Ultramicroscopy 1 (1975) 97-112 © North-Holland Publishing Company

TOPOGRAPHICAL CONTRAST IN THE TRANSMISSION ELECTRON MICROSCOPE A.G. CULLIS* and D.M. MAHER Bell Laboratories, Murray Hill, New Jersey 07974, USA Received 27 June 1975

An adaptation of the Foucault method for topographical imaging in the transmission electron microscope is described in detail. The image contrast is produced by selection of electrons which have suffered differential phase retardations in the specimen inner potential. Surface or interface displacements produce bright or dark image contrast, and the ultimate resolution approaches that of the atomic scale. The imaging method is applied in studies of both amorphous and crystalline objects. The possibility of performing quantitative measurements is demonstrated by the estimation of the inner potential of crystalline MgO.

1. Introduction

Schlieren) method in which electrons deflected in the object through small angles (typically 1 0 - 3 10-4 rad) were selected by the objective aperture. This resulted in the production of bright-dark image contrast which, in general, was related to specimen surface or interface displacements. The purpose of the present article is to describe the important features of the electron optical imaging conditions and to provide selected examples of the application of the technique in materials science. It should be noted that single side-band holography [6,7] is an indirect imaging technique related to that described in the present paper. However, application of the method has been limited somewhat by tile occurrence of random objective apertqre charging effects which must be corrected separately by image processing. For the light microscope, images of phase objects produced by the Foucault technique received theoretical interpretation by T6pler [8], Zernike [9,10] and Linfoot [11 ]. More recently, Faget, Fagot and Fert [ 12] applied various phase contrast imaging methods in the electron microscope and also made a preliminary study of the effects of intercepting electrons with a knife edge in the backfocal plane of the intermediate lens. In the present experiments, we shall be concerned with the selection of electrons in or near the backfocal plane of the objective lens using a standard objective aperture [3,4,13].

The study of specimen surfaces and interfaces in the transmission electron microscope (TEM) is of considerable importance. For example, in materials science, crystal growth phenomena may be studied through observations of surface step configurations; also, interfacial characteristics are of interest in investigations o f internal structures such as precipitates or cavities. Topographical features upon crystalline samples with wedge geometry may be studied directly at intermediate resolution by observations of "twobeam" thickness fringe displacements [ 1]. Alternatively, at high resolution, brightfield (BF) through-focus phase contrast effects may be interpreted in terms of surface structure [2]. However, another technique of direct transmission microscopy which yields highresolution, high-contrast images of topographical features was described recently by Haydon and Lemons [3]* and Cullis and Maher [4]. Image contrast was produced using an adaptation of the Foucault [5] (or * Now at Royal Radar Establishment, Malvern, UK. * The work of Haydon and Lemons, which concerned application of this imaging mode (termed "Optical Shadowing") to observations of biological objects, has come only recently to the authors' attention. The work described in the present paper forms part of an independent study, which treates the subject in greater detail and is concerned primarily with applications in materials science. 97

A.G. Cullis, D.M. Maher / Topographical contrast h7 TEM

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2. Origin of image contrast By analogy with Foucault imaging in the light microscope, image contrast under corresponding conditions in the TEM is produced by utilizing disturbances introduced into the transmitted electron wavefront by potential gradients within the object. The objective aperture is used to remove approximately half the spectra in the diffraction plane of the objective lens and the resulting image exhibits strong bright or dark contrast at the positions of displacement of object equi-potential surfaces. Since such surfaces may often be identified as clear structural boundaries (e.g. a specimen-vacuum interface), the image contrast generally will contain topographical information. If the object structures are sufficiently large, differential wave phase retardations may be interpreted in

terms of electron trajectory deflections. Then, image formation by the TEM objective lens may be described by constructions of the type shown in fig. 1. Here, the boundaries of an idealized hole in a specimen foil introduce trajectory deflections determined by geometrical optics. It is clear that, by discrimination between the different sets of electrons, a half-plane aperture will produce bright-dark hole image contrast as indicated. Such contrast is amplitude in nature (following the definition given by Heidenreich [14]). For an electron accelerating voltage E, a foil of inner potential V0 has an effective refractive index given by

Then, in fig. 1, the electron deviation (5) in each foil wedge termination (included angle ~) is given by ~ -~ 2(/~ - 1) tan (~/2).

v,

/ OA



OL

........

BFP

IP B ~;

.'/O

Fig. 1. Diagram illustrating image formation by an objective lens (OL) with semi-infinite half-plane aperture (OA) situated in the backfocal plane (BFP). The appearance of the object [bright (B) or dark (D)] when obsewed in the lens image plane (IP) is also shown.

(2)

The magnitude of the corresponding diffraction plane vector, k 0, is therefore dependent upon both the foil wedge angle and also its refractive index. However, the validity of this basic description of image formation is limited, in part, by the physical scale of the object structure. For a small object structural feature, the finite distribution of the diffraction spectra within the objective lens diffraction plane must be taken into consideration. Neglecting inelastic scattering effects, this is determined by the effective localization of the incident electron wave-packet within the structural feature of interest. Subsequent decomposition of the transmitted packet into its Fourier harmonics depends upon the size and shape of the object structure (this will be considered in detail in a full wave treatment of the process [15]). However, in the present discussion, we shall describe this decomposition in terms of an effective uncertainty in the electron's trajectory using the Heisenberg relationship between position and momentum. This has the merit of conceptual simplicity although, since it neglects the phase relationships between the scattered electron waves, interference phenomena are not taken into consideration. Nevertheless, for observations using the partially coherent illumination characteristic of a TEM fitted with a conventional thermionic electron source, this approach is generally satisfactory for the prediction of major image contrast features (see subsection 3.2.3).

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

For 100 kV electrons, passage through a thin object introduces only a small uncertainty into their forward momentum. However, if the lateral extent (R) of the object is small, localization of the transverse position of each transmitted electron renders its transverse momentum uncertain by a minimum of h/27rR, where h is Plank's constant. The electron scattering angle is then uncertain by >~)t/27rR, where )t is the electron wavelength, and this uncertainty has values of />6 × 10 -6 rad (ifR = 1000 A),/>6 X 10 -5 rad (if R = 100 A) or 1>6 × 10 - 4 rad (ifR = 10 A). However, the precise scattered electron angular distribution depends upon details of the shape of the object and must be determined from the Fourier transform of the object transfer function [16]. In the diffraction plane of the objective lens, the position of the central maximum of the uncertainty distribution for a uniform object corresponds to the geometrical optics case (defined by k 0 in fig. 1). The sign of the displacement of this maximum from the origin (that is, the sign of k0) still determines the sign of the half-plane topographical image contrast (that is, whether it is bright or dark). However, for constant k 0, if the size of the object is reduced, the width of the uncertainty distribution, Ak, increases so that when Ak ~> 2k 0 electrons are distributed across the diffraction aperture edge. Then, there may be a significant decrease in the amplitude of topographical contrast. Nevertheless, this loss of contrast may be partially compensated if the undeviated electron beam is further obstructed by the aperture edge so that the general background image intensity also decreases. In addition to these considerations, if an object structure introduces a sharp discontinuity into the electron wavefront (that is, the second derivative of the object phase transfer function achieves a large value), then significant image contrast is produced through the effects of diffraction [9,15]. A limiting case is that of a "square" phase step in the electron wavefront and, for example, a pair of such steps would bound the phase retardation introduced by a suitably aligned cubic object. If this retardation has a magnitude of ~7r, with fully coherent illumination, the cubeedge, half-plane image contrast has the same sign as that produced according to the simple considerations given previously. However, the edge scattering yields a symmetrical image for a phase retardation of 7r and an image with inverted contrast for a retardation of 3 7r.

99

Nevertheless, computer calculations [15] indicate that, with partially coherent illumination (divergence angle ~5 X 10 -4 rad), the strength of this contrast inversion is critically dependent upon the precise step orientation. For a step with rr or 3rr electron phase retardation, if the step riser deviates from exact alignment to the incident electron beam by more than ~2 × 10 -2 rad, refraction of electrons in the face of the riser gives contrast (as described earlier) which dominates the image. This indicates that direct topographical interpretation of the half-plane contrast is possible for all but very special objects which introduce, for example, sharp 3 rr electron phase shifts. Experimental observations of cubic MgO crystallites in a JEM 200 TEM suggest that this "anomalous" situation is not only uncommon, but also difficult to achieve even under carefully controlled conditions.

3. Microscope configuration and contrast formation 3.1. Basic imaging conditions

Selection of the required portion of the electron diffraction spectrum, given by an object structure, in the back-focal plane (BFP) of a TEM objective lens may be carried out ideally using an (objective) aperture situated exactly in the BFP. An "ideal" half-plane or topographical image could then be formed. (The finite circular geometry of conventional apertures is disregarded.) However, under normal operating conditions, the objective aperture is often substantially displaced either above or below the BFP. While this may be of little consequence for the formation of images with a symmetrically positioned aperture (for example, a conventional BF image), half-plane images exhibit certain special properties. In particular, they show a clear transition from bright-field to dark-field (DF) conditions. Furthermore, the minimum angle through which electrons must be scattered in order to contribute to the image varies with position in the image. Although this may be inconvenient for some studies, it gives the opportunity of determining scattering angles from simple measurements upon micrographs. Therefore, since it is an expected normal mode of operation it will be described below. However, if somewhat degraded microscope resolution is acceptable, the objective lens BFP may be brought into coin-

100

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

OL

BFP

"'~"

OA

"I'"

electrons originating at point 03 may yield a DF image outside the region 1112 at 13. Nevertheless, the direction of scattering at O 3 must be as illustrated by path 1 in fig. 2, since electrons deflected in the opposite direction (path 2) are obstructed by the aperture. Furthermore, the greater the distance between 03 and 02 the greater the angle of scatter required for electrons to pass through the aperture along path 1. Therefore, electrons contributing to a DF image point must be scattered in the object through an angle greater than a minimum angle determined by the distance of that image point from 12 (or I1). If scattered electrons (angular deviation 5) contributing to 13 graze the aperture edge, ~_= R(a + b) d

Db

(3) '

where the parameters have assignments as shown in fig. 2. The corresponding value of 5 is given by = (r/d) A ,

R---d. Fig. 2. Diagram illustrating image formation by an objective lens (OL) with axial, finite aperture (OA) displaced below the backfocal plane (BFP). Object points O1-3 correspond to image points 11-3, respectively, and the electron scattering in the object plane is illustrative only.

cidence with the aperture plane by use of one of the techniques described by Blackburn, Curtis and Ferrier [17]. Fig. 2 shows image formation by the objective lens under conditions of uniform, parallel, object illumination. Undeviated electrons passing through object points O l and 02 are focussed by the lens to the axial point in its BFP, having grazed the edges of the objective aperture which, though axial, is displaced below the BFP. In this manner, a BF aperture-limited zone (ALZ) is formed in the image region between I 1 and I2, this being projected onto the final fluorescent screen by subsequent lenses (not shown). Undeviated electrons passing through object points outside the region O102 (for example, 03) are obstructed by the aperture and do not contribute to the image. However, electrons which have been scattered in the object are focussed to off-axis points in the lens BFP and such

(4)

where A is the diameter of the aperture (measured in radians) projected into the BFP of the lens. Now, if the objective lens magnification is in the usual range of 20-25 X, then b >>a and combining eqs. (3) and (4) we obtain ~ RAID.

(5)

This relationship may be used to determine the angles through which electrons must be scattered in order to contribute to specific DF image features (see sub. section 3.2.1). Also, it should be noted that eq. (5) is valid even if the objective aperture is displaced above the BFP. The image region in which topographical half-plane contrast may be observed is that of transition from BF to DF at the boundary of the ALZ and the contrast is produced by electron scattering in the object through angles of typically 10 -3 to 10 -4 rad. In order to examine the topographical contrast, the boundary of the ALZ must be projected onto the final screen of a TEM at high magnification. This is conveniently carried out either by laterally displacing the objective aperture or by tilting the incident electron beam. For microscopes with two independent beam tilt control circuits the latter mode permits rapid return to high resolution BF conditions. However, the displaced ap-

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

erture arrangement would be expected to be capable of producing images of highest resolution since these are formed on the optical axis of the objective lens. The correction of image astigmatism is discussed in sub section 3.2.4. A holey carbon film is a convenient test object to demonstrate image formation. However, although a typical hole may be idealized as shown in fig. 1, the size of the wedge terminations requires that the effects of diffraction must be considered in a detailed contrast calculation. Since, in this section, we shall be concerned only with the sign and approximate amplitude of the contrast, the arguments of the last section will be appropriate. Figs. 3a and b show images of the same region of a holey amorphous carbon film and display transitions from BF to DF in two orthogonal directions, that is, they correspond to orthogonal regions of the perimeter of an ALZ. In each case, sloping regions at the edges of specimen holes yield bright or dark images depending upon their spacial relationship with respect to the periphery of the ALZ. Edges which are oriented towards the BF region scatter electrons strongly into the DF images. However, edges oriented away from the BF region scatter electrons strongly in the opposite direction, so that they yield dark images just within the periphery of the ALZ. Specimen edges which are parallel to radii of the circular ALZ give no topographical contrast. Now, it is clear that if a specimen hole of the type shown in fig. 1 were placed between object points 0 2 and 0 3 in fig. 2, the mean electron deflections introduced would be precisely those required to produce the observed contrast. However, the contrast amplitude would decrease with increasing distance from the ALZ boundary due to the operation of eq. (5). Therefore, there is a satisfactory correlation between theory and experiment. Fig. 4 shows the edges of holes in an amorphous carbon film imaged with topographical contrast at high resolution. It is evident that fine structural detail can be seen and the strong bright-dark hole contrast asymmetry is maintained in the DF region of the micrograph. If sharp discontinuities in the electron wavefront were an important source of image contrast, one would expect to observe bright contrast in DF [10] as evidence for the associated scattering. Therefore, maintenance of the strong hole contrast asymmetry suggests that such effects may be neglected under the

101

Fig. 3. Transmission electron images of holey amorphous carbon film showing topographical contrast near the region of transition from BF to DF. a) and b) contain the same image region, with BF to DF transitions in orthogonal directions and associated complementary topographical contrast.

usual conditions of high magnification imaging. However, if the electron beam divergence is reduced sufficiently, the presence of some scattering of this type may be revealed by a brightening of otherwise dark hole edges in images of the ALZ boundary in DF (see, for example, results in subsection 3.2.1). For general agreement between theory and experiment, it is also required that if the objective aperture

102

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

Fig. 4. Transmission electron image of holey amorphous carbon film showing details of structure revealed by topographical contrast. is displaced axially above the lens BFP the radial symmetry of the image contrast should invert. This is easily seen from fig. 2, since electrons traversing trajectory 2 now reach the DF image whilst those following trajectory 1 are removed by the aperture. An image recorded under such conditions is shown in fig. 5, and it is clear that the bright-dark hole contrast symmetry with respect to the ALZ is reversed, as predicted -- for example, compare fig. 3. Since the symmetry of the bright-dark topographical image contrast is dependent upon both the axial and the lateral position of the objective aperture, it is convenient to introduce a vector which characterizes the mean direction of scattering suffered by electrons which contribute to each particular image region. The vector k 0 shown in fig. I is suitable for this purpose and its use eliminates the need to consider details of the microscope mechanical alignment for the interpretation of micrographs. If discontinuities in the trans-

mitted electron wavefront do not introduce important image contrast, it is a simple matter to use fig. 1 to determine the sign of the bright-dark topographical contrast for certain useful cases - see fig. 6. It is also easy to demonstrate that features such as depressions or islands yield their respective contrast asymmetries whether they are situated on either the top or the bottom surface of the object. Examples of the image contrast produced by small surface depressions and protuberances are shown in fig. 7. 3. 2. Effect o f changes in imaging conditions 3. 2.1. Electron accelerathTg voltage The dependence of the effective refractive index of an object upon the TEM electron accelerating voltage [eq. (1)] ensures that the "scattering power" of the object increases with decreasing accelerating voltage. This may be demonstrated by measuring the elec-

103

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

Fig. 5. Transmission electron image of holey amorphous carbon film showing inverted topographical contrast (for example, compare fig. 3) obtained by axial displacement of objective aperture. tron deflections required to produce topographical contrast at different accelerating voltages. If a specimen foil is imaged at low magnification, measurement from the boundary of the ALZ to the furthest position in DF at which topographical contrast appears gives a value of R (that is, Rmax) which may be related through eq. (5) to the maximum angle of associated electron scattering (6max)" This is illustrated in fig. 8, which shows the same area of a holey carbon film imaged at electron accelerating voltages of 50 kV and 200 kV. In the figure, the different values of R max are indicated, and these may be interpreted directly in terms of tSmax since D and A of eq. (5) were held constant to within a few percent. Ideally, 10-3 rad, image contrast is generally reduced since, for many electrons which penetrate the object of interest, the objective aperture is effectively displaced by a significant amount from the half-plane position. This reduction in contrast may become unacceptable for objects which scatter electrons through the smallest angles, although by further attentuation of the main

beam with the aperture and longer image plate exposure contrast may be partially restored. If the beam divergence is ~ 10 -4 rad, certain interference phenomena, characteristic of fully coherent illumination, appear either as modifications of the original contrast or as background contrast fluctuations [15]. Therefore, values of divergence in the region of 5 × 10 -4 rad are particularly useful and generally may be obtained by partial collimation of the electron beam for observations at intermediate to high magnification. For specimen illumination using a divergent electron beam, the range of angles over which electrons pass through the specimen plane ensures that the boundary of the ALZ (fig. 2) will not be sharply defined. This leads to the production of the graded background illumination which is visible in some of the micrographs displayed in the text.

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

50kV

200 kV



.,

105

.-

¢"x

,,2.

Fig. 8. Transmission electron images showing the same area of an amorphous holey carbon film and illustrating the differences in extent of DF electron scattering for accelerating voltages of 50 kV and 200 kV (arrows indicate regions in which hole edge contrast became undetectable on original electron image plate).

3. 2. 4. Image astigmatism Since electrons which pass close to the edge of the objective aperture also contribute a large portion of image information, correction of associated image astigmatism is generally important, especially for high resolution studies. In the absence of defocussing Fresnel or contour fringes under DF conditions, this may be carried out by minimizing the spurious streaking of background image contrast features. Difficulties in the astigmatism correction procedure will be aggravated if the aperture edge has an irregular configuration, or if contaminant material at the aperture edge accumulates an electrostatic charge.

Fig. 9. Transmission electron images of same area of holey amorphous carbon film showing effect of objective lens defocus upon topographical contrast: a) ~5 # under focus; b) near focus; c) - 5 u over focus.

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A. G. Cullis, D.M. Maher / Topographical contrast f17 TEM

4. Examples of topographical imaging 4. 1. Observations o f MgO crystallites

Crystallites of MgO are especially well suited to demonstrations of topographical contrast since they have a regular cubic growth habit. Indeed, many workers have studied the splitting of electron diffraction spots .by refraction effects at the cube faces (for example, Sturkey and Frevel [19], Cowley and Rees [20], Honjo and Mihama [21], and Moli~re and Niehrs [22]). In this way, the value of V0 for MgO has been determined together with higher order Fourier coefficients of the lattice potential. For the present observations, MgO crystallites were prepared by suspending a TEM specimen grid in the smoke produced by the combustion of Mg in air. Figs. 10a, b, and c show a BF through-focus series of micrographs displaying an assembly of MgO cubes in various orientations. It is immediately evident that, for conditions of small underfocus, all cubes exhibit bright peripheral edge contours, although contours given by edges overlapping each cube matrix are uniformly dark. However, for conditions of small overfocus, the contrast exhibited by edge contours is reversed. Moodie and Warble [23] recently pointed out that such contour contrast is dependent upon the sign of the second derivative of the object projected potential [24]. This has a geometrical interpretation in terms of refraction through the cube faces as illustrated in fig. 11, which shows a cube aligned as a Fresnel biprism with diad axis parallel to the incident electron direction (for example, cubes such as A in fig. 10). Fig. 11 demonstrates that bright edge contours may be produced by the overlap of electron wavefronts, giving excess intensity. Dark contours may result from the intensity deficiency between diverging wavefronts and these observations are analogous to the out-offocus imaging of magnetic domain walls [25]. However, exact calculation of each contour intensity requires that the phase relationships between the scattered and unscattered electrons be taken into account, together with consideration of the incident beam divergence. When the MgO cubes were imaged using the displaced aperture mode, the various cube faces gave markedly different contrast since electrons passing through them suffered refractive deviations characteristic of

the various face inclinations. Figs. 10d and e show micrographs obtained using aperture shifts in opposing directions. Each of these images may be interpreted using the diagrams given in fig. 6, although only cubes which scattered electrons under kinematical conditions (for example, B and C) are characterized by lattice potential V0. The relationship between the BF, bright or dark, cube-edge fringes and the sheets of electron intensity displaced by refraction at the cube faces is especially well demonstrated by transition between the BF and topographical images under conditions of moderate defocus. In this way it was found that each set of BF, bright edge fringes did, indeed, occur in the same image position as the corresponding topographical face contrast where this had overlapped the undeviated electron beam. The regular MgO cube geometry also gives the possibility of estimating V0 by observations of refraction scattering in DF and the use of eq. (5) as described in section 3.2.1. To demonstrate this, an MgO cube was first oriented with its diad axis parallel to the incident electron beam (as at A in fig. 10) and then tilted by a few degrees to achieve kinematical conditions of electron diffraction. Next, at low magnification and with approximately parallel illumination, the crystaUite was aligned at the edge of the ALZ such that the line of bright-dark transition within the MgO biprism was normal to the direction of the local vector k O. Finally, while maintaining this alignment, the MgO crystallite was traversed in the DF region of the image, and the position at which the bright-dark biprism refraction contrast could no longer be seen was determined from a series of micrographs. For an accelerating voltage of 200 kV, the latter measurement gave a value of R in fig. 2 of 1.9 mm, while D = 45.5 mm. From a separate measurement of the objective aperture diameter in relation to a standard diffraction pattern it was found that A = 1.77 × 10 -3 tad (nominally, a 10/lm aperture). Then, eq. (5) shows that electrons, in passing through one half of the MgO biprism, suffer a mean angular deviation of 7.3(8) × 10 -5 rad. Since the cubic habit of MgO ensures that the prism angle is ½n, use of eq. (2) (a = ½n) yields the effective refractive index (~t) of MgO, /a = 1 + 3.6(9) × 10 -5 .

A.G. Cullis, D.M. Maher

Topographical contrast in TEM

-

107

\

d

/ .

:?..

t, S

Fig. 10. Transmission electron images of array of cubic MgO crystallites: a) BF, near focus; b) BF, under-focus; c) BF, over-focus, d) and e) with topographical contrast showing effect of inversion ofko.

A.G. Cullis, D.M. Maher / Topographical contrast in TEM

108

under focus

B

D

B

D

over focus

Fig. 11. Dia~am illustrating mean directions of electron deflection introduced by MgO biprism. Formation of bright (B) or dark (D) edge contrast in under- or over-focused images is also demonstrated.

Then, from eq. (1) 1 + 3.69 × 10 -5 = (1 + V0/2 × 105) 1/2 , or,

V0 "~ 14.8 V . It is difficult to estimate the errors in this determination although they are expected to be introduced mainly through uncertainties in the measurement of R. Uncertainty in the refraction scattering angle would have given a scattered electron distribution with a width at half maximum of ~2.6 × 10 -5 tad (cube edge length ~>1500 A; see section 2). Since this was taken into consideration in the experimental measurements, the above value of V0 is unlikely to have a permissible error range of >~---2 V. Indeed, there is good agreement between this result and the value (uncorrected for dynamical effects) of 14.28 +- 0.18 V given by Miyake, Fujiwara and Suzuki [26] for 200 kV electrons. Furthermore, the above method may be extended to determinations of V0 for individual regularly shaped crystallites of other materials. 4.2. Observations o f cavities in materials

When a crystal is of thickness, for example,

1500 A and contains small, spherical cavities (~

Topographical contrast in the transmission electron microscope.

An adaptation of the Foucault method for topographical imaging in the transmission electron microscope is described in detail. The image contrast is p...
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