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{\bf\Large    Scanning Transmission Electron Microscopy: An 
Experimental Tool for Atomic Scale Interface Science}

\vspace*{4ex}
\noindent
N. D. Browning$^1$, E. M. James$^1$, K. Kishida$^1$, I. Arslan$^1$,
J. P. Buban$^1$, J. A. Zaborac$^1$, S. J. Pennycook$^2$, Y. Xin$^{1,2}$ and G. Duscher$^{1,2}$ $^*$
\end{center}
\vspace*{2ex}

\noindent
{\small\it $^1$Department of Physics (M/C 273), University of Illinois at Chicago,
845 West Taylor Street, Chicago, IL 60607-7059. USA.\\
$^2$Solid State Division, Oak Ridge National Laboratory, P.O. Box 2008, 
Oak Ridge, TN 37831-6030. USA.\\
$^*$Current Address: Department of Physics and Astronomy, Vanderbilt University, 
Nashville, TN. USA.\\}

\noindent

\vspace*{6ex}

\centerline{\bf Abstract}
\noindent
Although internal interfaces have long been known to dominate the performance of many materials systems 
critical to modern technology, there has yet been little incontrovertible evidence pointing to the 
fundamental origin of the structure-property relationships.  However, the recent development of direct 
imaging and analysis techniques in the scanning transmission electron microscope (STEM) has provided a 
new experimental pathway to obtain information on the local atomic structure, chemical composition and 
bonding at interfaces on the fundamental atomic scale.  This is precisely the information that is required to 
unravel the complexities of interfaces and opens up a new paradigm for investigating the structure-property 
relationships at internal interfaces.  In this paper we discuss the practical aspects of the experimental STEM 
techniques and demonstrate the resolution possible in current commercially available instrumentation.  The 
application of these techniques to the study of internal interfaces is highlighted by a discussion of the 
analysis of homophase interfaces in SrTiO$_3$, Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_10$ and YBa$_2$Cu$_3$O7-? and the heterophase 
interfaces between GaAs and Au, and between Si and molecular beam epitaxy (MBE) grown II-VI 
semiconductors.\\ \vspace*{8ex} \hrule\vspace{1ex}
{\small\noindent Corresponding Author:           Professor Nigel D. Browning,
					Department of Physics (M/C 273),
					University of Illinois at Chicago,
					845 West Taylor Street,
					Chicago, IL 60607-7059. USA
					Tel: 		312-413-8164
					Fax:		312-996-9016
                                        e-mail:         Browning@uic.edu}


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\noindent
 1. INTRODUCTION

Internal interfaces have long been known to be the key to many mechanical and electrical properties 
[1,2].  Extensive microstructural evaluations have been performed recently on for example, metal-oxide 
interfaces [3-5], semiconductor-oxide interfaces [6,7], semiconductor-metal interfaces [8,9] and grain 
boundaries [10-14] important for a wide variety of technological applications.  In many cases, the length 
scale over which the analysis was performed depends on the particular property that was being tested for, 
and more often than not, the availability of high-spatial resolution instrumentation.  Obviously, the study of 
interfaces is a huge field and we cannot hope to cover it all here.  In this paper, therefore, we concentrate on 
the analysis of interfaces where understanding the complexities of the structure-property relationships 
requires fundamental atomic scale information.  In particular, we will describe the requirements for the 
instrumentation to obtain the atomic scale information and will focus on the recently developed incoherent 
Z-contrast imaging [15] and electron energy loss spectroscopy (EELS) [16] techniques in the scanning 
transmission electron microscope (STEM).  Furthermore, we will describe the use of basic theoretical 
models to correlate multiple imaging and analytical techniques together and finally, present some examples 
demonstrating materials interface problems where these techniques have provided fundamental atomic 
scale information on the structure-property relationships.\\

\noindent
2. EXPERIMENTAL TECHNIQUES

The key to high-resolution STEM is the formation of an electron probe of atomic dimensions.  Figure 1 
shows a schematic of the experimental microscope conditions and the relationship between the probe, the 
specimen and the various detectors that we will be discussing in the upcoming sections.  Essentially, 
whether we consider a dedicated STEM [17] or one of the more modern TEM/STEM instruments [18], the 
electron optics of the microscope above the specimen are aligned in such a way as to make the probe as 
small as possible on the surface of the specimen.  For a given acceleration voltage the size of the probe is 
dependent on the spherical aberration coefficient of the probe forming lens.  As the general principles of 
aligning and optimizing the probe are the same for all STEMs we only discuss here the specifics of probe 
formation in the JEOL 2010F TEM/STEM as an example of how the process works experimentally [18, 
19].
Figure 2 shows the electron optical arrangement of the probe-forming system in the JEOL JEM-2010F.  
The de-magnification of the Schottky field emission source in this microscope is achieved by an 
electrostatic gun lens and a twin condenser lens system. One difference compared to the cold field emitter 
generally used in dedicated STEM, is that the Schottky electron source has a much larger emission area.  
Each element of the source is assumed to emit incoherently and therefore leads to an incoherent broadening 
of the probe.  However, this is overcome by a large de-magnification factor between source and probe.  The 
drawback in terms of instrument performance is that this is at the expense of decreasing the amount of 
current in the probe.  In particular, by using the C1 lens near maximum excitation, a cross-over is formed 
between the two condensers and a large source de-magnification can then be achieved (probably a factor of 
ten greater than is necessary in the cold field emission STEM).  C2 and the gun lens can then be used to 
tune the probe coherence further, depending on the probe size that is required.  
This tuning and optimizing of the electron probe can be achieved most readily with the electron 
"Ronchigram", or "shadow image".  This is because the intensity, formed at the microscope Fraunhofer 
diffraction plane, varies considerably with angle, and this variation is a very sensitive function of lens 
aberrations and defocus [20, 21].  When the excitation of each illumination electron optical component (i.e. 
lens, stigmator) is slightly changed, very small misalignments become apparent by translations in the 
pattern that depart from circular symmetry.  Furthermore, the presence or absence of interference fringes in 
the pattern indicates the amount of incoherent probe broadening due to instabilities and the effect of a finite 
source size.  Figure 3 shows schematically the ray diagram for Ronchigram formation.  The probe remains 
stationary and the post-specimen intensity is recorded as a function of angle by a CCD camera or 
equivalent device.  
Typical Ronchigrams at the amorphous edge of a specimen are shown in figure 4.  At large defocus, 
the electron cross-over is at a relatively large distance from the specimen, and a projection image is 
observed.  As Gaussian focus is approached, an angular dependence to the magnification emerges, due to 
lens aberrations and the manner in which they change the phase of the electron beam.  At slight underfocus, 
the azimuthal and radial circles of infinite magnification can be seen [21].  These are the angles at which 
defocus and spherical aberration effectively cancel and are characteristic of Ronchigrams from a round, 
probe-forming lens.  Axial astigmatism can be very accurately corrected by exciting the stigmator coils so 
that these Ronchigram features are circularly symmetric.  As the beam is focused, the central, low angles 
display the highest magnification.  The coma free axis is clearly defined by this position and all alignment 
and positioning of detectors and apertures can be performed with respect to this spot.  The prime advantage 
of using a Ronchigram is that the coma-free axis is directly visible.  In other alignment methods, the current 
or voltage center of the objective lens must be used as the reference and this is not always sufficiently 
accurate.  Next, the illumination beam alignment can be very accurately checked by wobbling first the 
condenser lens excitation and then the microscope high tension.  If there is a misalignment of the beam 
between condenser and objective lenses, there will be a periodic translation of Ronchigram features as the 
wobbling takes place.  This can be corrected using the condenser alignment coils so that the features only 
oscillate in and out about the coma-free axis [22-24].


The probe has now been aligned with respect to the coma-free axis.  Control of its intensity distribution 
is now dependant on the exact illumination lens settings and the size of the STEM objective aperture that is 
subsequently inserted to exclude aberrated beams at high angles.  Figure 5 shows Ronchigrams from a thin 
region of Si <110> at slight defoci.  Diffraction effects are clearly present in the pattern and lattice fringes 
are observed if the probe coherence is great enough. Also, at large defocus, when a shadow image at low 
magnification is visible, the crystal Kikuchi lines are seen (figure 5).  Since the coma-free axis position is 
already known, it simple to adjust the specimen tilt so that the desired zone axis is aligned precisely, for the 
sub-micron specimen area that is of interest in the experiment.  The microscope and the specimen are now 
in precisely the optimum conditions to perform experiments at the highest spatial resolution available.  It is 
now only necessary to define the type of scattered signal that will be collected as a function of the probe 
position to form the experimental image.\\

\noindent
2.1. Z-CONTRAST IMAGING

Z-contrast images [14,15,17] are formed by collecting the high-angle scattering (40-100 mrad at 200 
kV [18]) on an annular detector (Figure 1).  Detecting the scattered intensity at these high-angles and 
integrating over a large angular range effectively averages coherence effects between neighboring atomic 
columns in the specimen.  Thermal vibrations reduce the coherence between atoms in the same column to 
residual correlations between near neighbors [25,26], a second order effect.  This allows each atom to be 
considered as an independent scatterer.  Scattering factors may be replaced by cross sections, and these 
approach a Z$_2$ dependence on atomic number.  This cross section effectively forms an object function that 
is strongly peaked at the atom sites, so for very thin specimens where there is no dynamical diffraction, the 
detected intensity consists of a convolution of this object function with the probe intensity profile (Figure 6) 
[17].  The small width of the object function (~0.02 nm) means that the spatial resolution is limited only by 
the probe size of the microscope (the optimization of which is achieved using the Ronchigram, as described 
above).  For a crystalline material in a zone-axis orientation, where the atomic spacing is greater than the 
probe size, the atomic columns are illuminated sequentially as the probe is scanned over the specimen.  An 
atomic resolution compositional map is thus generated, in which the intensity depends on the average 
atomic number of the atoms in the columns.  
This result also holds true for thicker specimens.  It has previously been noted that for specimens in 
zone-axis orientations, the STEM probe forms narrow spikes around the atomic columns as it propagates 
[27].  This effect is caused by the coherent nature and large angular spread of the STEM probe, which leads 
to the tightly bound s-type Bloch states adding constructively and the less localized states interfering 
destructively [17].  This effect is enhanced for scattering processes such as high-angle thermal diffuse 
scattering that are localized at the atomic cores, causing a great reduction in beam broadening.  With only 
one dominant Bloch state, dynamical diffraction effects are largely removed and manifest only as a 
columnar channeling effect, thus maintaining the thin specimen description of the image as a simple 
convolution of the probe intensity profile and an object function, strongly peaked at the atom sites (Figure 
6).
The phase problem associated with the interpretation of conventional high-resolution TEM images is 
therefore eliminated.  In thin specimens, the dominant contribution to the intensity of a column is always its 
composition, although due to the higher absorption of the heavy strings the contrast does decrease with 
increasing specimen thickness and in very thick crystals there is no longer a high resolution image.  The 
effect of changing focus is also intuitively understandable as the focus control alters the probe intensity 
profile on the surface of the specimen.  For defocus less than the optimum Scherzer condition, the probe 
broadens causing the individual columns not to be resolved.  For higher defocus values the probe narrows 
with the formation of more intense tails, causing sharper image features but compositional averaging over 
several columns.  The optimum focus condition therefore represents a compromise between high resolution 
(narrow probe profile) and the desire for a highly local image (no significant tails to the probe).  This also 
corresponds to the optimum probe for microanalysis [16, 28,29].
At defects and interfaces, structures can become extremely complicated, causing difficulties in 
determining the precise 3-dimensional composition.  However, provided an atomic column is continuous 
through the crystal, reconstructions will only result in a change in column intensity and not a contrast 
reversal [14].  The atomic structure in the region of defects and interfaces can therefore still be determined 
largely from the image, and used to position the electron probe for EELS [16, 28, 29].  \\


\noindent
2.2. ELECTRON ENERGY LOSS SPECTROSCOPY (EELS)

As can be seen from Figure 1, the annular detector used for Z-contrast imaging does not interfere with 
the low-angle scattering used for EELS [30].  This means that the Z-contrast image can be used to position 
the electron probe over a particular structural feature for acquisition of a spectrum [16, 28, 29].  The 
physical principle behind EELS relates to the interaction of the fast electron with the sample to cause either 
collective excitations of electrons in the conduction band, or discrete transitions between atomic energy 
levels, e. g. 1s$\rightarrow$2p transitions [30].  The ability to observe discrete atomic transitions allows compositional 
analysis to be performed by EELS (the transitions occur at characteristic energy losses for a given element).  
Furthermore, the transitions to unoccupied states above the Fermi level allows the degree of hybridization 
between atomic orbitals to be determined, i.e. information on local electronic structure (bonding) changes 
can be ascertained.

To be able to correlate the spectrum precisely with the structural feature seen in the image, it is 
essential that the spectrum have the same atomic resolution as the Z-contrast image.  In order to achieve 
this atomic resolution, the range over which a fast electron can cause an excitation event must be less than 
the interatomic spacing.  Hydrogenic models [31,32] show that for the majority of edges accessible by 
conventional energy-loss spectrometers ($Delta$E < 2 keV) the object functions are localized within 0.1 nm of 
the atom cores [33-35].  Hence, like the Z-contrast image, we have an object function localized at the atom 
cores and an experimental probe of atomic dimensions.  For crystalline materials in zone-axis orientations, 
providing we maintain a large collection angle (15-30 mrad), coherent effects will be averaged and the 
description of the spectrum in terms of a convolution of the probe with an object function is valid (Figure 
6).  An important aspect of this experimental approach is that the probe channeling discussed for Z-contrast 
imaging will also preserve the spatial resolution of the spectrum, thereby allowing atomic resolution 
analysis of the electronic structure to be achieved even with large collection apertures.  Of course specimen 
drift is also a problem, but for the acquisition times of less than 5s used in all practical applications 
discussed here, the 1\AA /minute drift of the microscope does not induce a significant broadening effect.\\

\noindent
2.3. INTERPRETING THE ATOMIC RESOLUTION RESULTS

The combination of Z-contrast imaging and EELS allows us to obtain precise information on the
atomic structure, chemical composition and electronic structure at interfaces and defects on the atomic 
scale.  However, having obtained this wealth of information, the question remains as to how to incorporate 
it into a model for the interface that will allow us to understand the structure-property relationships.  There 
are many theoretical methodologies that can be used to understand the structure-property relationships, 
ranging in complexity from ab-initio calculations [36] to empirical pair potentials that have their origins in 
crystal chemistry [37].  Although we acknowledge here that the optimum analysis of interfaces requires the 
use of ab-initio calculations, we will only discuss the more simple pair potentials and their application to 
the materials problems described in later sections.  The reason for doing this is that, although the models 
provide only approximate solutions, the pair potentials allow us to deal with very general boundary 
structures, and the approximations at least allow us to capture the basics of the physical processes occurring 
at the interfaces being examined.\\

\noindent
2.3.1. Simple Structural Models

The aim of the analyses described later in this paper is to determine the complete three-dimensional 
structure of an interface and to use this to infer the structure-property relationships.  Hence, what is 
required in the initial stages is a simple means of verifying that the number of atoms and approximate 
structure observed in the Z-contrast image of the interface is correct.  One means to do this is through 
combined distance least squares and bond-valence sum analysis of the Z-contrast image [38].  This 
distance-valence least squares analysis (DVLS) is based on a concept that was originally proposed by 
Pauling [37].  In Pauling's rules for crystal chemistry, it is assumed that the formal valence state of a given 
atom is composed of contributions from all the nearest neighbors.  Additionally, the contribution to the 
valence from each of the neighbors should be as uniform as possible, i.e. the contributions to the formal 
valence state of an atom are shared equally between the nearest neighbors.  These ideas have been further 
developed by Altermatt and Brown [39,40].  In a systematic study of crystal structures they find that the 
contribution of a single bond to the formal valence-state of the atoms involved follows the empirical 
relationship
\begin{equation}
S = exp [ (r_{ij}-r_0 )/B ]
\end{equation}
where $r_{ij}$ is the bond-length, $r_0$ is an equilibrium value for each atom pair and B is a constant (=0.37).  
While this relationship is determined only for perfect crystal structures, there is every reason to believe that 
the same basic principles will apply for interfaces.  (We know that the structure exists as we have an image, 
and if the same elements are involved it is reasonable to assume their bonding will be similar).  It is 
therefore possible to utilize this very simple pair potential between two atoms to check if the atoms in a 
proposed boundary structure are in a reasonable environment [14].  If the valence is too high, the bond 
length is too short and vice-versa.  Furthermore, the equilibration of the bonds to the nearest neighbors 
using the distance least squares aspect of this formulation effectively forms a very basic energy 
minimization of the structure.  Although such a minimization is by no means as accurate as ab-initio 
calculations, a benefit of this simple approach is that it requires minimal computation capacity and within 
the errors (~10\%), can verify that the number of atoms and their positions in the structure are physically 
reasonable [14,38].\\

\noindent
2.3.2. Multiple Scattering Simulations

Having defined the numbers of atoms and their positions taken from the image to be physically 
reasonable with the bond-valence program, we are now in a position to use these positions to simulate the 
energy loss spectrum.  As we know the atomic location from which the spectrum was acquired, we can 
construct atomic clusters from defined locations in the interface and use them to simulate the spectrum with 
multiple scattering analysis [41-44].  Although multiple scattering theory was originally developed for the 
analysis of X-ray absorption spectra, its application to EELS is straightforward [45] (only the method of 
excitation has changed from an X-ray to an electron).  Multiple scattering calculations model the density of 
unoccupied states by considering the scattering of the photoelectron created during the excitation process, 
from neighboring atoms.  The many paths which may be taken by a photoelectron alter the matrix elements 
for a particular transition due to constructive or destructive interference which occurs between the outgoing 
and returning photoelectron wave (figure 7).  In effect, the resultant energy loss spectrum may be described 
as a simple absorption edge of hydrogenic form, due to an isolated atom, with intensity modulations due to 
the atomic structure of the solid (figure 7), i.e. the absorption $\alpha(E)$ is given by
\begin{equation}
\alpha(E)=\alpha_0(E)[1+\sum_{n=2}X_n(E)]
\end{equation}
where $\alpha_0(E)$ is the atomic absorption and $X_n(E)$ is the multiple scattering signal of order $n$ ($n>1$) 
which contains all the structural information [46].  Since this description of the unoccupied density of states 
is based on a real space cluster of atoms, several unique opportunities are presented for the analysis of 
interfaces.  First of all, a lack of symmetry does not seriously affect the calculation, so as with the bond-
valence analysis we can deal with very general interface structures.  Additionally, the effects of dopant 
atoms may be simply investigated by substituting atom types within the cluster and recalculating the 
scattering.  Multiple scattering therefore allows spectral changes to be directly interpreted in terms of 
structural changes.  As we have a starting structural model for interfaces in the Z-contrast image (refined by 
bond-valence), with this multiple scattering analysis we can incorporate the third dimension and any 
compositional changes into complete models on which to base the interpretation of the structure-property 
relationships.\\

\noindent
2.4. APPLICATION OF STEM TECHNIQUES TO MATERIALS PROBLEMS

One of the main principles behind the use of the STEM to solve interface problems is that the 
analytical and imaging techniques can be correlated together with atomic resolution (using in the most 
simple case bond-valence and multiple scattering analysis to achieve the correlation).  This provides extra 
information that allows us to investigate the very complex structural and chemical behavior that can occur.  
As an example of the use of correlated techniques and basic interpretation tools described above to 
investigate atomic scale phenomena, we describe here the analysis of edge dislocations in metal-organic 
vapor phase epitaxy (MOVPE) grown GaN thin films [47].  These structures are of fundamental interest to 
the materials science community, as a high density of threading dislocations appears to have a benign effect 
on GaN high efficiency light emitting diodes. The origin of the benign effect remains unclear as although 
early work [48, 49] suggested that threading dislocations are not non-radiative recombination centers, the 
increase in optical properties that is achieved [50] by reducing the threading dislocation density in the 
epitaxial lateral overgrowth method [51], provides circumstantial evidence that dislocations do in fact have 
a deleterious effect.  Furthermore, recent more direct evidence indicates that threading dislocations can be 
optically and electrically active [52-59].  
Figure 8 shows a Z-contrast image obtained from the VG HB603 U dedicated STEM (the alignment, 
operation and resolution of which is the same as the JEOL 2010F described in earlier sections.  The only 
difference being that this instrument has a cold field emission gun). The core clearly shows the eight-fold 
ring structure, as previously reported [60].  On the basis of the prior theoretical calculations, this n-type 
sample grown under N-rich growth conditions (The sample is also doped with Si at a level of
$\sim 2\cdot 10_{18}$ cm$^{-3}$
and has a free carrier mobility is about 200 cm$^2$/Vs) is expected to show a Ga-vacancy core structure
[54].  Since atoms contribute to the image according to their mean square atomic number (Z), the light N 
atoms contribute only 5% of the image contrast in a full GaN atomic column.  Thus it is immediately 
apparent from the image that the Ga vacancy concentration must be much less than 100\%. At the typical 
thicknesses used for Z-contrast imaging, the image intensity is roughly proportional to the number of atoms 
in a column [17].  Therefore our sensitivity to Ga vacancies is limited just by the statistical variations in 
column intensities close to the dislocation core.  Integrated columnar intensities showed a mean deviation 
of 15\%.  From this data we therefore estimate the Ga vacancy concentration to lie in the range 0-15\% per
c-axis repeat, which implies a significantly lower line charge than previously assumed for threading 
dislocations in GaN. 
The local electronic structure in the core can be investigated using the Nitrogen K-edge EELS 
spectrum.  This absorption edge gives information on transitions from the 1s core level to the unoccupied 
density of states in the conduction band with 2p symmetry.  Figure 9 shows the dislocation image obtained 
from the 2010F with the larger beam diameter used for EELS (For spectroscopy, the probe size is increased 
from the 0.14nm resolution limit to 0.2nm in order to provide more signal). Figure 9 also shows 
experimental nitrogen K-edge spectra obtained from several pure edge dislocation cores as well as from 
nearby perfect regions of the film for comparison.  Each spectrum is the summation of 13 spectra from 8 
dislocation cores with an acquisition time of 5 seconds for each individual spectrum and with an energy 
dispersion of 0.2eV/channel.  The experimental collection conditions (see earlier sections) result in an 
energy resolution of 1.2eV.  A power-law background subtraction has been used [30], but otherwise the 
spectra are as acquired.  
It can be clearly seen that there are dramatic changes in the fine structure of the Nitrogen K-edge 
spectra on and off the dislocation core.  In particular, in the core spectrum, the first peak 2.2eV above edge 
onset (398eV) rises significantly relative to the second peak.  Simulations of the electronic structure using 
the multiple scattering methodology of the FEFF 8 [43] codes described in earlier sections of this paper are 
also shown in Figure 10 (the clusters were built using the bond valence analysis also described earlier).  
These simulations take full account of the experimental conditions in the relative weighting of the in-plane 
and c-axis component of the experimental spectrum [61] and show a similar trend to the experimental 
results.  The increase in absorption just beyond the band gap is most likely due to the broken symmetry in 
the region of the core [62]. 
The combination of the Z-contrast image and EELS therefore provides significant information on the 
local atomic and electronic structure changes at the dislocation core.  In particular, it is noteworthy that no 
absorption is seen in the region of the band gap.  This is consistent with any Ga vacancy induced acceptor 
states being full, as expected if the dislocation line is charged.  However, the Z-contrast image suggests that 
the vacancy concentrations in the core may be less than previously considered, which may explain the 
benign effect of threading dislocations on the electrical and optical properties.  However, a full 
understanding of this subtlety requires extensive investigation by ab-initio methods, which are currently 
underway.  We must, of course, also consider the effect of screw dislocations and mixed dislocations in 
attempting to draw definitive conclusions between the structure of dislocations and the bulk properties of 
the film.  Here our intention is simply to point out that the experimental tools to make such measurements 
now exist. \\

\noindent
3. HOMOPHASE INTERFACES

The first set of interface problems that we describe relates to homophase interfaces, or grain 
boundaries.  In this set of problems, the material a distance of $\sim$1nm either side of the interface can be 
described as being bulk like in structure.  Our aim in performing the atomic resolution STEM analysis is to 
understand the relationship between structure and properties in this 1-2 unit cell region at and around the 
grain boundary plane.\\

\noindent
3.1. SrTiO$_3$

SrTiO$_3$ has been the subject of many recent investigations.  Although each of the individual 
investigations had specific reasons, the wealth of information that is available on SrTiO$_3$ is really due to its 
existence as the most basic of perovskite materials [63].  However, unlike the perovskites being developed 
for high-$T_c$ superconductors [64], ferroelectrics [65], novel dielectrics [66] and colossal magneto resistance 
materials [67], it shows none of the detailed electronic and ionic functions of those materials.  For our 
purposes, this means it can be used to investigate some of the fundamental structures and processes that 
occur at grain boundaries in perovskites [14, 68, 69].

Figure 11 shows a typical Z-contrast image obtained from a 36o[001] tilt grain boundary in SrTiO$_3$ (the 
image was obtained from a VG HB603 STEM).  From analysis of this boundary and images from other 
symmetric and asymmetric [001] tilt boundaries [68,69] it can be seen that the boundary plane is composed 
of distinct repeating "structural units".  The structural unit model [1,70] for grain boundaries is formally 
equivalent to dislocation core models [71].  However, rather than characterizing the dislocations by a series 
of cores with defined Burgers vectors, the structural unit model focuses on the atomic arrangements within 
the core.  This is of particular use for the study of oxide grain boundaries, where the atomic arrangement 
can lead to different bonding interactions between the metal and oxygen atoms.  The structural units needed 
to construct all [001] tilt grain boundaries in SrTiO$_3$ are shown in Figure 12 [68,69].

As can be seen from Figure 12, the structural units can be centered on either of the cation sub-lattices.  
This experimental observation of structural units on both the Sr and the Ti sub-lattices immediately 
highlights an advantage of this methodology in investigating the structure-property relationships of grain 
boundaries.  The chemistry of the A and B sites in the perovskite structure (formula ABO$_3$) is different, and 
it can be expected that dislocation cores on the different sub-lattices will exhibit different chemical effects.  
This factor is not included in dislocation core models, where the only discriminating factor for each core is 
a Burgers vector that is independent of the atomic structure in the core.  Furthermore, if we examine the 
structural units more closely, we see that there are locations where the columns appear too close together.  
In such situations, like-ion repulsion should preclude such a structure.  However, if we remember that the 
Z-contrast image, like any transmission image, is simply a 2-D projection of the 3-D crystal structure, a 
solution to this problem is for only one of the two sites in each perovskite block in the c-direction to be 
occupied.  We would still see two columns in projection, but avoid like-ion repulsion.  An alternative view 
of these "half-columns" is that they are a single atomic column that is distorted through the thickness of the 
crystal in a regular manner, i.e. a 2 x 1 reconstruction.

To understand the effect of this 2 x 1 reconstruction on the electronic properties of the grain 
boundaries we can get further information from EELS. The oxygen K ionization edge and titanium L$_{2,3}$ 
ionization edge obtained from the grains and the boundary are shown in figure 13.  As can be seen from the 
figure, there are still two peaks in the Ti L$_{2,3}$ edge and therefore the crystal field remains, and the Ti atoms 
at the boundary must still be octahedrally coordinated.  There is also a reduction of the crystal field, which 
is explained simply by a distortion of this octahedral coordination. The $\pi^*$maximum (1st peak) of the O-K 
ionization edge is lower at the grain boundary than in bulk while the $\sigma^*$ maximum (2nd peak) is higher. 
These changes have been associated with the distortion of O-Ti-O bond angle [72] and is also consistent 
with behavior observed in TiO$_2$ [73]. To summarize, two features change at pristine grain boundaries: the 
distance of the first two peaks of the Ti-L$_{2,3}$ and the peak ratio of the first two peaks in the O-K edge. From 
these changes we can say that Ti remains basically octahedrally coordinated by O, but the distortion of the 
octahedra results in Ti-O bond angles deviating from 180$^\circ$.  These conclusions have been verified by bond-
valence calculations and multiple scattering analysis of the 25$^\circ$ [001] tilt grain boundary structure [45].

Having defined the changes in both the atomic and electronic structure that occur at undoped or 
pristine grain boundaries, we are now in a position to evaluate how the incorporation of a dopant atom at 
the boundary affects the properties.  In the case of acceptor like dopants, i.e. Fe$^{3+}$ substituting for Ti$^{4+}$,
there
has been observed to be significant segregation of the acceptors at the boundary [74] and the occurrence of 
Schottky barrier-like transport behavior [75].  In this experiment, Mn acceptors were diffused into the grain 
boundary plane by annealing a 36$^\circ$ [001] tilt boundary bicrystal covered with MnO$_2$ paste at 1350$^\circ$C in air 
for 5.5 hours.  The Z-contrast image of this boundary, in figure 14, shows that there is no secondary phase 
formed at the boundary and the boundary itself has the same structural units as observed for the pristine 
boundary shown in figure 11 [29, 76].

 Ti-L$_{2,3}$ edges were obtained while the beam was scanned in a rectangular area of about 1.5 unit 
cells (0.6nm$\times$1.0 nm ).  The Ti-L$_{2,3}$ edges from the grain boundary core and bulk are shown in figure 15.  
Consistent with the pristine grain boundaries, the crystal field splitting is reduced, but the onset of the edge 
did not shift in energy.  We can therefore conclude that the Ti atoms have the same distorted octahedral 
oxygen coordination at this boundary (this seems appropriate as the image shows the same structural units).  
A quantification and comparison of the Ti-L$_{2,3}$ ELNES with results from the pristine grain boundary is not 
possible due to  differences in spatial and energy resolution.

Single atom column resolution was however obtained for the O-K and Mn-L$_{2,3}$  edge. The 
numbers in figure 16 correlate with the positions the beam was located (see figure 14) while spectra were 
taken.  The ELNES of the O-K edge and the intensity of the Mn-L$_{2,3}$ edge can be seen to change 
dramatically from column to column.  The maximum intensity of the Mn-L$_{2,3}$ edge coincides with the 
reconstructed Ti-O columns at the core of the dislocation unit [14, 68, 69].  This result is not surprising as 
Mn is expected to substitute for Ti.  However, the Mn signal was also seen up to 2 nm away from the 
boundary. This distribution profile was to be expected from the way the sample was prepared; the Mn fast 
diffused along the grain boundary and then proceeded more slowly into the bulk.

To determine the oxidation state of Mn we performed an analysis of the Mn-L$_{2,3}$ near-edge fine 
structure. More than 90\% of the Ti-L$_{2,3}$ ELNES are due to transitions between 2p and d symmetry 
conduction bands.  In the following we will therefore ignore any contributions from 2p$\rightarrow$s transitions.  We 
analyzed the ratio between the continuum (chosen to be represented in the area between 20 to 40 eV after 
the onset) and the sum of the L$_3$ and L$_2$ peaks, which is a symmetry independent way of determining the 
filling of the d bands [30]. The L$_3$/L$_2$ ratio alone is not a good measure for the oxidation state because the j-j 
coupling between initial and final states (causing the variation of the L$_3$/L$_2$ ratio) is influenced by symmetry 
changes apparent at grain boundaries. Our analysis indicates a less filled d band at the grain boundary.  
Comparing this analysis with the results from bulk manganites [77] suggests a 4+ oxidation state of Mn in 
the bulk and a 3+ oxidation state at the grain boundary core.

To obtain the atomic column resolved ELNES of the O-K edge, we sacrificed energy resolution 
for the sake of increased signal.  The $\pi^*$ and $\sigma^*$ peaks are not resolved in figure 16.  To clarify whether the 
observed changes in the ELNES can be correlated to a structural change for examples of the anions, we 
performed multiple scattering calculations with the same energy resolution as the experiment.  For these 
calculations we used the same structure as for the pristine 36$^\circ$ grain boundary and replaced the Ti in the 2 x 
1 reconstructed columns with Mn.  The results in figure 17 show an extremely good correlation between 
experiment and theory.  The observed changes of the O-K edges at the grain boundary therefore primarily 
reflect the reduced symmetry at the location where the spectra are taken.  It should be noted that the spectra 
described earlier for the pristine boundaries represent an integration over the entire boundary plane and so 
the column to column fluctuations in fine structure on this scale were not observed.

These results indicate that the cation grain boundary structure can reliably be determined with Z-
contrast imaging and that with the Ti-L$_{2,3}$ edge and the O-K edge data, we can go further and show that 
octahedral coordination is maintained, although distorted, at {\it both} doped and pristine grain boundaries.  
Intrinsically, such studies also give us information that shows the valence state of the Mn acceptors to be 
+3 in the boundary plane and +4 only 1nm away from the boundary plane (this information is only 
available by EELS).  For the future, to fully understand what is happening at these grain boundaries and 
determine whether oxygen vacancies play a role in determining the Mn valence and the electrical activity, 
we need to perform the EELS measurements with higher energy resolution (i.e. resolve the $\pi^*$ and
$\sigma^*$
peaks).  We also need to employ more sophisticated ab-initio simulations to interpret the data.  However, 
that said, the experimental pathway is well defined and we should be able to use this approach to finally be 
able to reveal the microscopic origin of electrical activity at grain boundaries in perovskites.\\

\noindent
3.2. YBa$_2$Cu$_3$O$_{7-\delta}$

As one of the first high-Tc superconductors to be discovered [78], the electrical properties of grain 
boundaries in YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO), have been well documented over the last ten years [79-81].  
Essentially, it has been found that the critical current, $J_c$, that can be passed across a grain boundary falls 
off exponentially with increasing misorientation angle [79-81].   There have been several models to account 
for this that have focussed on the suppression of the superconducting order parameter by the long range 
strain fields around the dislocation cores in the boundary plane [82,83].  However, at larger angle grain 
boundaries, the overlap of the individual strain fields [71] may make the use of such concepts 
inappropriate.  As we have shown from the study of grain boundaries in SrTiO$_3$ (previous section) there is 
an alternative formalization to consider dislocation cores at grain boundaries; the structural unit model.  
Here we discuss the structural unit model for high-angle grain boundaries and how it can be used to infer 
the properties of both low- and high-angle boundaries.
As can be seen from the Z-contrast image of a high-angle [001] tilt grain boundary in YBCO shown in 
figure 18, the grain boundary plane is composed of the same structural units as the SrTiO$_3$ [001] tilt 
boundaries (figure 12) [84].  Given that the two materials are both perovskites with similar lattice 
parameters (for YBCO $a\sim b\sim 3.8$ \AA and for SrTiO$_3$ $a=b=3.905$ \AA) and that this YBCO thin film was grown by 
laser ablation [85] on a SrTiO$_3$ bicrystal substrate, this similarity may not be surprising.  However, it does 
mean that we can use similar concepts to understand the properties of YBCO boundaries as were developed 
for SrTiO3 in the previous section.  One major point that should be noted for the analysis to follow, is that 
high-resolution TEM and Z-contrast imaging results from YBCO films grown on various substrates have 
shown the grain boundary planes to be facetted on the nanometer length scale with a predominantly 
asymmetric boundary plane [84, 86,87].  For this type of boundary, the Z-contrast images show that the 
structural units exist with the reconstructed columns on the Cu-O sub-lattice (equivalent to the Ti-O sub-
lattice in figure 12).  Given that the integrity of the Cu-O planes is known to be key to the doping in the 
bulk structure, the disruption of these planes is already a good indication as to why there is a decrease in the 
critical current at grain boundaries.

Further information on the effect of these structural units on the doping at the grain boundary plane can 
be obtained from EELS [88-90].  In particular, for p-type superconducting compounds, such as YBCO, the 
doping mechanism can be explained by considering the structure to consist of conduction CuO$_2$ layers 
separated by charge reservoir blocks.  The interaction of the charge reservoir blocks with the conduction 
layers leads to the formation of the charge carrying holes in the predominantly Oxygen 2p-Copper 3d 
valence band.  As EELS is sensitive to the density of unoccupied states in the region of the Fermi surface, 
this means a quantified measurement of the number of charge carriers can in principle be obtained from 
both oxygen and copper core-edge spectra.  For EELS in the STEM, the characteristic core edges that are 
readily accessible by the spectrometer are the oxygen K-edge (1s$\rightarrow$2p transitions) and the copper L$_{2,3}$-edge 
(2p$\rightarrow$3d transitions).  For YBCO, the most accurate means of quantifying the number of holes is through 
the pre-edge feature on the oxygen K-edge [89] using a series of Gaussian functions (Figure 19).  Using 
this method, the hole concentration can be quantified to $\sim$5\% accuracy.  Also shown in figure 19 is a 
quantified measurement of the hole concentration around a 30$^\circ$ [001] tilt asymmetric grain boundary in a 
YBCO film grown by laser ablation [91].  As can be clearly seen from the profile, there is a significant 
depletion in the number of charge carriers at the grain boundary.

To investigate the origin of this charge depletion at grain boundaries, we can use the bond-valence 
analysis described earlier. In a perfect unit cell of YBCO, the valences of most of the elements involved 
change very little between YBCO7 and YBCO6 (<10\%).  The exception to this is copper.  In fully 
oxygenated YBCO the copper (1) valence is $\sim$2.3, whereas in fully oxygen deficient YBCO the copper 
valence is $\sim$1.2 [94], although the copper (2) valence changes by <10\%.  This implies that the copper (1) 
valence can be used as a very sensitive measure of the number of charge carriers present in the structure. 
To investigate this effect further, the structures of asymmetric boundaries at other misorientation angles 
were constructed from the structural units using continuity of grain boundary structure principles [70].  As 
a first approximation the boundaries were considered to be straight, i.e. consist of one particular grain 
boundary plane.  For boundary misorientations of 11.4$^\circ$ (boundary plane (100)/(510)), 18.4$^\circ$ (boundary 
plane (100)/(310)), 26.6$^\circ$ (boundary plane (100)/(210)), 33.7$^\circ$ (boundary plane (100)/(210)), and 45$^\circ$ 
(boundary plane (100)/(110)), the copper (1) valence as a function of distance from the boundary core can 
then be calculated from bond-valence sum analysis.  In figure 20, the valence of each copper (1) site is 
plotted against its distance from the boundary.  Again, it is clear from this plot that the boundary perturbs 
the local electronic structure sufficiently to create a non-superconducting zone, but more importantly, it is 
seen that the width of this zone increases with misorientation angle.  These plots can now be used to define 
a grain boundary width.

An alternative approach to defining the grain boundary width, which is equally valid, is to use the 
semiconductor picture and consider the formation of a Schottky barrier at the grain boundary [92,93].  This 
Schottky barrier leads to a charge depletion layer above $T_c$, and therefore a lack of superconducting charge 
carriers when the material is cooled below the transition temperature.  In this model, we do not consider the 
details of the grain boundary arrangement as we do with the bond-valence scheme, only we say that each of 
the structural units is responsible for the formation of a localized electronic state in the grain boundary 
plane.  Using standard dislocation core models for the distribution of each structural unit as a function of 
the misorientation angle [71], we can therefore calculate the density of localized states that is present for 
each boundary plane (Table 1).

If we view this excess of charge as a 2-dimensional sheet, we can expect that this results in a 
compensating depletion layer either side of the boundary, the width of which is given by [1]
\begin{equation}
S_{gb} = N_{bulk} w           
\end{equation}
where $S_{gb}$ is the number of localized boundary states, $N_{bulk}$ is the bulk carrier doping and $w$ is full 
width of the depletion zone.  As we know the number of localized states at the boundary increases with 
misorientation angle, it is easy to see the depletion layer width must do the same. To quantify the width of 
the depletion zone at grain boundaries we need only insert the value of the bulk carrier doping 
($N_{bulk}=4/3V_{cell}$).  Using this criterion, the depletion zone width can be calculated.  In the same way as for 
the bond-valence model, we have therefore obtained an increasing barrier width with increasing 
misorientation angle.  Which model contains the most accurate representation of the physical process 
involved has yet to be determined (the bond-valence model is structural, which must obviously have some 
validity, but the potentials are empirical and can therefore lead to errors, while the Schottky model does not 
consider the origin of the charge states).
With either the bond-valence picture or the Schottky barrier model, we have an increasing barrier 
width with increasing misorientation angle. The magnitude of the superconducting tunneling current across 
a barrier can be calculated from
\begin{equation}
J_c = J_{c0} exp(-2\kappa\Delta)
\end{equation}
where $J_{c0}$ is the bulk critical current, $\Delta$ is the interface (depletion layer) width and
$\kappa$  is the decay constant
(7.7/nm) [94].  For each of the grain boundary misorientations shown in table 1, the width can be used to 
determine the expected tunneling current for a constant applied voltage: the criterion used experimentally 
to measure critical currents.  In Figure 21, the tunneling current as a function of misorientation angle for 
asymmetric boundaries is plotted and compared with a range of experimental critical current measurements 
(here the widths are taken from the Schottky model, but can equally well be taken from the bond-valence 
model).  For the boundary widths defined above, the structural unit model quantitatively reproduces the 
trend of exponentially decreasing critical current with increasing misorientation angle.  The fact that the 
line goes through the highest values of the experimental data is to be expected as in this analysis we have 
only considered the intrinsic effect of the boundary.  If we add the effect of processing induced oxygen 
deficiency, the charge depletion width would obviously increase, thereby lowering the critical current.  This 
could be a reason for the scatter in the experimental $Jc$ values.  It should also be noted that this analysis can 
be extended to low-angle grain boundaries.  Rather than using the strain field to estimate the relative area of 
superconducting material, we now use the relative area caused by the distribution of the structural units.  As 
such, the structural unit model can cover the whole range of misorientation angles.\\

\noindent
3.3. Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10}$

Another perovskite material that is currently being developed for technological applications is 
Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10}$. Highly-textured Ag-sheathed (Bi,Pb)$_2$Sr$_2$Ca$_2$Cu$_3$O$_y$ (Bi-2223) composite tapes have 
significant potential for the development of superconducting motors, magnets, and transformers. The Bi-
2223 phase is one of the Bi-based superconductors (BSCCO) that are represented by the general formula 
Bi$_2$Sr$_2$Ca$_{n-1}$Cu$_n$O$_y$ (where $n$=1,~2 or~3). Although relatively high critical-current density ($J_c$) values up to 
70kA/cm$^2$ have been obtained in multifilamentary Bi-2223/Ag tapes, these $J_c$ values are still less than a few 
percent of those of thin films [64]. This suggests that even though the cores are textured, grain boundaries 
still have strong effects on the supercurrent transport phenomena. From a morphological point of view, 
several models have been proposed to describe the current transport mechanisms in the BSCCO/Ag tapes. 
However, since the large-scale configuration of the boundaries are mainly considered in these models, the 
underlying mechanism controlling the properties has yet to be clarified. In order to elucidate the role of the 
grain boundaries, detailed studies on the atomic structure as well as the chemistry change at the boundary 
are required.

Here we use the Z-contrast imaging technique to analyze Bi-2223/Ag tapes containing 19 filaments 
and have a $J_c$ level of more than 60kA/cm$^2$ at 77K in self field (provided by American Superconductor).  
Short and transverse cross section samples were prepared by the standard TEM sample preparation 
methods.  The microscopic study was performed in the JEOL 2010F TEM/STEM described in earlier 
sections. As the lattice parameter for this material is quite large, $\sim$0.4nm, the size of the electron probe used 
for the experiments was selected to be 0.16 nm to increase the signal/noise in the images [18].

The majority of the grain boundaries observed in these tapes are c-axis twist boundaries.  Figure 22 
shows twist boundaries that are imaged with the incident beam oriented parallel to the [110] direction in the 
upper half of the images.  In the lower half several sets of two bright lines are observed which correspond 
to the BiO double layers viewed end on.  From these images it is quite obvious that the boundary is 
atomically flat and located in the middle of the double BiO layers.  Such results are consistent with 
previous conventional high-resolution TEM images [95], but the advantage of Z-contrast imaging is that 
the nature and the location of the boundary can be directly identified from the raw images without 
simulation. Another key point from these images is that although no amorphous layers are observed at the 
boundaries, local phase variations are often observed (the lack of a phase variation shown in figure 22 (a) is 
actually the minority case). In figure 22 (b) three unit cells of Bi-2212 phase are observed on the upper side 
of the boundary and a half unit cell of Bi-2201 phase on the lower part are present ($T_c$=20K as opposed to 
110K for Bi-2223).  Also, in the lower part of the image a half unit cell of the Bi-2234 phase is seen near 
the boundary.  Both the type and number of phases formed at/near the boundary is found to vary from 
boundary to boundary.  Such local phase variations at/near the boundary should have a strong influence on 
the local transport phenomena of the supercurrent as the thickness of the secondary phases is typically 
larger than the coherence length, especially in the framework of the brick- wall model [96].

Another typical set of grain boundaries usually present in BSCCO/Ag tapes is small-angle c-axis tilt 
boundaries. A characteristic of this type of the boundary is that basal planes of one grain are parallel to the 
grain boundary plane. This type of boundary has been considered to play a dominant role in transporting 
the supercurrent in the railway-switch model [97]. Figure 23 shows an 11$^\circ$ tilt boundary imaged with the 
incident beam oriented parallel to [110] orientation of each grain. These two images were obtained from the 
same area (there is a slight mis-tilt precludes imaging both grains simultaneously).  Periodic formation of 
the $n$=1,~2,~3 and~4 phases in upper grain and $n$=2~and~3 in the lower grain is observed along the boundary. 
Since the angle between the [110] of both grains is less than 0.1$^\circ$, a grain boundary structure can be 
constructed from these two images.  Figure 23 shows a schematic diagram of the grain boundary structure. 
In this figure, we can see again that the boundary forms on the BiO layers and that the type of phase formed 
varies periodically along the boundary.  We should also note that this periodic formation of different phases 
at the boundaries is also observed at small-angle c-axis tilt boundaries with a twist component. These 
different phases are expected to have different transport properties and the periodic local formation of 
different phases along a grain boundary plane may have important effects on the supercurrent transport not 
only through c-axis twist boundaries but also through small c-axis tilt boundaries, i.e. weak links are 
formed.\\

\noindent
4. HETEROPHASE INTERFACES

The examples that we have considered so far have concerned the determination of the structure and 
bonding at homo-phase interfaces, i. e. those interfaces where the material either side of the interface is the 
same.  We now turn our attention to hetero-interfaces where the material on either side of the interface is 
different.  This is the type of interface that is prevalent in semiconductor devices where the interface is 
either between the substrate and a thin film or between the different electronic components in the device, 
e.g. metal-oxide, semiconductor-oxide, metal-semiconductor.\\

\noindent
4.1. GaAs/Au

The first example [98] that we will consider here is the interface between gallium arsenide (GaAs) and 
Gold (Au).  This particular system has been studied extensively in an effort to ascertain the fundamental 
physics behind the formation of Schottky or Ohmic contacts between metals and semiconductors.  An 
ohmic contact between GaAs and Au was fabricated by alloying at 420$^\circ$C for 15 seconds after growth.  The 
interface region exhibits spiking with Au protruding approximately 50 nm into the GaAs.  The Au grains 
are aligned with the (1\=10)  plane approximately parallel to the interface.  Figure 24 shows a Z-contrast 
image at relatively low magnification showing one of the Au spikes, and the atomic resolution structure of 
the interface 50 nm away from the spike is shown in figure 25.  The image shows Au terminating on the 
(1\=10)  plane which results in a lattice mismatch of 2.5\% with respect to the (001) terminated GaAs.  An 
atomic step in the interface is present near the image center and the resolution here is approximately 
0.15 nm.  In figure 26 an angled section of one of the protruding spikes is shown.  The Au forms a (111) tilt 
boundary with GaAs (the angle is approximately 18$^\circ$) and a twin boundary is seen in the bulk Au where the 
angle of the interface changes.  Finally, figure 26 also shows a third example of the interface structure 
along one side of a spike.  Au is faceted along the close packed $\{$111$\}$ plane with steps every one to two 
atomic columns.  These preliminary results show that it is possible to identify the interface structure in 
heterophase interfaces directly using the Z-contrast technique.  Work is continuing in this area to correlate 
the types of interface structures with the electronic properties.  This will be achieved by a comparison with 
Schottky interfaces and also by looking at the Ni/GaAs system where EELS can be used to investigate the 
bonding changes at the interface.\\

\noindent
4.2. CdTe / Si (As)

As a final example of the use of STEM to investigate interface properties, we show an analysis of the 
effect of Arsenic (As) passivation of Silicon (Si) substrates on the subsequent growth of the II-VI 
semiconductor Cadmium Telluride (CdTe) [99, 100]. The interest in the growth of CdTe on Si is motivated 
by its potential use as an alternative substrate for the subsequent growth and fabrication of
Hg$_{1-x}$Cd$_x$Te
infrared detectors [101,102].  In this regard, the growth of single domain CdTe with the (111)B orientation 
(a short notation for the  Te polar surface, with(111)A denoting the Cd polar (111) surface), is particularly 
desirable as this orientation requires the least Hg flux for growth of Hg$_{1-x}$Cd$_x$Te by molecular beam epitaxy 
(MBE) [103].  This is also the standard orientation for HgCdTe growth in liquid phase epitaxy, and could 
be used for CdS/CdTe high efficiency solar cells grown by MBE .

In this work, two films were grown by MBE on nominal Si (111) substrates under similar growth 
conditions except that the substrates were cooled under a different initial flux, i.e. either As flux or Te flux. 
The microstructures of the two films grown on the Te and As treated Si (111) substrates are shown in 
Figure 27.  It is immediately obvious from the low magnification images that the two films have different 
structural features.  The film grown on the Te treated substrate has very faulted microstructure, containing 
different twin grains, planar defects on two sets of $\{$111$\}$ planes, and threading dislocations (Figure 27(a)).  
Furthermore, the polarity of the film is determined to be (111)A from the convergent beam electron 
diffraction (CBED) pattern (Figure 27(b)).  The film-substrate interface is also very rough, with 15nm 
modulations into the Si substrate due to the Te flux reacting with Si during cooling (Figure 27(c)).   A very 
different quality of film is observed for growth on the As-passivated substrate (Figure 27(d)).  Apart from 
the few wide lamellar microtwins confined to the 0.8 $\mu$m region close to the interface and a few threading 
dislocations, the epilayer is single crystal with excellent structural quality over large areas.  Double crystal 
X-ray rocking curves from the CdTe (333) reflection using Cu-K$\alpha_1$ and a Si (133) crystal monochromater 
gives measurement of the full width at half maximum (FWHM) of 87 arcseconds for a 5$\mu$m thick layer.  
The selected area diffraction pattern from the CdTe/Si interface shows the perfect alignment of CdTe (111) 
layer relative to the Si (111) substrate (Figure 27(e)).  The polarity of the film is confirmed to be (111)B by 
CBED(Figure 27(f)).  We should note at this point that this initial analysis of the general film 
microstructures highlights one of the advantages of the modern TEM/STEM instruments, i.e. that you can 
perform detailed phase contrast imaging and diffraction work in TEM mode prior to the more detailed 
STEM analysis.

The difference in the quality of the films therefore appears to be related to the difference in the initial 
flux treatment of the Si (111) surface.  Examining the CdTe/Si interface by energy dispersive X-ray 
spectroscopy (EDS) shows that the As that is initially deposited on the Si surface remains there for the 
subsequent growth of the CdTe film (Figure 28).  The three spectra show that only when the 1nm probe is 
placed at the interface is there an As signal present (the two other spectra are obtained $\sim$5nm from the 
interface). Furthermore, quantifying the spectra shown in figure 28 gives an estimate of the As 
concentration close to one monolayer.  These results are consistent with the in situ reflection high energy 
electron diffraction (RHEED) observations before initiation of the CdTe growth, and confirmed by x-ray 
photoemission spectroscopy [104].

Having generated a general picture of the film morphology and the composition of the film-substrate 
interface we can now move on to examine the interface in more detail using atomic resolution Z-contrast 
imaging.  Figure 29 shows a raw atomic resolution Z-contrast image of the CdTe/Si interface, and the same 
image after Fourier filtering.  The elongated white spots in the image are atomic columns separated by 
distances smaller than the 1.5\AA resolution of the microscope.  The first CdTe layer can be easily 
ascertained by the intensity difference at the interface, as CdTe has a higher atomic number than Si or As.  
The extra planes of the misfit dislocations are indicated, and the cores of the misfit dislocations are clearly 
seen located at the interface between the CdTe film and the substrate. By drawing a Burgers circuit around 
the cores, the edge component of the Burgers vector is 1/4[112], which is parallel to the interface, 
providing the explanation as to why there is no tilt of the epilayer with respect to the substrate.  The 
average spacing between misfit dislocations is 1.9nm.  These are the grown-in misfit dislocations that have 
relieved the majority of the mismatch strain.  
 

Z-contrast images (Figure 29) from a different area along the same interface, show that the first few 
layers of CdTe can also be deposited in a twinning position relative to the substrate.  This indicates that 
CdTe can initially nucleate in two orientations with a twinning relationship.  This means the film adopts 
either the substrate orientation with ABCABC$||$ABC ..., or in a twinning position to the substrate with 
ABCABC$||$BACBAC ..., where A, B, or C denotes the atomic double layer.  It must be pointed out from the 
high-resolution observations that no islands or grains other than the few coherent twin boundaries are found 
in the region at the interface, the twinned islands are of small quantity, and the film/substrate interface is 
atomically flat.

The above experimental observations show that As is crucial in obtaining the desired (111) B film with 
high crystalline quality.  There are two main factors that result in the single domain high crystalline quality 
epitaxial CdTe (111)B growth on Si(111); the As-passivated Si(111) surface which results in the(111) B 
polarity and the nature of atomic steps and terraces on the nominally Si(111) surface which give rise to 
layer growth free of multi-domains [99].  It is well known that As replaces the outermost Si atoms of the 
double layer during passivation of the Si(111) surface in the MBE growth process [105], and it is known 
from the above investigations that As stays there after the growth.  Both imply that As is present at the 
interface as a monolayer separating CdTe and Si during the growth.  Based on the As-Cd, As-Te bond 
formation energies [106], it is likely that Cd is favored as the first atomic layer forming bond with the As at 
the interface, where the bonding configuration proceeds in a fashion such as Si-As-Cd-Te across the 
interface as shown in Figure 30.

Even though it is known that Cd atoms have a very low sticking coefficient and would re-evaporate 
from the surface under only a Cd flux, the resultant CdTe (111) B layer growth implies that the presence of 
Te atoms supplied by stoichiometric flux is sufficient to stabilize the Cd on the surface.  This occurs 
through a transition layer at the growth front.  CdTe is initiated with Cd atoms forming one bond with As 
and three bonds with Te, producing a Te stabilized growth surface, which finally results in the (111) B 
growth.  Because of the high interfacial energy associated with the large lattice mismatch between CdTe 
and Si and the requirement of low temperature initiation, layer deposition starts with island nucleation.  
CdTe nucleation could initiate both at step edges and on the terraces, and because the atomic structures of 
the Si (111) surface comprise double layer steps giving the same atomic configuration from terrace to 
terrace, all the nuclei would have only two possible positions, i.e. the twining positions.  In this system, the 
associated lattice mismatch energy is the same for the two possible depositions.  However, the twinning 
position nuclei might have a higher interfacial energy due to the "faulted" stacking sequence across the 
interface, and therefore the majority of the nuclei would adopt the orientation of the substrate (as is 
observed experimentally).  Growth then proceeds in layer by layer fashion soon when the substrate 
temperature is raised to normal growth temperature after several tens of monolayer deposition.  Because 
there is no tilt between the nucleating islands, the coherent double positioning boundaries are easily 
eliminated after a short nucleation stage. \\


\noindent
5. CONCLUSIONS

The ability to perform detailed atomic scale analyses of interfaces using correlated Z-contrast imaging 
and EELS is now well established on commercially available microscopes.  The further addition of other 
techniques, such as EDS, CBED and phase contrast imaging, will further enhance the level of 
characterization possible in the future.  Such information allows us to begin to unravel the complexities of 
the structure, composition and bonding changes that can occur at interfaces and from that, develop a 
fundamental understanding of the structure-property relationships.  For many materials systems currently 
being developed, this can provide the pathway to the realization of new technologies.\\
 
\noindent
6. ACKNOWLEDGMENTS

Aspects of this work were performed in collaboration with S. Sivananthan, S. Rujiwarat, P. D. 
Nellist, V. P. Dravid, K. D. Johnson, R. P. Rodrigues, F. Omn\'es, B. Beaumont, J. P. Faurie, P. Gibart, J. L. 
Reno and A. G. Baca.  The microscope facilities at UIC were purchased with support from the NSF under 
grant number DMR-9601792.  Research performed on the semiconductor systems was supported by NSF 
under grant number DMR-9733895, research on the superconductors was supported by NSF under grant 
number DMR-9803021, and research on SrTiO$_3$ was supported by DOE under grant number DE-FG02-
996ER45610.  This research was also supported in part by contract number DE-AC05-96OR22464 with 
Lockheed Martin Energy Systems.
\newpage
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\newpage
\noindent
FIGURE CAPTIONS

Figure 1: Schematic of the detector geometry for a general STEM.

Figure 2: Schematic of the probe forming optics in the JEOL 2010F STEM.

Figure 3: Simplified ray diagram showing the formation of an electron Ronchigram.

Figure 4: Experimental electron Ronchigrams of a thin amorphous carbon layer.  (a) large underfocus -
Rays at all angles cross the optic axis after the specimen and a shadow image of the specimen edge is seen.  
(b) small underfocus - Low angle rays cross the optic axis after the specimen.  High angle rays cross before 
the specimen, because of the effect of spherical aberration.  The shadow image therefore changes in 
magnification as a function of angle and critical angles occur where there is infinite radial and azimuthal 
magnification.  Departures from circular symmetry indicate the presence of astigmatism.  (c) Gaussian 
focus - The lowest angle rays cross the axis at the specimen; higher angle rays cross before it, due to the 
effect of spherical aberration. (d) overfocus - Rays at all angles cross the axis before the specimen and 
shadow image of the specimen edge is visible.

Figure 5.  Ronchigrams of a thin region of silicon <110> showing diffraction effects and fringes arising
from the specimen periodicities.  Visibility of the characteristic fringes depends on precise tilting of the 
specimen and the amount of probe coherence in a direction perpendicular to the relevant crystal lattice 
plane.  (a) small underfocus - Lattice fringes are visible near the Ronchigram center and they become 
heavily distorted further out in angle.  The distortion is due to phase changes introduced by the lens 
spherical aberration.  (b)  near Scherzer focus -  The central fringes become large and wide.  Their area 
corresponds to the entire overlap region between zero-order and relevant diffracted beams.  (c) slight 
overfocus -  Fringes are visible with size and spacing that decreases with increasing angle from the 
Ronchigram center. (d) the probe is well overfocused showing the Kikuchi lines.

Figure 6: The specimen consists of an array of atomic columns (a) for which the potential for high-angle
scattering can be represented by an object function (b).  The experimental image can be interpreted as a 
simple convolution of the experimental probe and the object function (c).

Figure 7: (a) Multiple scattering calculations model the density of unoccupied states by considering the
scattering of the excited photoelectron from neighboring atoms.  The resultant energy loss spectrum may be 
described as a simple absorption edge of hydrogenic form, due to an isolated atom, with intensity 
modulations due to the atomic structure of the solid (b).

Figure 8: Z-contrast image of a pure edge dislocation core obtained with 0.13 nm resolution in the VG
Microscopes HB603 U.

Figure 9: (a) Z-contrast image of the pure edge dislocation core with a 0.2 nm beam in the JEOL 2010F to
give sufficient current for (b) the experimental EELS spectra obtained from the core column.

Figure 10: Multiple scattering simulations of the experimental GaN bulk and core spectra showing that the
main features in the spectra can be reproduced by considering clusters containing no vacancies.


Figure 11: Z-contrast image of a 36$^\circ$ [001] tilt grain boundary in SrTiO$_3$.

Figure 12: Structural units for [001] tilt grain boundaries in SrTiO$_3$.  The B unit is equivalent to a (100)
dislocation core and the C unit to a (110) dislocation core.

Figure 13:  (a) Oxygen K-edge and (b) titanium L-edge from the bulk and 25$^\circ$ [001] tilt grain boundary in
SrTiO$_3$.  These spectra are taken to be representative of all undoped grain boundaries in SrTiO$_3$ due to the 
similarity of the structural units shown in figure 12.

Figure 14: High magnification Z-contrast image of a nominally undoped ?5 36$^\circ$ [001] tilt grain boundary in
SrTiO$_3$ (a) and (b) high-magnification Z-contrast image of the ?5 36$^\circ$ [001] tilt grain boundary after Mn 
doping.

Figure 15: Ti L-edges from the bulk and the grain boundary plane in the Mn doped sample.

Figure 16: (a) Oxygen K-edge spectra and (b) manganese L-edge spectra taken from atomic locations
defined in the Z-contrast image shown in figure 14.

Figure 17: Comparison between experimental oxygen K-edge spectra and multiple scattering simulations of
the distinct oxygen sites in the Mn doped grain boundary plane.

Figure 18: Z-contrast image of a high-angle [001] tilt boundary in YBCO.  The structural units are the same
as those observed for SrTiO$_3$ grain boundaries.

Figure 19: (a) the number of charge carriers in the copper oxygen planes can be quantified by fitting
gaussian functions to the main features in the Oxygen K-edge spectrum and (b) the quantified hole 
concentration around a 30$^\circ$ [001] tilt grain boundary in YBCO showing significant hole depletion.

Figure 20: The Cu(1) valence (calculated from the structural units using bond-valence analysis) as a
function of distance from the grain boundary plane for a series of high-angle [001] tilt grain boundaries in 
YBCO.

Figure 21:  A comparison of the tunneling current calculated from the grain boundary widths shown in
Table 1 with the experimental $J_c$ measurements from a number of research groups.

Figure 22: Z-contrast images of the c-axis twist boundaries in Bi-2223/Ag tapes (a) without and (b) with
local phase variations at/near the boundary. Positions of the grain boundaries are indicated by arrows. The 
numbers (n) in the figures represent the types of phases (Bi$_2$Sr$_2$Ca$_{n-1}$Cu$_n$O$_y$).

Figure 23: (a,b) Z-contrast images and (c) a schematic diagram of a small-angle (11$^\circ$) c-axis tilt boundary
in a Bi-2223/Ag tapes.  Phase variations are also observed at this grain boundary plane.

Figure 24: Low-magnification Z-contrast image of the Au spikes protruding into GaAs at the GaAs/Au
interface.

Figure 25: Atomic resolution image of the interface $\sim$50nm away from the Au spike.

Figure 26: (a) and (b) Atomic resolution Z-contrast images of the interface structure in the Au spike.

Figure 27: (a) Low magnification bright field TEM image showing a cross-sectional view (in the [1-10]
direction) of the sample grown on Te treated Si(111) substrate.  The image highlights the presence of many
twin domains, planar defects and threading dislocations and the inset CBED pattern shows the film has the 
(111) A polarity. (b) Low magnification bright field TEM image showing a cross-sectional view (in the [1-10] 
direction) of the sample grown on the As passivated Si (111) substrate.  The image shows a very large area of 
high crystalline quality with only the presence of lamellae twins being observed close to the interface with the 
substrate. The inset selected area diffraction pattern shows the alignment of the epilayer with the substrate and 
the inset CBED pattern shows the film has the (111) B polarity. 

Figure 28: Energy dispersive x-ray spectra of (a) CdTe layer; (b) CdTe/Si interface; (c) Si substrate,
confirming the presence of a monolayer of As at the interface.

Figure 29: (a) A raw atomic resolution Z-contrast image of the CdTe/Si interface viewed along the [1-10]
direction with (b) showing the Fourier filtered image of (a). (c) Atomic resolution Z-contrast image of a 
different region along the interface showing twin oriented layer growth with (d) showing the corresponding 
Fourier filtered image of (c).  (e) Schematic showing the two possible orientations of the epilayer 
corresponding to (a) and (c) respectively (A,B and C denote a double atomic layer).

Figure 30: (a) Sketch of the atomic configuration across the interface of the CdTe(111)B on As passivated
Si(111) with a misfit dislocation core superimposed on the experimental Z-contrast image.  Cd is the first 
atomic layer to bond with As, and the structure proceeds from this initiation process into a film with B 
polarity.   

Table 1: The distinct structural units shown in figure 12 can be combined to form all [001] tilt grain
boundaries in YBCO.  Assuming that each structural unit corresponds to an "equivalent" oxygen vacancy 
allows a density of localized states in the boundary to be determined, and a corresponding depletion layer to 
be calculated from equation 3.
\end{document}
