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T.E.M. TECHNIQUES FOR THE ATOMIC LEVEL CHARACTERISATION OF NANOMETRE SCALE
MULTILAYERS
W. Stobbs
To cite this version:
W. Stobbs. T.E.M. TECHNIQUES FOR THE ATOMIC LEVEL CHARACTERISATION OF
NANOMETRE SCALE MULTILAYERS. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-33-
C5-40. �10.1051/jphyscol:1987505�. �jpa-00226676�
T.E.M. TECHNIQUES FOR THE ATOMIC LEVEL CHARACTERISATION OF NANOMETRE SCALE MULTILAYERS
W.M. STOBBS
Department of Materials Science and Metallurgy, Pembroke Street, GB-Cambridge CB2 3QZ, Great-Britain
Abstract - The transmission electron microscope techniques which can be applied to the atomic level characterisation of interfaces, heterostructures and multilayer systems are described. Many of the approaches required are indirect. This is partially because of the need to differentiate the effects of a displacement from those of a composition change and partially because of the general problem of ensuring that a given structural model provides a unique fit between a set of simulated images and those obtained
experimentally.
1. Introduction
The quantitative structural and compositional characterisation of an
interface, whether between different phases or at a grain boundary is as difficult as it is rewarding. Before proceeding to the assessment of what can and cannot be done using-current state of the art T.E.M. techniques for the characterisation of multilayers with "superlattices" of interfaces it is worthwhile assessing the difficulties which have to be overcome for a single interface. There are three individual measurements which need to be made for such boundaries and these can be enumerated as:
1 ) The quantification of the rigid body coincident site lattice displacement for a homophase boundary,
2) The measurement of the concentration of any boundary plane segregant,
3 ) The characterisation of the local relaxation structures associated with the
presence of any intrinsic boundary defects.
The general problem is exacerbated by the fact that the solutions of these individual problems are not independent of one another. For example for a low C homophase boundary a rigid body displacement is necessarily paralleled by a local change in the scattering potential which is in principle of the same form as would be the result of the replacement of a layer of atoms at the boundary by others of a different species. How then can we distinguish between the effects of segregation and those of a rigid body displacement? This question is fundamental to the unique solution of a boundary characterisation problem and it is thus fortunate that individual techniques can be more or less independent of the magnitudes of each of these two parameters. Clearly if the concentration of any segregant could be determined by some direct technique, such as quantitative EELS, then the effect of this segregant's presence on the elastic scattering potential could be included in
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987505
JOURNAL DE PHYSIQUE
a simulation of the high resolution imaging behaviour with which experimental micrographs might be compared when measuring the rigid body displacement.
Unfortunately however, EELS is neither readily made particularly quantitative nor can the form of a local concentration gradient be determined given the spread of any electron probe used for even very thin foils. Quantitative assessments of grain boundary segregation by this direct approach are sufficiently rare to be noteworthy [l]. As we will see however an alternative approach has been found for the measurement of composition changes at a boundary using the elastic scattering and in Section 2 we thus discuss this and the other methods required for a boundary's full characterisation.
2. Boundary Characterisation Methods
The simplest approach we can take here will be to examine in turn the approach best taken for each of the three individual measurements enumerated in Section 1.
2.1 The Rigid Body Displacement
At first sight this might seem the simplest of the three measurements to make accurately. Advances in high resolution electron microscopy over the last few years have long since allowed the recognition of atomic spacings of well below 0.2 m. Equally, with a microscope of such a resolution the scattering due to a laterally large weak phase object with atomic spacings of say 0.25 nm will be well represented in the interference image where, for such an object, the intensities seen can be related directly, through the contrast transfer behaviour of the microscope, to the projected potential of the object. This is no longer true however, even for a weak phase object, if a single interplanar spacing is changed as it will be at a boundary, even if the change is an increase to say 0.3 m. The problem is related to the Fourier representation of a square well: in order that the true planar positions at and near to the boundary plane are properly
represented in the image the microscope must transfer information about the second Fourier components at least and this, for the example considered, would imply a need for a resolution better than 0.15 nm. In actual fact the direct
interpretation of small displacements using the comparison of modelled simulations with experimental image series is still more difficult simply because few real boundaries will approximate sufficiently accurately to a weak phase object. This means that unless independent means can be found to determine the various
parameters affecting an image series (defocus, specimen thickness, beam tilt, lens characteristics etc) a unique solution is unlikely.
Fortunately, at least for a limited range of boundaries, such as the C3, which exhibit a common reflection across them when appropriately orientated, there is no need to rely on the complex details of such image simulations. The fringe
positions within about 2 nm of the boundary position in the image will still be non uniform and very dependent on the conditions. However, as long as the imaging conditions are identical on either side of the boundary, then whatever the relationship of the fringed image to the atomic positions relatively far from the boundary this will be constant so that the image shift will accurately represent the C.S.L. displacement. Such a shift can be measured to a much higher accuracy than the microscope resolution: the accuracy attainable is related to the size of the uniformly scattering regions whose relative positions are required. The approach has been used to provide measurements of the rigid body displacements at twin boundaries in copper and gold yielding values to an accuracy about a hundred times better than the microscope "resolution" [ 2 , 3 ] , while approaches have also been found to give an indication of any systematic error caused by, for example, foil bending [ 3 ] . It is worth noting that whereas it is essential that the boundary to be analysed by normal high resolution methods must exhibit a uniform projection this is not necessary for the method described above, nor is it when using the moire method [ h ] which relies on the same principles. The limitations of such methods for more general boundaries will be clear and have been discussed
2 . 2 The Boundary Composition
As has been noted above a rigid body displacement will produce a change in the scattering potential which could be misinterpreted as being due to a local
fluctuation in the composition. However if the rigid body displacement has been determined by one of the methods discussed in Section 2 . 1 then this can be included in high resolution image simulations and the local boundary composition then adjusted to provide a match between the simulations and an experimental image series. Interestingly, and rather fortunately, the approach does not require high resolution imaging: the Fresnel effects seen at the edge of a foil, where there is a change in the scattering potential, have long been familiar in the correction of astigmatism and the assessment of beam coherence. However it has been demonstrated that the intensity of such fringed images of a boundary, as a function of defocus, can be related to the magnitude of the localised change in scattering potential
[61. The method is surprisingly accurate and given care can yield results limited
by the accuracy of foil thickness measurements to about
25%.
Also the approach is increasingly sensitive the more localised the change in potential, as can be understood on the basis of a Fourier analysis of the problem, so that it is ideally complementary to the use of quantitative EELS. Of course EELS still has to be used to provide qualitative data on the nature of the element segregated to the boundary and the approach is inapplicable if the concentration of more than one element is locally changed. The method is still being refined in the laboratory and it is becoming clear that not only can the magnitude of a local concentration change be determined but so too can the form of the local concentration gradient. It has for example been demonstrated using the method that the thickness of the SiOinterlayer at a chemically oxidised surface of silicon (where the layer geparates silicon from SiO ) does not exceed 0 . 5 nm in thickness (courtesy of F.M. Ross).
2
Vitek has recently assessed the influence of segregation on the diffraction at homophase interfaces 171 comparing the effects of a bulk displacement and
segregation while noting the difficulties in separating the effects. This in turn emphasises the importance of using independent methods, if at all possible, for the measurement of these two parameters. When a high resolution dark field Fresnel method was used to assess the rigid body displacements at C3 twin boundaries in gold [ 8 ] the inconsistency of the results with those previously obtained by the measurement of lattice fringe shifts [31 allowed the inference that segregation was the cause. Furthermore refinement of the Fresnel data using the displacement from the fringe shift measurements would then allow the quantification of the change in scattering potential caused by segregation.
2 . 3 Localised Relaxation Structure Assessment at a Boundary
Given the problems, as enumerated in Section 2.1, in the use of high
resolution techniques for the measurement of even a rigid body displacement it will be clear that the situation is far more open to misinterpretation when the problem is to characterise the local form of the intrinsic grain boundary defects
characteristic of a given interface geometry. Nevertheless several authors have tackled the problem and many beautiful micrographs have been obtained. Of recent work it is noteworthy that significantly useful information can be obtained about
the relative energy of different geometrically possible types of defects for a given boundary geometry without recourse to too detailed a comparison of image simulations with the experimental data 191. Krakow et a1 [10,111 have however suggested that the detailed nature of a theoretical boundary defect structure can be related to the local image form, given that care has been taken, after digital image processing. While the uniqueness cf image fits of the type described has been questioned 1121 they were very clearly achieved. That this was so is however less surprising when it is remembered that the localised image distortions, which
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tend to arise relative to the true atomic projections, both when the original image is formed, and as tend further to be emphasised when the image is Fourier filtered, are those that tend to even up local variations in the spacings. Equally these are of course just the type of displacements which generally tend to lower the energy of an unrelaxed boundary structure [eg 131. Some effort has been put into the assessment of the inaccuracies which can result from too direct an interpretation of atomistic images of localised boundary displacements [eg 141 and although it is clear that Fourier filtering will in general exacerbate the problem most computer modelled simulation analyses tend to be limited by the wrap around effects inherent in periodic continuation, with the result that the conclusions drawn 1141 might well be too optimistic. The problem needs further work particularly if it is noted that it has recently been demonstrated that inelastically scattered electrons
can
contribute detail in a high resolution image [l51 given also that the inelastic crass sections tend to change at a defect [eg 161.
While we thus see that this usage of high resolution techniques is, at least for defects which can be viewed in projection, one of the most potentially
rewarding for the electron microscopist it is non the less an application for which the unique nature of the solutions obtained is open to doubt. For this reason it is arguable that data obtained by the use of the weak beam technique 1171 on the form of the local displacement field of a boundary defect could well be less prone to misinterpretation. Attempts have been made to use the method quantitatively in a "mapping approach" [l81 by means of which the unknown displacement field of a boundary defect is assessed by comparison of its images with those of defects in the matrix whose displacement fields are known. The full analysis of the technique
[l91 is however discouraging in that simplistic interpretations are rarely viable because of dynamical effects. These, though not dominant at high deviation
parameters, can be sufficiently different for a boundary defect and a matrix defect at the deviation parameters actually required to mean that simulations are still required.
3. Multilayer Structure Characterisation
Having now discussed the relative quality of the different techniques available for the characterisation of a single interface we must assess the extra complications caused by the presence of a "superlattice" of such interfaces when it is the structural characterisation of a nanometre scale multilayer which is
required.
Multilayer systems tend to be of two general types: those which are, or are nearly, lattice matched and exhibit little strain but a periodic (or aperiodic) change in composition (eg GaAs-AlGaAs) and those which exhibit both compositional and lattice spacing variations (eg GaAs-GalnAs). For semiconductor multilayer systems (as are usually grown'by MBE or, increasingly, MOVPE), the features of interest which are generally required for the modelling of the physical properties tend to be:
1) the amplitude and form of the compositional modulation 2) the layer thickness
3) its crystallographic vicinality as a function of the growth direction 4) the form of any interface steps or dislocations.
Considering firstly systems as epitomised by GaAs-AlGaAs the most appropriate T.E.M. techniques available for obtaining the required data have been discussed from an industrial viewpoint elsewhere [20] and will only be summarised here given that the general approach has also been described in Section 2.
The amplitude of the compositional modulation in this system can be measured by techniques which are of special relevance to 111-V alloy systems in that the contrast in an 002 type reflection is, on a kinematic basis, sensitively related to
techniques [22] and for typical values of of -0.3 to 0.4 in AlxGa As it transpires that the quantitative application of Ehe dark field methAdxcan yield values to 20.03, this error including the effects of inelastic scattering though these generally seem to lead to a systematic tendency for the aluminium content to be underestimated [22].
Since the lattice parameter varies very little with changes in the aluminium content normal CBED techniques are inapplicable. However it has been suggested that the splitting of high order HOLZ lines as a function of the Bloch wave current channelling at the cube normal can yield the A1 content to a similar accuracy [23].
It is questionable however whether the required degree of lateral localisation can be achieved. It should be noted that EDX techniques are generally of little value for a fine multilayer because of beam spreading unless the average composition is measured and the localised composition determined indirectly by measurement of the relative thicknesses of the different types of layers present. The approach can only be applied for an extended multilayer in a uniform foil.
Another technique of some merit for the determination of the composition involves the assessment of the relative contrast of the layers in a cleaved wedge (of accurately known thickness at any point in the image) when viewed at the cube normal. Given the thorough computational analysis that has been reported for this method [241, the technique probably provides the most accurate quick method for a composition measurement.
An interesting application of the Fresnel technique, as discussed above (Section 2.21, lies in the measurement of the abruptness of the compositional changes in such multilayers. For MBE grown GaAs/AlGaAs layers the composition change is generally considered to occur over a monolayer. The quantification of image series such as that shown in figure 1 is however currently suggesting that this assumption is probably optimistic. Even qualitatively the lack of detail in the Fresnel contrast suggests a relatively smooth change in scattering potential.
This in itself however points to the fact that the local scattering potential has to be related on the atomic scale to the projected chemical composition [25] using Poisson's equation. On the other hand the Fresnel method could be used fairly straight forwardly for more interdiffused layering as in 11-V1 systems.
The thickness of the layers and their vicinality can be readily assessed to near monolayer accuracy by a combination of dark field and high resolution
techniques but it should be noted that it is important to obtain images at a series of specimen tilts using the 002 reflection approximating to the growth direction.
Once the vicinality has been determined the average step density can be inferred, however it has been suggested that the form of the steps present can be determined by the optical filtering of high resolution images. This is dubious for the reasons discussed in Section 2.3, and in general the nature and form of the steps present in a vicinal multilayer remains the problem of greatest difficulty in the assessment of this type of multilayer. High resolution images obtained at the cube normal exhibit greater interlayer contrast than at for example (110) [261 but steps are likely to lie along <110> so that, in the end, this latter type of image will have to be quantitatively assessed. For this reason a variety of methods, including the centre stop dark field technique, have been examined for the improvement of the interlayer contrast while retaining atomic resolution.
Unfortunately it appears that the effects of inelastic scattering make this
practically rather difficult technique of only marginal value 127,281 (until energy loss filtering becomes more generally available at high resolution [ 1 5 ] ) .
Accordingly the extremely indirect approach of using reflection microscopy on the surface of a cleaved multilayer looks of increasing potential given that, as has been demonstrated, surface cleavage steps seem to be associated with multilayer steps [28].
C5-38 JOURNAL DE PHYSIQUE
d - e 50
Figure 1. The images shown are of an irregular GaAs/Al Ga As heterostructure provided and designed by G.E.C. The micrographs form $ar&-gf a through focal series as obtained at a low convergence to emphasise the Fresnel effects associated with the changes in scattering potential at the layers. For this type of irregular heterostructure the Fresnel contrast is different at different layers and is emphasised in different regions at specific defoci (the coherence area being larger than the layer thicknesses). It is this fact which makes the analysis of the contrast particularly sensitive to the shape of the projected scattering potential and thus allows an analysis of the atomic level localisation of the composition.
(Courtesy of E.G. Britton and F.M. Ross.)
Considering now the characterisation of multilayer systems exhibiting
modulation of both lattice parameter and composition, the two semiconductor systems which are receiving increasing attention are ~aAs/lnGaAs and Si/Ge. In the former case it is well known that in an 002 dark field image lnGaAs layers exhibit the opposite contrast, relative to GaAs, than that expected on simple structure factor grounds. This is alarming and indicates that it will be some time before the same levels of quantification will be achieved for this type of strained system as can already be attained for GaAs/AlGaAs. The full reasons for the contrast reversal are not known but the contrast seems to be sensitive both to the sense of the reflection used for a given specimen wedge and to the foil thickness. The relative importance of inelastic scattering and stress relaxation have not yet however been quantified. In general the importance of treating the foil surface relaxation of the periodic stresses in a strained multilayer properly L291 cannot be
underestimated but it is fortunate that the effects of foil relaxation become less important as the ratio of the layer spacing to the foil thickness is decreased.
It must be concluded that the characterisation of typical strained 111-V multilayer systems by T.E.M. techniques is, at least quantitatively, in its infancy. However from a more optimistic viewpoint remarkable advances have been made in the analysis of epitaxially strained metallic multilayer systems made by sputtering techniques [ 3 0 ] . It has for example been demonstrated that the well known anomalous physical properties of such systems which tend to peak at critical wavelengths of about 2 nm are in fact associated with a Fermi surface driven "phase
fringe spacing variations were measured as a function of defocus (using non axial methods which, for the purpose are more sensitive than the standard axial approach
1321) and these were then compared with simulations for a range of models embodying different periodic strains but a form for the chemical modulation assessed (to an accuracy of 1-2 atomic planes) using the Fresnel method.
4. Discussion
In the above description of the newer techniques which can be applied using a transmission electron microscope
I
have concentrated on a description of those methods which are required when a multilayer is to be characterised as fully as possible. Such characterisations can take a considerable time (months!) and are worthwhile only when either there is new physics involved, as appears probable for fine metal multilayers 1311 or when very careful modelling of for example the lasing properties of a semiconductor multilayer are required.In general the current rapid expansion in the use of 111-V layered systems technologically puts considerable pressure on the ability of the crystal growers to make systems of very precise forms as specified by the physicists. When such systems don't work the usual approach in an industrial laboratory is to use x-ray techniques to provide an initial analysis of what went wrong. This appears to be mainly because T.E.M. methods have the reputation of being both time consuming and difficult to apply. In fact the data normally required by a crystal grower, are whether or not the layers are of the correct thickness and have approximately the right composition or are irregular in some way perhaps as a result of stress relation by dislocation nucleation. In a properly equipped and experienced laboratory data of these types can be obtained using T.E.M. in a matter of hours and furthermore it is precisely these sorts of data which are most easily
misinterpreted in the analysis of x-ray results which are better applied to uniform or multilayer systems!
5. Acknowledgements
I am grateful to Prof. D. Hull for the provision of laboratory facilities and to several companies including British Telecom, Johnson Matthey, G.E.C., Philips and S.T.L. for support. The particular multilayer shown in figure 1 was designed and provided by G.E.C. I would also like to thank C.S. Baxter, C.B. Boothroyd, E.G. Britton, F.M. Ross and E.J. Williams for their help in the development of much of the work described here.
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