Expected contribution of the field-emission gun to high-resolution transmission electron microscopy

Micron,Vol.25, No. 3, pp. 223-226,1994 Copyright© 1994ElsevierScienceLtd Printedin GreatBritain.All rightsreserved 0968-4328/94$7.00+ 0.00

Pergamon

0968-4328(94)E0007-C DEVELOPMENTS

Expected Contribution of the Field-Emission Gun to High-Resolution Transmission Electron Microscopy F. Z E M L I N

Fritz-Haber-Institut der Max-Planck-Gesellschaft Faradayweg 4-6, D-14195 Berlin, Germany

For more than two decades great efforts have been made to equip electron microscopes with a field-emission gun (FEG) as a beam source (Crewe and Saxton, 1971; Tonomura and Komoda, 1971). Its high coherence, due to high brightness and small source size, is recognized as an important advantage over the thermionic source, in particular for electron holography--the latter is not discussed in this paper. Early experimental results have confirmed these features (Munch, 1975; Ohtsuki and Zeitler, 1977). But many years had to elapse until the field emitter reached its technical maturity and was sufficiently robust to become applicable as a reliable beam source for the transmission-electron microscope (TEM). For some years now, electron microscopes equipped with cold- or heat-supported FEGs have been commercially available. These microscopes are, however, much more expensive than the conventional ones with a thermionic source. The electron microscopists in the various fields must weigh the pros and cons of these two kinds of beam sources. Some characteristic features of the beam sources with regard to their influence on the quality of high-resolution micrographs and diffractograms are discussed below. In particular, the advantages of the F E G for electron microscopy of radiation-sensitive biological specimens are discussed. With biological specimens it is desirable to image both the coarse and the fine structures, i.e. a very large space-frequency range from low to high resolution (3 A) is of interest. In material science, the problems are different; main interest lies in high point resolution ( < 2 A) and this can be achieved using a 200 kV electron microscope with an objective lens with a small spherical aberration coefficient. Also in this field a F E G is recommended if for analytical purposes the STEM-mode is required. Most biological specimens are weak-phase objects. The contrast at electron-microscopical imaging thus follows the theory of phase-contrast transfer. The 'ideal' phasecontrast transfer function (PCTF) of the TEM is described by the following equation: B(ct)=sin 2 r c ( ~ ~4-Af~2"]'22 J

spherical aberration coefficient, Afrepresents the change in defocusing. This P C T F is considered 'ideal' because it is valid under two ideal conditions. (1) The specimen should be a pure weak-phase object, and (2) the beam source should allow illumination of the specimen with a monochromatic plane wave. With such a parallel wave (fl = 0 in Fig. 1), the whole illuminated area is 'in phase'; the lateral coherence length r i would then be unlimited. In practice, however, the illumination is only partially coherent, i.e. each point of the specimen is illuminated by plane waves with varying directions and varying wave lengths. The variation in the beam direction leads to the so-called 'partially lateral coherence' and the variation in wave lengths leads to the so-called 'partially temporal coherence'. The partially lateral coherence is generated by the illumination aperture. The wave vectors of the illuminating beam impacting the specimen plane form a cone (see Fig. 1). The half aperture angle of this cone is called 'illumination aperture fl' which, like ri, can be considered a measure for the coherence fl = 2/r i. A rigorous calculation of the degree of coherence necessary and sufficient for phase contrast using the van Cittert-Zernike theorem is given by Born and Wolf (1975). They found for a circular illumination aperture the lateral coherence width r c = 0 . 1 6 r i. In principle it is

effectivesource

Z

specimen planW e~

X

(1)

Here, ~ is the diffraction angle of the spacing r; ct = 2/r. 2 is the de Broglie wave length of the electrons, Cs is the

Fig. 1. Illumination aperture fl and lateral coherence rc. r~=0.16 ;//3. 223

224

F. Zemlin

always possible to increase the lateral coherence arbitrarily by demagnifying the illuminating source and/or by magnifying the distance / (see Fig. 1). But the increase of the coherence obtained in this way leads to a decrease of the beam density, the latter being proportional to the second power of the illuminating aperture. Using a thermionic source for high-coherence illumination, therefore, entails a very low beam density which, in turn, requires extremely long exposure times. A higher coherence with sufficiently strong beam density can be achieved with a F E G due to its 1000 x higher brightness. In Table 1 a comparison of these two types of sources is described using typical values. Table 1. Comparison of the typical parameters of a thermionic source and a FEG Thermionic source Illumination aperture fl Lateral coherence width

r~=O.16"2/fl

Brightness b Solid angle oJ-27z(1-cos fl)

1.6.10 -4 rad 37/~ 10 6

Field-emission gun 5 ' | 0 - 6 rad 1200

A cm- z sr- ~

109 A cm- 2 sr- i

8- 10-8 sr

8- 10-11 sr

50 eA 2 sec 1

50 eA 2 sec- 1

09 ~-~ Trfl 2

Current density in specimen plane j = b - 09

compare the thermionic source with the F E G , their typical parameters are selected: thermionic source: / ? = 1 . 6 . 1 0 -4 rad AE/E= 1.6. 10-5; field emission g u n : / ? = 5 • 10 - 6 rad AE/E=8 l 0 - 6 . The P C T F s are calculated for two foci. First, at Scherzer focus Afl = x / ~ 2 (see Fig. 2a) and second at Af2 = 3 x / ~ A (see Fig. 2b). The spherical aberration coefficient C~= 1.0 mm, the chromatical aberration coefficient C~ = 1.0 mm, the acceleration voltage is U = 100 kV. In Fig. 2a, the inner curve belongs to the thermionic source, the outer curve to the FEG. It is apparent that the fading to high frequencies is significantly weaker using a FEG. However, at low spatial frequencies (large spacings) the gaps in the P C T F curves are identical for both illuminating sources. The microscope at this defocus has the effect of a high-pass filter; there is a lack of phase contrast from oo until about 20 A. The well known procedure of retrieving the low spatial frequencies of the specimen is defocusing. In Fig. 2b, the P C T F s at 3x~sA underfocus are shown. The gap at low space frequencies is more or less filled. (At stronger defocus the first m a x i m u m of the P C T F would shift further to lower space frequencies.) The advantage of the F E G is evident at high spatial frequencies (spacings at •

+1 Adjusting

the

same

current

density

(Table

1;

50 e / ~ 2 sec) in the specimen plane involves, in the case of

a F E G , a lateral coherence width that is about 32 times larger than that using a thermionic source. The influence of partially lateral coherence on the phase-contrast image was described by Frank (1973) by means of an exponentially decreasing function called 'lateral envelope'. This function dampens the ideal phasecontrast transfer function B towards the high spatial frequencies, i.e. reduces the resolution. The mathematical procedure is to multiply the ideal P C T F (1) with ez(c~,/?).

0

-1

T

0

1/16 1/8

1/5 l/z,

V3

1/2 1/r [ 1/~, ]

(a) +1 where/? is the illumination aperture. The partially temporal coherence is generated by the varying wave length of the electrons (energy spread of the electron beam). Monochromaticity would, of course, be optimal for the constructive interference used in phase contrast imaging. But in practice all beam sources emit electrons with varying energy. The effect of this energy spread on the phase contrast image is also described by an envelope of the P C T F , the so-called 'temporal envelope' e.~ (Hanszen and Trepte, 1971; Frank, 1976; Zeitler, 1990):

r,,(~t, AE/E) = exp(-- (Cc/)~)2(AE/E)2ct4).

0

-I

,~

0

1/16 I/8

l

I/5 V4

,

I/2 1/r D/,A]

(3)

Here, Cc is the chromatical aberration coefficient, AE/E is the energy distribution. Figure 2 illustrates how the effect of both the lateral and the temporal coherence attenuates the PCTFs. In order to

,

I/3

(b) Fig. 2. Phase~zontrast transfer-functions, inner curves due to thermionic source (dashed) outer curves due to field-emission gun. (a) Scherzer focus Af-x~,).. (b) Focus AJ=3v/~)~.

Expected Contribution of the Field-Emission Gun

225

about 3 A). While the phase contrast belonging to the movements occur in the specimen, which blur the image thermionic source is reduced to about 50% in this range, and thus reduce the resolution. This smearing effect is the PCTF belonging to a FEG is still about 85%. This caused by inelastic scattering which, in turn, breaks difference appears rather modest; in practice, however, molecule bonds and warms and charges the specimen. this is a very valuable advantage, because the contrast of These movements can be minimized by small-spot biological structures is in itself very weak. The goal is to scanning. The intermittent non-radiated margins of such retrieve information about the complete range of spatial small spots act like a stabilizing buffer. However, the frequency. For this reason it is necessary to record focus small-spot illumination is accompanied by an unaccepseries and to synthesize their information by image 'table reduction of the coherence of the electron beam. processing (Typke et al., 1982). Focus series recorded with This problem is solved by using an electron microscope an electron microscope with FEG result in artifact-free with a FEG. The size of the source of the field emitter is structure determination, because the reversal of the very small, so that specimen areas of about 100 A in contrast due to the oscillating PCTF can be corrected. diameter can be illuminated with very high coherence and The loss of information due to poor coherence, however, hence imaged with good phase contrast. Moreover, this advantage of the FEG permits the small-spot scanning cannot be remedied. An electron microscopist accustomed to working with with dynamic focusing on tilted specimens (Zemlin, 1989). a microscope of poor coherence will perhaps in the This procedure is useful for three-dimensional structure beginning be confused by the unusually strong Fresnel analysis. It is well known that the difficulties in electron interferences. He will even observe so-called 'delocalizations' which, however, as Fresnel artifacts, are eliminated microscopy increase with high resolution (imaging small by adequate image processing of focus series (Otten and spacings). It is also difficult to record diffraction patterns with high resolution (diffraction at large spacings), but a Coene, 1993). A serious problem with biological specimens is the high microscope equipped with a FEG is also well suited for radiation sensitivity. The structures often disintegrate accomplishing this task, yielding fine-structured diffracduring the exposure at doses at low as 1 e/A2 (Stenn and tion patterns. If, for example, the illumination aperture Bahr, 1970). Hence the dose for imaging must be kept f l = 5 • 10 - 6 rad, then a diffraction resolution r=0.37 gm minimal, i.e. no illumination dose should be wasted by is obtained (U= 100 kV). The limiting condition is ~t> 2fl poor optics. For this reason as well, the electron with ~ = 2/r (see Fig. 3). The spacing 0.37 gm adjoins the microscope with a FEG is recommended. range of light-wave length, i.e. there is no gap between light- and electron diffraction. The FEG also allows special specimen-preserving imaging procedures, e.g. 'small-spot scanning' (HenderThe high-quality diffraction is particularly important son and Glaeser, 1985; Downing, 1988). The problem is because in electron crystallography the amplitudes of the that during the exposure of radiation-sensitive specimens, structure factors are retrieved from the electron-optical

/~ illumination

specimen

k

r

_ _

lion angle of spacing r

///111\\\

//1111\\\

=

/!1l -1

0

aperture

°:

+

+1

Fig. 3. Diffraction resolution depending on illumination aperture ~ > 2/7.

226

F. Zemlin

diffractograms and the corresponding phases from the images (Unwin and Henderson, 1975). It seems that the expectations of electron microscopists with respect to the FEG are well founded even for reaching atomic resolution for macromolecules (Zhou and Chiu, 1993). Acknowledoements--The author is grateful to S. Herrmann and R. Schmidt for providing the Computer plots.

REFERENCES Born, M. and Wolf, E. (eds.) 1975. Principles of Optics. Pergamon, New York.

Crewe, A. V. and Saxton, G., 1971. Proc. 29th Ann. EMSA Conf. 12, 12-13. Downing, K. H., 1988. Ultramicroscopy, 24, 387 397. Frank, J., 1973. Optik, 38, 519-536. Frank, J., 1976. Optik, 44, 379-391. Hanszen, K. J. and Trepte, L., 1971. Optik, 32, 519 538. Henderson, R. and Glaeser, R. M., 1985. UItramicroscopy, 16, 139-150. Munch, J., 1974. Optik, 43, 79-99. Ohtsuki, M. and Zeitler, E., 1977. Ultramicroscopy, 2, 147 148. Otten, M. T. and Coene, W. M. J., 1993. Ultramicroscopy, 48, 77-91. Stenn, K. and Bahr, G. R., 1970. J. Ultrastruct. Res., 31, 526-550. Tonomura, A. and Komoda, T., 1971. Proc. 29th Ann. EMSA Conf. 12, 6-7. Typke, D., Hegerl, R. and Kleinz, J., 1982. Ultramicroscopy, 46, 157 173. Unwin, P. N. T. and Henderson, R., 1975. J. molec. Biol., 94, 425~,40. Zeitler, E., 1990. In: Biophysical Electron Microscopy, Hawkes, P. W. and Valdre (eds.). Academic Press, New York, pp. 289-308. Zemlin, F., 1989. J. EM Technique, 11, 251-257. Zhou, Z. H. and Chiu, W., 1993. Ultramicroscopy, 49, 407~416.