar

Johnson, D. E. (1980). Post specimen optics for energy loss spectrometry. Scanning Electron. Microsc. 1, 33–40.Google Scholar

Killat, U. (1974). Optical properties of C₆H₁₂, C₆H₁₀, C₆H₈, C₆H₆, C₇H₈, C₆H₅Cl and C₅H₅N in the solid and gaseous state derived from electron energy losses. J. Phys. C, 7, 2396–2408.Google Scholar

Klemperer, O. (1965). Electron beam spectroscopy. Rev. Prog. Phys. 28, 77–111.Google Scholar

Krahl, D. & Herrmann, K.-H. (1980). Experiments with an imaging energy filter in the CTEM. Micron, 11, 287–289.Google Scholar

Krivanek, O. L., Ahn, C. C. & Keeney, R. B. (1987). Parallel detection electron spectrometer using quadrupole lens. Ultramicroscopy, 22, 103–115.Google Scholar

Krivanek, O. L., Manoubi, T. & Colliex, C. (1985). Sub 1 eV resolution EELS at energy losses greater than 1 keV. Ultramicroscopy, 18, 155–158.Google Scholar

Krivanek, O. L. & Swann, P. R. (1981). An advanced electron energy loss spectrometer. Quantitative microanalysis with high spatial resolution, pp. 136–140. London: The Metals Society.Google Scholar

Kuyatt, C. E. & Simpson, J. A. (1967). Electron monochromator design. Rev. Sci. Instrum. 38, 103–111.Google Scholar

Livingood, J. J. (1969). The optics of dipole magnets. New York: Academic Press.Google Scholar

Metherell, A. J. F. (1971). Energy analysing and energy selecting electron microscopes. Adv. Opt. Electron Microsc. 4, 263–361.Google Scholar

Parker, N. W., Utlaut, M. & Isaacson, M. S. (1978). Design of magnetic spectrometers with second order aberrations corrected. Optik (Stuttgart), 51, 333–351.Google Scholar

Pearce-Percy. H. T. (1978). The design of spectrometers for energy loss spectroscopy. Scaning Electron Microsc. 1, 41–51.Google Scholar

Rose, H. & Plies, E. (1974). Entwurf eines fehlerarmen magnetischen Energie Analysators. Optik (Stuttgart), 40, 336–341.Google Scholar

Rose, H. & Spehr, R. (1980). On the theory of the Boersch effect. Optik (Stuttgart), 57, 339–364.Google Scholar

Scheinfein, M. & Isaacson, M. S. (1984). Design and performance of second order aberration corrected spectrometers for use with the scanning transmission electron microscope. Scanning Electron Microsc. 4, 1681–1696.Google Scholar

Shuman, H. (1980). Correction of the second order aberrations of uniform field magnetic sections. Ultramicroscopy, 5, 45–53.Google Scholar

Shuman, H. & Kruit, P. (1985). Quantitative data processing of parallel recorded electron energy-loss spectra with low signal to background. Rev. Sci. Instrum. 56, 231–239.Google Scholar

Strauss, M. G., Naday, Y., Sherman, I. S. & Zaluzec, N. J. (1987). CCD base parallel detection system for EELS spectroscopy and imaging. Ultramicroscopy, 22, 117–124.Google Scholar

Wien, W. (1897). Vert. Deutschen Phys. Res. 16, 165.Google Scholar

Zanchi, G., Perez, J. P. & Sevely, J. (1975). Adaptation of magnetic filtering device on a one megavolt electron microscope. Optik (Stuttgart), 43, 495–501.Google Scholar

Zanchi, G., Sevely, J. & Jouffrey, B. (1977). Second order image aberration of a one megavolt magnetic filter. Optik (Stuttgart), 48, 173–192.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 394-397