Aperture contrast in thick amorphous specimens using scanning transmission electron microscopy

Ultramicroscopy 1 (1975) 127-136 © North-Holland Publishing Company

APERTURE CONTRAST IN THICK AMORPHOUS SPECIMENS USING SCANNING TRANSMISSION ELECTRON MICROSCOPY**

David J. SMITH School o f Physics, University o f Melbourne, Parkville, Victoria, 3052, Australia

and Department o f Physics, Arizona State University, Tempe, Arizona 85281, USA

and

J.M. COWLEY Department o f Physics, Arizona State University, Tempe, Arizona 85281, USA

Received 7 May 1975

The contrast observed in thick amorphous specimens using a scanning transmission electron microscope (STEM) can be considerably improved by the use of an optimum collector aperture angle. The size of this angle can be calculated by con- sidering the variation of electron current transmitted through the specimen as a function both of the specimen thickness and of the angle of collection subtended at the specimen. Typically these calculations predict optimum angles to be several times the half-width of the elastic scattering distribution, often 10 -1 rad or more.

Observations of biological sections of up to 2/am in thickness using scanning attachments of commercial transmission microscopes have verified these results at beam voltages of 50, 100 and 200 kV. Wide angle convergent beam diffraction patterns were used to give accurate values of the effective angles represented by the various collector apertures. Once the linearity of the detector-amplifier system had been established, operation in a line modulation mode enabled quantitative measurements to be made of the image contrast. Such measurements also offer a quick effective method of comparing electron beam penetrations.

1. Introduction

It is well known that a scanning transmission electron microscope (STEM) offers considerable advan- tages over the conventional transmission electron microscope (CTEM) for the study of thick specimens [ 1-5,17]. For such a specimen multiple elastic and inelastic scattering events will result in both an angular broadening and a spread in energy o f the electron beam emerging from its bo t tom surface. In the CTEM the angular broadening results in the " t o p - b o t t o m effect" as proposed by Hashimoto [6] whereby detail near the bo t tom surface of the specimen is imaged with bet ter resolution than detail near the top surface. In the STEM it leads to a "reverse" top-bo t tom effect as predicted and demonstra ted experimental ly by Reimer and his associates [1,4] with the top surface being imaged with more clarity. The energy spread of

** Part of this work was reported at the 9th Ann. SEM Sym- posium, IITRI, Chicago (April 1975).

the beam results in further loss of resolution and contrast in the CTEM due to chromatic aberration in the post ,specimen lens system. In the STEM this limitation is avoided and, according to the calculations of Sellar and Cowley [2] for materials of low atomic number, this could lead to significant increases of factors of 3 to 4 in contrast, relative to CTEM, for a specimen of about 1/am thickness at 100 kV, or increases

in penetrat ion of factors of 3 to 4 for equivalent resolution in a given material. The advantage decreases slowly with voltage but is still substantial at 1 MV. Similar results have recently been obtained by the more elaborate calculations of Groves [17].

The Reciprocity Principle [ 7 - 9 ] has frequently been invoked for the interpretat ion of STEM images

[10,11]. The normal TEM mode of operat ion corre- sponds to the use of a small detector aperture angle in STEM and in this situation one may observe the familiar phase contrast imaging of thin specimens and the dynamical diffraction contrast for defects in crys- tals [11 ].

127

128 D.J. Smith, J.M. Cowley / Aperture contrast in thick amorphous specimens using STEM

For very thick specimens the use of a small detector aperture leads to the same difficulties of weak images as for CTEM because the transmitted electrons are spread over a broad angular range by multiple scattering. It is difficult to avoid this limitation with CTEM since for thick specimens the phase-contrast modes are no longer effective and the predominating form of image contrast is aperture contrast arising because scattered electrons are stopped by the objective aperture.

It is the object of this paper to demonstrate through theoretical calculations and confirmatory experimental evidence that with STEM the difficulties of ob- taining useful contrast for thick amorphous specimens may be largely overcome and that contrast can be optimized by the use of the appropriate, large detector aperture angles.

2. Theory and calculations

In passing through a thin layer of specimen material an incident electron beam is scattered both elastical- ly and inelastically. For the predominant inelastic scattering processes (plasmon or single-electron excita- tions) the angular distribution of scattered electrons is very much narrower than that for elastic scattering and the angular distribution of the transmitted electrons can be assumed to be due to elastic scattering only.

There will be wide-angle inelastic scattering due to the interactions of electrons with phonons but for amorphous materials this will be compensated to a good approximation by the decrease in purely elastic scattering described by multiplication of the atomic scattering factors by a Debye-Waller factor.

The angular spread of electrons passing through a specimen may then be described in terms of the average atomic scattering factors for stationary atoms f(u), where, in the usual small angle approximation, u is the two-dimensional reciprocal space vector, components u, o, and magnitude U = lul = (2 sin 0)/?, and 0 is half the scattering angle.

For an incident beam of angular distribution h(u), the angular distribution after transmission through a layer of thickness Az is then

gl(u) = h(u) * gO(u), (1)

where

gO(u) = exp (-taAz} 5(u) + Az f2(u) (2)

and * represents a convolution integral. We have here ignored the fluctuating component

of the angular distribution associated with the correla- tion in atom positions, i.e. we have assumed a com- pletely random distribution of atoms. Such an assumption is justifiable in a multiple-scattering situation for which the fluctuating components tend to cancel out.

Because a thin specimen is an almost pure phase object for electrons it can be assumed that all electrons are transmitted, so that fgo(u)du = 1 and the absorp- tion coefficient/1, for the unscattered beam, is given by

u =ff2(u) du. (3)

Taking the Fourier transform of (1) then gives

Gl(r)=H(r) Go(r)

= H(r) [exp {-taAz) + AzP(r)] , (4)

where P(r), Go(r ) and H(r) are the Fourier transforms off2(u) , gO(u) and h(u) respectively.

The effect of transmission through successive layers of thickness Az is represented by successive convolu- tions of ( I ) with gO(u) or successive multiplications of (4) by Go(r ). For n slices we have

Gn(r ) = H(r) [exp {-taAz} + AzP(r)] n .

In the limit that n tends to infinity and Az tends to zero so that n Az = t, where t is the specimen thickness, we obtain

Gt(r ) = H(r) exp {-tat} lim [ I + Az P(r)] n r l . - ¢ . o o

= H(r) exp {t[P(r) - ta]}. (5)

The inverse Fourier transform of Gt(r ) then gives the angular distribution, gt(u), which may be calculated from the known form of f (u ) using suitable approxi- mations.

For a collector aperture which transmits or ex- cludes all electrons with lul ~< U 0, the bright-field and dark-field image signals are given respectively by

uo '2_ I B = J 27rUgt(U) dU, I O = f 2rrUgt(U) dU.

t~

o Vo (7)

D.J. Smith, J.M. Cowley/Aperture contrast in thick amorphous specimens using STEM 129

1.0

4.0

D.E :~" "-,, / \

/ T-5 "

I I I I 1 2 ,I ' ~ Uo/U,

"" ~ / B.E

T - 5 / / ~ C o n t r a s t dl/dT xlO/

~ /. . . . . . Contrast/Noise

Fig. 1. Values of the "contrast" dl[dT and the ratio of contrast to electron noise (dl]dT)[11/2 plotted for bright field and dark field STEM images as a function of Ul/Uo, the ratio of the collector aperture Size to the angular half width for single elastic scattering. The curves are given for various values of the thickness T measured in units of the mean free path for. elastic scattering.

The quantity of interest is the variation of the image signal with variation of the specimen thickness, t, or with variation of the scattering power of the specimen, equivalent to a variation of t. For bright-field this is given by

Uo

dlB/dt = f 2rrU (d/dt gt(U)} dU, (8) 0

or, putting

gt(U) = f H(r) exp (t[P(r) -/a]} 27rr JO(2nUr) dr, o

we obtain, by inverting the order of integration,

dlB/dt = 27rU 0 : H(r) [P(r) - / a ] 0

× exp {t[P(r) -/a]} Jl(2rrUor) dr. (9)

As a measure of the contrast of the image we may then consider the relative change of signal strength

(dlB/dt)/1 a for bright field or, correspondingly (dlD/dO[I D for dark field. However, for STEM these ratios do not normally give a useful measure of the performance of the instrument since it is customary to enhance the contrast for particular portions of the specimen which are nearly uniform in thickness by subtracting an arbitrarily selected fraction of the average intensity. The limitation for such contrast enhancement is set by the statistical fluctuctuations of the electron beam current which may be assumed to be proportional to 1112. Hence it may be preferable to

the ratios (dlB/dt)]I 1/2~ and (dlD/dt)/1112 as indi- use

cations of image quality. Values of these ratios and of the differentials

dlB/dt and dlD/dt , are plotted in fig. 1 for various values of specimen thickness T, measured in units of the mean-free path for elastic scattering i.e. T =/at. The abscissa is the half-angle of the collector aperture, U0, measured in terms of the characteristic scattering angle U 1 for the elements present. For the purposes of the calculation it was assumed that f2(u) could be represented by the gaussian exp {-U2/U2}. It has been assumed that the angular distribution of the incident beam, h(u) is relatively narrow so that we may put H(r) = 1. This represents a good approximation, especially for thick specimens.

The curves of fig. 1 may be regarded as universal curves, applicable to all compositions of the specimen and all electron wavelengths, to the extent that the f2(u) curves for all elements may be approximated by the same gaussian shape. It is known, of course, that a gaussian is not a good approximation for most f2(u) curves and that the shape of t h e f 2 curve does vary considerably with the atomic number and also the de- gree of ionization and bonding of atoms. However, the main purpose of fig. 1 is to indicate the most desirable aperture size to be used for a particular specimen and it is seen that the aperture size is not very critical because the maxima or minima of the curves are very broad. Hence this figure may serve its purpose reason- ably well for a wide range of specimens.

Since it is assumed that all electrons incident on the specimen are transmitted, it follows that the values of dlB/dt and dlD/dt tend to zero as U 0 tends to infinity and the curves in fig. 1 are symmetrical about zero since dlB/dt + dlD/dt = O.

The same aperture size will give the optimum contrast for both bright and dark field. For this aperture

130 D.J. Smith, J.M. Cowley/Aperture contrast in thick amorphous specimens using STEM

size the number of electrons in the bright and dark- field images will be approximately equal. Hence the difficulty encountered in CTEM, that images of thick specimens are very weak, is avoided.

When the ratio (d l /d t ) / I 1/2 is taken, it is seen that the optimum aperture size suggested for bright field imaging is somewhat less than for dark-field. The extent to which this indication should be followed in practice will depend on factors of experimental con- venience.

3. Experimental details

In experiments designed to verify these theoretical predictions it is necessary to correlate determinations of the composition and thickness of specimens, the measurement of detector angles, and the actual measurement of contrast. Observations were made both with a JEM IO0-B electron microscope with an ASID scanning attachment at Arizona and with a JSEM-200 microscope at the Australian National University, Canberra. The JEM IO0-B has a top-entry goniometer stage and the level of the specimen within the microscope could be adjusted by use of a small annular spacer in the specimen holder. The JSEM-200 has a side-entry stage and adjustments to the specimen height can be made by means of a small screw provided outside the column. This latter instrument can be op- erated at 50, 100, and 200 kV, and is very convenient for comparing the changes in penetration when operating in the STEM mode as the accelerating voltage is raised.

The majority of observations were made on thick biological specimens which approximate the idealized amorphous specimens for which the calculations were made. The material was fixed with osmium tetroxide, dehydrated, embedded in epoxy and then sectioned using an LKB Ultrotome ultramicrotome to nominal thicknesses of 1 and 2 lam. It is well known that the preparation of a biological section by use of a micre- tome involves an inherent uncertainty in the estimation of thickness of possibly twenty percent or more. Also when a specimen is placed in the vacuum of a microscope and irradiated with the electron beam, a mass loss of an unknown extent may occur. The resul- tant variability of results was illustrated in our experiments with other samples of the same nominal thick-

ness. Rat liver sections nominally 1/am thicJ~ showed approximately the same scattering as the marine vibrio specimens, but a section of elephant gut tissue, also nominally 1/am thick, appeared to have roughly twice the actual thickness. Microscopists may well be inter- ested in the question of maximizing penetration and/ or contrast for "real" specimens of this sort rather than for some idealized specimens. However in at- tempts to obtain some quantitative data, and to avoid these complications, some initial experiments have been made on evaporated films of A1, Cu and Au, for which the thickness could be determined with reasonable accuracy by use of a vibrating quartz crystal thickness monitor. The films were formed by evapora- tion on to room-temperature substrates and appeared to be near-amorphous. No diffraction spots or rings could be discerned, and a directly transmitted beam could not be distinguished for the specimens used.

The normal objective aperture strip of the TEM was used to provide the detector apertures when operating in the STEM mode. The effective collection angles could not be deduced from simple geometric consider- ations because both specimen and the apertures were immersed in the magnetic field of the objective lens and the excitation of this lens was increased by varying amounts for operation in the STEM mode.

The measurement of collector aperture sizes was made as follows. When the incident beam is focussed on a single crystal with the scan switched off, using a large illumination aperture, a wide angle convergent beam electron diffraction (WACBED) pattern is formed [12]. The geometry of the line patterns pro- duced is similar to that of Kikuchi lines. The identifi- cation of line pairs whose angular separation is known then provides a reference for measurement of the detector aperture angles. A typical pattern, shown in fig. 2, is taken from a silicon wedge at 100 kV. Multi- ple exposures, first with the specimen in place and then with the various (objective) detector apertures in place, enable all relevant data to be recorded on a single plate. In similar fashion the illumination angles due to the smaller condenser apertures can also be measured. For determination of the experimental curves at higher angles, especially for thicker specimens, it was found necessary to increase the physical dimensions of the collector apertures. For exarnlale with the JSEM-200 the aperture sizes used were nominally 100,200,300 and 400 tam in diameter.

D.J. Smith, J.M. Cowley / Aperture contrast in thick amorphous specimens using STEM 131

Fig. 2. Wide angle convergent beam diffraction pattern from a silicon wedge at 100 kV showing an (013) type zone axis and fea- turing 400 and 13i type K-line pairs. Superimposed are the outlines of 20, 40, 60, and 120 ~m objective (collection) apertures. The largest restricting "aperture" is the bottom pole-piece of the projector lens.

A problem faced using a STEM attachment of a CTEM is that the post-specimen lenses provide a physical restriction to the maximum effective collection angle for electrons reaching the electron detector, which in most cases is below the projector lens. Some increases in this maximum can be obtained by low- ering the specimen to decrease the focal length of the objective lens. However in practice a far greater gain comes from making use of the unique electron-optical configuration of a "second-zone" lens. By positioning the specimen close to the region where simultaneous CTEM and STEM operation becomes possible (in a symmetrical Riecke-Ruska lens this would be in the center of the lens), WACBED patterns showing angles as large as 2 X 10 -1 rad have been seen. However, because of distortion at large angles, and the difficulties of alignment of the lenses and calibration of angles in

this case, some compromise has to be made. For example, in the JEM 100-B a spacer in the specimen holder of 0.64 mm thickness lowers the specimen to the "symmetrical" position whereas a spacer of 1.00 mm was used for the actual experiments. For both the JEM 100-B, and for the JSEM-200, a maximum collection angle of about 1.2 × 10 -1 rad was used, although in some cases of interest larger angles would have been preferred. Of course, for a specially designed STEM, without post-specimen lenses to ob- struct the beam, such difficulties could be avoided.

Judgements of the relative contrast and "quality" of series of micrographs will inevitably be quite sub- jective, especially when adjustments to the amplifier and/or display systems can drastically affect the images obtained. Instead, a line-modulated display mode was used as this enables quantitative measurements of

132 D.J. Smith, J.M. Cowley /Aperture contrast in thick amorphous specimens using STEM

the contrast to be made. First the linearity of the detector-amplifier-display system to the incident electron beam intensity was established, as follows. With the lens currents, the video amplifier and display systems set up as though ready to take a scanning picture, the line- (or deflection) modulation mode was chosen. With no specimen present, a composite picture was then taken from the screen of the display monitor showing the various signal heights as the beam current from the gun was increased. A graph of beam current against monitor signal height showed no departure from linearity except for currents well in excess of the 50/aA normally used for STEM operation.

4. Results and analysis

The series of micrographs shown in fig. 3 was taken without alteration to any part of the detector-amplifier-display system except for selection of the differ- ent detector apertures. A change of contrast of various features of the specimen over the range of collection angles is apparent. However the large variation in signal levels with aperture size, which results in under- exposure or over-exposure for small or large angles, then confuses the estimation of picture quality. Fur- thermore, manipulation of amplifier gains, brightness levels etc. can give pictures of seemingly similar quali-

., ?..

~ ,

~ , ~

~ d m

Fig. 3. Successive STEM images from a 1 ~m section of marine vibrio specimen at 100 kV, with collection angle sizes of (a) 2.6 X 10 -2, (b) 5.0 X 10 -2 , (c) 7.5 X 10 -2 , and (d) 12.0 X 10 -2 rad, with no alteration of beam current or video amplifier con- trois between scans. Picture width is 5 #m.

D.J. Smith, J.M. Cowley /Aperture contrast in thick amorphous specimens using STEM 133

Fig. 4. "Best" image from a 1 ~m marine vibrio specimen at 100 kV with a collection angle of 12.0 × 10 -2 rad, after adjustments to the video system. Compare this with figs. 3(b), (c) and (d).

ty, particularly if the specimen is relatively uniform. This is shown in fig. 4 which was taken following the series of fig. 3, with a total aperture angle o f 1.2 X 10 -1 rad, after extensive adjustment to the

video system (and several trial photos). The need for the more quantitative line-modulation scans for measurements of contrast is obvious.

The normal operating procedure followed is to first set up the microscope for regular STEM operation and find the position of best focus before switching to the line-modulation mode. The intensity level, measured for the incident beam with no specimen, is indepen- dent o f the detector aperture size since in all cases the collection angle is larger than the incident illumination angle. This level then provides a reference marker for maximum intensity whilst the use of a grid wire, or an aperture, to block the beam will provide the zero intensity level. Contrast and bias controls are then adjusted to give a large separation between these references on the monitor screen. Traces on the screen for successive line scans with the various detector apertures may then be photographed and measured. In fact if the high voltage and the current from the gun were conditioned for some time before operation, it was found possible to take a whole series of scans with the four detector apertures, plus the final projector "aperture", and record them on the same photograph. An example is shown in fig. 5. The specimen in this case

Fig. 5. Line-modulation scans from a 2/am section of marine vibrio specimen at 200 kV with total collection angles of 2.6, 5.0, 7.5, 10.0, and 12.0 × 10 -2 rad. Picture width is 5/am.


is a 2/.tm section of marine vibrio membrane FLxed in osmium tetroxide and embedded in epoxy 812 with an operating voltage of 200 kV. From such photographs the average intensity relative to the unscattered beam, plus the variation in height of the various contrast features, can be easily measured.

From the variations of the intensity corresponding to particular structural details in such sets of line scans it was possible to verify the form of the variation of dlB/dt as predicted in fig. 1.

For a nominal thickness of 1/am of a marine vibrio specimen, the optimum collector aperture angle (2¢0) was measured as 9 × 10 -2 , 5.5 X 10 -2 and 3.0 × 10 -2 rad for voltages of 50, 100 and 200 kV. Con- verting these angular apertures to values o f U0(= 2k - I sin [q~0/2]) gives U 0 = 0.83, 0.75 and 0.60 A-1 respectively. If we take a value U 1 = 0.4 A -1 , which seems reasonable for carbon atoms, the maximum of dlB/dt is seen to occur for Uo/U 1 ~ 2, which would be appropriate for T ~ 5, or a mean free path for elastic scattering of about 2000 for 100 kV if the thickness is assumed to be close to 1/~m. This rough value for the mean free path is in reasonable agreement with various theoretical esti- mates [13]. The results on the elephant gut tissue would suggest a mean free path roughly half as great.

For a marine vibrio specimen of nominal thickness 2/am, the maximum values of dlB/dt appeared to be well outside the attainable range of collector aperture angles for 50 and 100 kV, but for a voltage o f 200 kV the optimum seemed to be about 1.3 X 10 -1 rad, giving U 0 ~ 2.6 & - l , Uo/U~ 6.5 and T ~ 10.

For some of the linear traces and some of the images recorded the effect of electron noise was apparent. However our experiments to date have not al- lowed any clear indication of the relevance of the ratio (dlB/dt)/I1B/2 as a measure of image quality.

5. Pene.tration

The ease with which the relative intensity ratios can be measured as the detector aperture is changed when using the line scan mode suggests the use of this mode to determine the variation of penetration (ratio of observed to incident intensities) with voltage or with collector aperture size. To demonstrate this, the specimens were observed with the JSEM-200 at 50

AI-0.48-100

A I - 1 .5-200 i Cu-0.5-200

0.10- Cu-1.0-200 AI-1.0-100

0 2 4 6 8 10 2 ii D (× 10 -2)

Fig. 6. Relative intensity of beam transmitted through near- amorphous films of aluminum, copper and gold of various thickness as a function of detector angle at 50, 100, and 200 kV. Total incident angle of 2a i = 1.1 × 10 -2 . For each curve the label indicates the specimen metal, the thickness in t~m and the voltage in kV, respectively.

100, and 200 kV and multiple line scans were recorded at each voltage. The ratios of average transmitted intensity to the incident intensity for several metal f'tlms are plotted in fig. 6 with the detector angle and frac- tional transmitted intensity as axes. In fig. 7 the

"transmission" T = (logloIo/IAv) -1 as defined by Curtis et al. [14] is plotted against accelerating voltage for 1/~m and 0.5 btm sections of elephant gut wall tissue. The usefulness of the plots against voltage is obviously limited by the small number of points but at least the trend with voltage can be seen.

While penetration, def'med by IAV/Io, is not necessarily an indication of the amount of information ob- tainable from thick specimens, it may be used as a rough indication of the way in which picture quality depends on such variables as specimen thickness, electron energy and aperture sizes. A review of such indi- cations for CTEM has been given by Cosslett [15]. The variation of penetration with voltage is seen from figs. 6 and 7 to be much the same as for CTEM. Com-

D.J. Smith, J.M. Cowley / Aperture contrast in thick amorphous specimens using STEM 135

5"

4-

3-

2-

1.

,T

~ lO.O,qO -2

7.5

5.0

2.6x10 -2

• ~ : ', _-.__ 50 100 200 kV

T

10'

8

6

4"

2'

~ 10.0x10-2

7.5

5.0

2.6x10 -2

, , ; ::___ i i

50 100 200 kV

Fig. 7. Transmission T = (logtolo[IAv)-1 as a function of accelerating voltage for various detector aperture angles. The

1 tam section of specimens were (A) a 1 tam section and (B) a 2 elephant gut wall tissue.

parison of the results for A1 and Cu suggests that an increase of the voltage by a factor of two or a decrease in thickness by a factor of three is required to com- pensate for an increase in the atomic number by the same factor.

Measurements in the line-scan mode could obviously be useful for the rapid determination of the optimum collector aperture sizes for any type of specimen since it has been established that for the optimum aperture the penetration will be approximately 0.5. Also if such measurements were made up to high scattering angles, differentiation of the curves such as those of fig. 6 may well be a useful means for the measurement of angular distributions of electron scattering.

6. Conclusion

The taking of SEM micrographs of thick specimens normally involves the adjustment of aperture sizes, the gain and brightness controls and so on until the image appears, subjectively, to be optimized. The treatment given here has provided a basis for the sys- tematic determination of the optimum setting for one of the variables, the collector aperture size. For specimens which are well within the usable range of thickness, the optimum aperture size is larger than those conveniently available with commonly used instruments. In a companion paper [18], it is shown that considerable contrast enhancement of STEM images of thick specimens can be achieved by suitable energy filtering and the requirements for optimum contrast

are not necessarily compatible with the usual mode of operation of energy analysers. Hence there is a need for STEM instruments designed specifically for use with thick specimens, incorporating both large collector apertures and suitable energy filters, so that the full capabilities of the STEM mode may be exploited.

Theoretical treatments of the resolution and contrast of STEM for thick specimens [1,2] have been based on the assumption that both contrast and resolution are determined by the intensity distribution across the incident electron beam. This geometric optics assumption may be appropriate for the coherent imaging of an amplitude object or for incoherent dark- field imaging (e.g. images given by inelastically scattered electrons) when the collector aperture is reason- ably large. For the usual case of coherent imaging in bright field of phase objects these treatments are relevant only for thick specimens for which coherent in- terference effects (phase contrast) are not important and the contrast is mainly aperture contrast.

These treatments are also limited in that they make the implicit assumption that all electrons transmitted through the object are detected or else that the fraction detected is the same for CTEM and STEM. The fact that in practice a much greater fraction of the transmitted electrons can be detected in STEM implies that the advantage of STEM over CTEM for the study of thick specimens is enhanced. Some indication of the advantage of STEM in this respect, particularly for dark-field images, has been given by Crewe and Groves [13] and Groves [17] for the particular detector geometry of their instrument.

The analysis by Strojnik [16] of the resolution limits imposed on STEM imaging by electron noise was also based on the geometric optics assumption and the assumption that all transmitted electrons are detected. The results of this analysis should apply with only minor modification for thick specimens if the optimum aperture size is used and approximately half the transmitted electrons contribute to the image. The resolution attainable for thick specimens is limited by multiple scattering effects [1,2] so that it can rarely be better than 10 to 20 A. Hence it follows from Strojnik's analysis [16] that a thermionic emission gun should be adequate for the imaging of thick specimens, particularly for electron energies greater than 100 kV, although the additional brightness available from a field emission gun would, no doubt, be useful.


Acknowledgements

This work was supported by NIH grant GM-18204. The authors are indebted to David Emigh for assistance with calculations, to John Wheatley (at A.S.U.) and John Nailon (Zoology Department , U. of M.) for assistance with specimen preparat ion and to Dr. J.N. Boland and Dr. M.S. Paterson of the Australian Na- tional University for use of the JEOL JSEM-200 electron microscope. We wish to thank Dr. A.E. Spargo for his comments, support and interest. One of us (DJS) also received some financial assistance from a University of Melbourne Post-Graduate Research

Award.

References

[1] L. Reimer, in Scanning Electron Microscopy/1972, liT Research Institute, Chicago (1972) 197.

[2] J.R. Sellar and J.M. Cowley, in Scanning Electron Mi- croscopy/1973, liT Research Institute, Chicago (1973) 243.

[3] H. Koike, T. Matsuo, K. Ueno and M. Suzuki, in 30th Ann. Proc. EMSA, C.J. Arcenaux (Ed.), Claitor's Pub- lishing Division, Baton Rouge (1972) 452.

[4] P. Gentsch, H. Gilde and L. Reimer, J. Microscopy 100 (1974) 81.

[5] K.E. Easterling, in Electron Microscopy/1974, Vol. 1 (1974) 288.

[6] H. Hashimoto, in Proc. AMU-ANL Workshop on HVEM (1966) 68.

[7] A.P. Pogany and P.S. Turner, Aeta Cryst. A24 (1968) 103.

[8] J.M. Cowley, Appl. Phys. Letters 15 (1969) 58. [9] E. Zeitler and M.G.R. Thompson, Optik 31 (1970) 258,

359. [10] A.V. Crewe and J. Wall, Optik 30 (1970) 461. [ 11 ] G.R. Booker, D.C. Joy, J.P. Spencer and C.J. Humphreys,

in Scanning Electron Microscopy/1974, IIT Research Institute, Chicago (1974) 251.

[12] D.J. Smith and J.M. Cowley, J. Appl. Cryst. 4 (1971) 482.

[13] A.V. Crewe and T. Groves, J. Appl. Phys. 45 (1974) 3662.

[14] G.H. Curtis, V.E. Cosslett and R.P. Ferrier, in Proc. 4th Eur. Reg. Conf. Elec. Micros., Rome (1968) 61.

[15] V.E. Cosslett, in Modern Diffraction and Imaging Tech- niques in Material Science, S. Amelinckx et al. (Eds.), North Holland (1970) 341.

[16] A. Strojnik, in Scanning Electron Microscopy/1973, O. Johari (Ed.), IIT Research Institute (1973) 17.

[17] T. Groves, Ultramicroscopy 1 (1975) 15. [18] H.T. Pearce-Percy and J.M. Cowley, Optik, to be pub-

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Aperture contrast in thick amorphous specimens using scanning transmission electron microscopy