Measurement of the top bottom effect in scanning transmission electron microscopy of thick amorphous specimens

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1 (3 Journal of Microscopy, Vol. 100, Pt 1,January 1974, pp Received 1 January 1973; revision received 29 June 1973 Measurement of the top bottom effect in scanning transmission electron microscopy of thick amorphous specimens by P. GENTSCH, H. GILDE and L. REIMER, Physikalisches Institut der Univusitat Miinster, W. Germany, Elektronenmikroskopische Abteilung SUMMARY In Scanning Transmission Electron Microscopy (STEM) details at the top of thick specimens can be imaged with a better resolution than those at the bottom, because the scanning electron probe is broadened by multiple scattering. For quantitative measurement we used a test specimen consisting of a substrate film with an island-structured indium film and coated with polystyrene spheres of different diameters up to 1.1 pm. The fine detail contained in the indium film was observed and the beam broadening was that caused by the polystyrene spheres. This specimen was imaged with the spheres both above and below the layer, in a JEOL loob electron microscope with a scanning device. Electron energies from 20 to 100 kev were used. Images with the sphere below show a higher resolution than those with the sphere above and also those of conventional electron microscopical images at 100 kv and 200 kv. The broadening of the edges on the photographic film was recorded with a microdensitometer. The results can be compared with theoretical calculations by a Monte Carlo method. There is a good agreement with the experiments if one uses an effective aperture obtained by transmission experiments. INTRODUCTION Scanning Transmission Electron Microscopy (STEM) will be of use for thick specimen layers because at 100 kv in conventional Transmission Electron Microscopy (TEM) the resolution is limited by the chromatic aberration of the objective lens and the energy losses of the electrons passing through the specimen. The first successful experiments have been made with the TEM in the STEM mode (Koike et al., 1971; Nauta & Thompson, 1972; Thieringer, 1972). These show that there is an increase in resolution for specimens in the range of 1-2 pm thickness. This is because there is no imaging lens system below the specimen and therefore no effect due to chromatic error. The limitation in the STEM mode is caused by the diameter of the electron probe and by multiple scattering of the electrons inside the specimen. The latter results in a broadening of the electron beam with increasing penetration depth. This was postulated also by Hashimoto (1966) to explain some effects in the TEM of crystalline specimens and was called the top bottom effect (TBE). For the case of STEM in particular this 81

2 P. Gentsch, H. Gilde and L. Reimer effect causes a higher resolution for structures lying on the top of a specimen because this is scanned by the unbroadened beam; whereas details at the bottom are scanned by the broadened beam and are imaged with a lower resolution. Theoretical calculations of the TBE were made (Reimer, Gilde & Sommer, 1970; Reimer, 1972) using Monte Carlo methods. These also gave the dependence of effective electron beam broadening on the aperture. In this paper we report experiments to test this theory. EXPERIMENTAL METHOD In order to obtain the pure TBE, we used the following simple specimen structure. A thin indium film was evaporated on a carbon coated formvar supported film. The indium layer consists of small islands of flat crystals having sharp edges. This film was coated with some polystyrene spheres of different diameters simulating a typical biological specimen with that thickness. If the specimen is orientated in such a way that the spheres lie below the film, the indium islands are scanned by the unbroadened beam of about 5 nm diameter at 100 kv and 10 nm at 20 kv (Fig. la). These diameters of the scanning electron (a j Scanning \ / electron probe Fig. 1. Specimen structure and electron beam broadening in the two positions with the sphere (a) below and (b) above the indium layer. beam are obtained with a hairpin cathode. After inverting the specimen, and focusing again on the indium islands, the spheres lie above the film and we observe the additional broadening of the beam inside the sphere (Fig. lb). This effect is demonstrated in Fig. 2 showing STEM images with a 1.1 pm sphere (a) below and (b) above the indium layer. The edges of the crystals appear more diffuse in Fig. 2b. The very small indium crystals resolved in (a) cannot be detected in (b). For comparison, the same sphere is imaged with the conventional TEM mode at 100 kv in Fig. 2c. The much lower resolution caused by the energy losses of the electrons within the sphere demonstrates the advantage of the STEM mode in this range of thickness. In the TEM mode, contrary to STEM, the TBE causes a better resolution for details at the bottom of a specimen. However, the chromatic error is larger than the TBE and is also the same in the two positions of the sphere. 82

3 Top bottom eflect in STEM Therefore only one image with the sphere above the specimen is shown in Fig. 2c and d. The additional loss of resolution for details at the top of the specimen caused by the TBE should be more easily observed in the range MeV. At these higher electron energies the broadening by multiple scattering becomes comparable to or larger than the disc caused by the chromatic error (Reimer, 1972). Experiments are in progress to detect the small TBE differences in the TEM mode at 100 kv. Comparing the STEM and TEM images in Fig. 2, we notice an improved contrast range in STEM, because there is a S-shaped transfer function between video signal and viewing screen brightness. Figure 2a-c was obtained using a JEOL loob microscope with a scanning attachment. Figure 2d shows an image of the same polystyrene sphere above the specimen layer obtained with a JEOL 200A microscope at 200 kv. In comparison with Fig. 2c, a decrease of chromatic error with higher voltage can be seen. However, the sharpness of the indium edges has not reached that of the STEM mode at 100 kv. For example in STEM mode with a sphere of 1-1 pm diameter and 100 kv we measured a beam broadening of about 22 nm (see definition of r1,2 below). In TEM mode, however, at an objective aperture u = 1.75 x lo-' rad we obtained 60 nm at 100 kv and 28 nm at 200 kv (u = 2.2 x rad). Figure 3 shows a special arrangement of polystyrene spheres in the SEM and STEM mode. The SEM image (Fig. 3a) obtained by detecting the secondary electrons which are emitted at the top surface of the specimen shows, that one of the six spheres lies on the top of the other five. The SEM image was obtained at a primary energy of 100 kev and therefore shows more noise than for primary energies in the range of 20 kev. Figure 3a shows the influence of charging of the polystyrene spheres. But this charging has only an influence on the signal of the secondary electrons not on the signal of the transmitted electrons as confirmed by putting a conductive coating on the spheres. In the STEM image of the same sphere arrangement (Fig. 3b) we observe less resolution below the sphere in the middle than below the outer ones. One has to consider that there is not only a spatial broadening, but also an angular broadening at the bottom of the uppermost sphere. Therefore a further broadening of the scanning beam occurs when the electrons travel from the bottom of this sphere to the indium layer. QUANTITATIVE MEASUREMENT OF ELECTRON BEAM BROADENING To get quantitative information about the loss of resolution caused by the TBE, we made several exposures of the indium crystals and compared the sharpness of the edges seen through the spheres with that beside them. The parameters which were varied are the energy of the primary electrons (20,40,60,80 and 100 kv), the diameter of the spheres (0.234,0-481,0-71 and 1.1 pm) and the diameter of the objective diaphragm (30 pm, without diaphragm). The evaluation of the sharpness of the indium edges was made from microdensitometer records of the photographic negatives. The broadening without TBE is mainly caused by the diameter of the electron probe at the specimen. The current density within the unbroadened beam can be described by a Gaussian distribution j(r) = j o exp K-r/r0)21. (1) If the error disc of the pure multiple scattering is regarded as a Gaussian distribution with rs instead of ro, the current density in the broadened beam can also be described by a Gaussian distribution having the total characteristic parameter rt : rt2 = ro2 + r:. (2) 83

4 P. Gentsch, H. Gilde and L. Reimer Fig. 2. Images of an indium layer and the same polystyrene sphere with 1.1 pm diameter in the following operation modes: (a) 100 kv, STEM, sphere below the indium layer; (b) 100 kv, STEM, sphere above; (c) 100 kv, TEM, sphere above, 01 = 1.75 x rad; (d) 200 kv, TEM, sphere above, 01 = 2.2 x rad.

5 Top bottom effect in STEM 85

6 P. Gentsch, H. Gilde and L. Reimer 86 Fig. 3. (a) SEM, and (b) STEM images of spheres at 100 kv.

7 Top bottom effect in STEM Taking a photometer record in the x-direction from the edge of an indium crystal one has to expect an intensity record Z(x) (Fig. 4), which can be described by integrating j(xyy) in the y-direction from the limits - co to + co and in the x-direction from 0 to x: I(x) = j: s I 2 AXY y)dxdy = { J j, exp ( - (x2 + y2)lro2)dxdy = Io(42>ro2+(X/~o> = Zo+(x/ro>. (3) +(x/r,) is the Gaussian error function with lim,,,+(x/r,) = 1. Z(x) gives the number of electrons within a Gaussian distribution which have an x-coordinate lower than x (dotted area in Fig. 4). 1 I Fig. 4. Integration of a Gaussian distribution (equation 3). We now define a characteristic width xliz of the Z(x) curve, which is chosen in such a way that half of all electrons in the Gaussian distribution fall between the marks x = _+0.5x1,, (Fig. 4). This means: (~I2>ro2+(X1,2Ir*> = I012 = (a/4)ro2. Solving for x1 one gets x1 rs = 0.48 To. For a Gaussian distribution x1 is proportional to To. The values of x,, without beam broadening are obtained from intensity records of the indium crystals beside the polystyrene spheres and the values xt, 1,2 with beam broadening from records of crystals below the centre of the spheres. Analogous to equation (2) we have xt2, 112 = xo2, x,2, 112. (4) One now can calculate the broadening xs, caused by the TBE from the experimental values x,, 112 and xt, 2. In the following xs, 112 is attributed to x ~,~. The results of these measurements are shown in Fig. 5 in which the values x1 are plotted as a function of sphere diameter, t, with the accelerating voltage as a parameter. In order to avoid the sharpness of the indium edges having an influence on x1,2 many measurements were made from different crystals for one data point in Fig. 5. The dependence of the diameter of the objective diaphragm could not be detected, although Monte Carlo calculations show that a very strong effect should be expected (section D). 87

8 P. Gentsch, H. Gilde and L. Reimer Sphere diameter f (pm) Fig. 5. Observed broadening of an electron probe by multiple scattering as a function of specimen thickness (density p = 1.05 g/cm3) and beam voltage. +, 20 kv; a, 40 kv; u, 60 kv; 0, 80 kv; 0, 100 kv. In addition to the parameter x~,~, the TBE can also be discussed in terms of rl;z which is defined in such a way that half of the transmitted electrons fall into the area m-1,z2 around the direction of the incident probe. One can easily show that the relation between and xli2 is given by rliz = 1.75~~~~. (5) COMPARISON WITH MONTE CARL0 CALCULATIONS The trajectories of 50,000 electrons passing through specimens of different mass thickness pt (p density, t thickness) have been simulated by a Monte Carlo program (Reimer et al., 1970; Reimer & Gilde, 1969). The electrons which started in a direction normal to the surface, and with coordinates (x, y, z) = (0, 0, 0) are distributed over a certain area at the bottom of the specimen. This local distribution can be characterized by the distance xli2 described above (Fig. 4). The value of xli2 will decrease with decreasing observation aperture a, because the probability of large angle scattering is greater among the highly displaced electrons. The results of the Monte Carlo calculations with different primary energies can be plotted in one diagram by using reduced parameters m for the mass thickness and for the beam broadening. IY~, characteristic angle (f(~?~) = f (8 = 0")/2, f(8) scattering amplitude); A = xj(1 + n), total mean free path between elastic and inelastic scattering events ; x,, mean free path for elastic scattering; n = uinel/uel, ratio of inelastic and elastic total cross sections (n = 2-5 as a value for carbon). 88

9 Top bottom effect in STEM Information about x, and 8, can be obtained by electron transmission experiments (Reimer & Sommer, 1968) and fitting the experiments to Lenz theory (Lenz, 1954). We used the following values from measurements on carbon: Eo (kev) xr (pg/cm2) , rad) Results of the Monte Carlo calculations are plotted in Fig. 6b. It can be seen from this figure that to a first approximation, is proportional to m and therefore from equation 6: x1/2 pt2 = (pt> p. 9 rn m i rn Reduced thickness rn., Fig. 6. Beam broadening in reduced parameters; (a) experiment and (b) Monte Carlo calculations. f, 20 kv; 40 kv; o, 60 kv; 0, 80 kv; 0, 100 kv. 89

10 P. Gentsch, H. GiIde and L. Reimer At equal mass thickness pt electron beam broadening will thus only be important for materials with low density p, like aluminium, or biological sections. The results of experimental TBE values of Fig. 5 are plotted in Fig. 6a with reduced parameters. At first sight there seems to be only slight agreement between Fig. 6a and Fig. 6b. Firstly the Monte Carlo calculations show a strong dependence on the size of the objective diaphragm, whereas experimental values are independent within the accuracy of measurement. Secondly, the whole shape of the 5,,,(m) curve through the experimental points of Fig. 6a does not correspond to any one of the Monte Carlo curves in Fig. 6b. For this reason the effective aperture aeff in the STEM mode must be independent of the objective diaphragm. However it must depend on the specimen thickness and the energy of the primary electrons. The first point is to be expected, because in the STEM mode a large illumination I I c P 5 o c-,o-l t- TEM 10 * 10-3 Aperture a 10-I rod Fig. 7. Electron transmission measurements of the effective objective aperture aeff in STEM at 100 kv. aperture (18 = 2 x rad) is used. Furthermore the focal length of the objective lens is much shorter than in TEM (with the specimen at the same position) and therefore the first diffraction image is no longer in the plane of the objective diaphragm. As far as the second point is concerned, at the moment we do not know the reason for this dependence of aeff upon specimen thickness. Perhaps it is important that in STEM mode, the intermediate lens is used, corresponding to a 9000-fold TEM magnification, to image the transmitted electrons through the pole pieces onto the detector below the viewing screen. By this an unknown selection of scattering angles can occur. In order to establish the value of aeff, we performed electron transmission experiments with the same specimen as in the TBE measurements, but without an indium layer. We measured the ratio T = j/jo of current densities through the sphere (j) and beside it (jo) at 100 kv as a function of three sphere diameters and three objective diaphragms in the TEM mode (illumination angle rad). One can obtain an accurate value of the objective aperture by taking a selected area diffraction diagram of an evaporated gold film and further exposure of the photographic plates with the diaphragm. The TEM calibration curves obtained 90

11 Top bottom efsect in STEM by transmission experiments were used to determine the effective STEM aperture. The values of T in STEM were measured with the same spheres and diagraphragms as in TEM above using a Y-modulation linescan across the sphere (Fig. 7). As expected, transmission experiments show that T and therefore the effective observation apertures in the STEM mode are nearly independent of diaphragm size, but increase with decreasing thickness. This method of obtaining effective apertures by transmission is justified because the same Monte Carlo calculations lead to the right value of transmission. The transmission at reduced thickness my reduced aperture a/s, and different electron energies can also be plotted in one diagram like that of the reduced beam broadening (1/2 (Fig. 8a, b in Reimer et al., 1970). In Fig. 8, the beam broadening parameter xllg is plotted as a function of sphere diameter t at 100 kv. The heavy curve represents the experimental results, the other curves Monte Carlo results for the indicated apertures. The three points are Monte Carlo results at the effective apertures obtained by interpolation of the thin curves. In this way we get a good agreement between theory and experiment. 15'[ - Experiment / o Sphere diameter I (prn) Fig. 8. Comparison of experimental beam broadening (heavy curve) and Monte Carlo results (3 points) when using aeff from Fig. 7. The thin curves are Monte Carlo results with the indicated apertures. ACKNOWLEDGMENTS We should like to thank the Deutsche Forschungsgemeinschaft for the loan of a JEOL loob microscope and Mr Schwaab who helped us to take the 200 kv micrographs on a JEOL 200A. References Hashimoto, H. (1966) Proc. AMU-ANL Workshop on High Voltage Electron Microscopy, 68. Koike, S., Ueno, K., Suzuki, M., Matsuo, T., Aim, S. &z Shibatomi, K. (1971) High resolution scanning device for the JEM-IOOB electron microscope.jeo1 News, 9e, No. 3,

12 P. Gentsch, H. Gilde and L. Reimer Lenz, F. (1954) Zur Streuung mittelschneller Elektronen in kleinste Winkel. Z. Naturf. 9a, 185. Nauta, R. & Thompson, M.N. (1972) A new scanning electron microscope attachment for the Philips EM 300G. Proc. Fifth Eur. Congr. Electron. Microsc., Manchester, 46. Reimer, L. (1972) Physical limits in transmission scanning electron microscopy of thick specimens. Proc. Fifth Ann. SEM Symposium, 197. IIT Research Institute Chicago. Reimer, L. & Gilde, H. (1969) Die Verbreiterung des Elektronenstrahls durch Mehrfachstreuung und ihre Bedeutung fur die Raster-Elektronenmikroskopie. Beitr. elektronenmikroskop. Direktabbildung von Oberflachen, 2, 81. Reimer, L., Gilde, H. & Sommer, K.H. (1970) Die Verbreiterung eines Elektronenstrahles ( kv) durch Mehrfachstreuung. Optik 30, 590. Reimer, L. & Sommer, K.H. (1968) Messungen und Berechnungen zum elektronenmikroskopischen Streukontrast fur 17 bis 1200 kev Elektronen. Z. Naturf. 23a, Thieringer, H.M. (1972) Transmission scanning electron microscopy and energy analysis with the Siemens Elmiskop 101. Proc. Fifth Eur. Congr. Electron Microsc., Manchester,