Koster G., Rijnders G. (Eds.) In situ Characterization of Thin Film Growth

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40 In situ characterization of thin ﬁlm growth

allowing many more zone axes to be seen. With the experimental geometry

shown in Fig. 2.5(b), two-thirds of the hemisphere is visible, although owing

to the at nature of the phosphorus screen the edges of the images will be

geometrically distorted.

Figure 2.6(a) shows a Kikuchi pattern, collected simultaneously with a

RHEED image using the dual screen set-up of Fig. 2.5(b), of a SrRuO

lm

grown on SrTiO

. This was collected right at the end of lm growth while

the substrate was still at 650 °C and exposed to an atomic oxygen ux of 1

¥ 10

atoms/cm

s. Figure 2.6(b) shows a simulated pattern of tetragonal

SrRuO

, with various zone axes indexed, and exhibiting the same orientation

as that of the experimental image.

2.5 Lattice parameter determination

Lattice parameters can be determined from Kikuchi patterns by directly

measuring the width and ratios of the low-order Kikuchi lines. To calculate

a d-spacing, half the angle subtended by the Kikuchi bandwidth can be

plugged into the Bragg equation. However, the band edge is not very sharp:

in the order of 1 mrad, as compared with the 20 mrad Kikuchi band width

for 30 keV electrons. This only allows an accuracy in the 3% range (Baba-

Kishi and Dingley, 1989b; Dingley et al., 1995; Wilkinson, 1996) for lattice

parameters.

The HOLZ rings found in many BKPs can also be used to help determine

lattice parameters. Measuring the HOLZ ring diameter allows the d-spacing

of the lattice planes perpendicular to the zone axis around which the ring is

(a) (b)

[111] [111]

[112]

[245]

[243]

[133]

[023]

[011]

[021]

2.6 (a) The Kikuchi pattern of a SrRuO

ﬁlm grown on a SrTiO

substrate at 650 °C and under a 1 ¥ 10

atoms/cm

s ﬂux of atomic

oxygen; zone axes are indicated. (b) The calculated Kikuchi pattern

for tetragonal SrRuO

with the same orientation. Reprinted with

permission (Ingle et al., 2010).



41Inelastic scattering techniques for in situ characterization

found to be calculated (Champness, 2001). This technique is more commonly

used in CBED measurements. In general the HOLZ rings are sharper than

the edges of Kikuchi bands; but they are not always present in BKPs, and

even when they are the gnomonic projection needs to be properly accounted

for. Michael and eades (2000) used this technique and were able to obtain

lattice parameter accuracies of better than 1% for many samples. However,

they found that the largest error was in dening the radius of the HOLZ

rings, and that error became quite large (up to 10%) for high atomic number

samples.

2.6 Epitaxial ﬁlm strain determination

Although determining lattice parameters from Kikuchi patterns is not very

accurate, determining changes in lattice parameters, and hence strains, can

be far more accurate. Troost et al. (1993) claim that by looking for changes

in the angles between major zone axes, a strain sensitivity of about 0.1%

is achievable. To study the elastic strain associated with epitaxial growth,

the basic set-up used by Troost et al. (1993) on Si

1-x

epitaxial lms

grown on Si substrates involved etching away, ex situ, the epitaxial layer

in one section of the sample. This allowed an SeM-based eBSD pattern

to be collected from an unstrained standard, and from the lm of interest,

without any changes in the beam conguration geometry. The image from

the unstrained standard could thus be directly compared with the image from

the epitaxial lm, allowing the determination of a change in angles between

major zone axes. A straightforward method for doing this is to subtract the

image of the unstrained substrate from that of the lm (see Fig. 2.7). It is

important to note that because this technique looks at the interzonal angles,

it will be sensitive only to strains that distort the shape of the unit cell, and

not to strains caused by hydrostatic expansion or contraction. With this

procedure, Troost et al. (1993) found a marked reduction in the interzonal

angle between the [100] and [111] zone axes of Si

1–x

, which provided

evidence of a tetragonal elongation of 2.5% for x = 0.34 and at 1.0% for

x = 0.16 along the [100] direction of the unit cell. High-resolution x-ray

diffraction measurements support these conclusions.

A further enhancement of strain sensitivity, down to about 0.02%, was

obtained by Wilkinson (1996) and Wilkinson et al. (2009), also on Si

1–x

epitaxial lms grown on Si substrates. A similar etching procedure was used

to provide a reference pattern for unstrained Si. Wilkinson (1996); Wilkinson

et al. (2009) increased the sensitivity of the measurement primarily by

increasing the sample-to-screen distance from 30 to 140 mm, thereby increasing

the angular resolution of the detector. Using a more light-sensitive camera

and computing the cross-correlation between multiple zone axes in both

the strain-free reference images and the strained images further enhanced



42 In situ characterization of thin ﬁlm growth

the ability to distinguish small changes in the location of the zone axes. In

addition, the use of multiple zone axes allowed the full strain tensor and

lattice rotations to be calculated.

The determination of elastic lattice strain in growing lms requires an image

of the substrate prior to growth, from which any change in the interzonal

angles can be detected as the lm is growing. Therefore, the ability of a

dual screen RHEED and Kikuchi capture allows the in situ study of elastic

strain as a function of lm thickness and other growth parameters, in real

time.

2.7 Kinematic and dynamic scattering

Kikuchi diffraction patterns are the result of multiple elastic and inelastic

scattering processes, and thus present an inherently dynamic scattering

problem. However, kinematic diffraction from a point source within the

sample can account for the geometry of the patterns, and is straightforward

to simulate. Obtaining patterns that can be easily compared with experimental

images requires a fairly large number of lattice planes to be included. It is

the dynamical scattering that leads to interference terms that produce the

more complicated features, particularly when two or more Kikuchi lines

intersect. generally the manifestations of dynamical scattering are found on

the low-order Kikuchi bands, which show intensity irregularities along the

band edges and high contrast within the bands.

The dynamical models for electron diffraction start with the Bloch wave

2.7 (a) Circular subsection of a BKP from Si after contrast

enhancement by background subtraction with superimposed

indexing of the lattice planes. (b) Image resulting from the

subtraction of a BKP of pure Si (100) from a BKP of an epitaxial

0.66

0.34

layer indicating the tetragonal elongation between the

[001] and [111] zone axes of the strained layer. Reprinted with

permission (Troost et al., 1993).

(a) (b)

100

211

111

101



43Inelastic scattering techniques for in situ characterization

approach to describe the diffraction of electrons by the crystal lattice. The

lattice provides a three-dimensional diffraction grating for the electrons that

are incident on the sample. Depending on the incidence angle of an incoming

plane wave relative to the lattice planes, the diffracted electrons interact

differently with the atoms which constitute the crystal. This is the basic

description of SEM-based ECPs (Reimer, 1985). A parallel beam of electrons

interacts with the sample and produces a given intensity of electrons that are

backscattered. As the angle of the incident beam of electrons is changed,

the backscattered intensity changes, and a pattern is built up that looks very

similar to a BKP. BKPs are, in fact, considered to be the reciprocal of ECPs

(Reimer, 1985). The reciprocity means that the observed intensity at a point

detector inside the sample, after diffraction of an incoming plane wave, is

the same as for a detected plane wave intensity after diffraction of waves

emanating from a point source inside the sample.

Winkelmann et al. (2007) created a three-step model of the dynamic

scattering in BKP. The rst step is the diffraction of a focused incident

beam, which produces a distribution of electrons within the sample. This

diffracted electron distribution is then subject to an inelastic process, which is

accounted for in the model by quasi-elastic backscattering from atomic nuclei.

The nal step is the reciprocal of the ECP model, where the quasi-elastic

backscattering generates point sources of electrons within the sample that are

then subject to diffraction from the surrounding lattice. The cross-section for

the quasi-elastic backscattering from the atomic nuclei and the probability of

nding an electron at the atomic nuclei provide the source strength for the

outgoing diffraction. In addition, the quasi-elastic backscattering also destroys

the coherence between the incident beam diffraction and the outgoing beam

diffraction. Wilkelman et al.’s application of the dynamical theory provided

simulated patterns which very closely reproduced experimental BKPs of

GaN, including HOLZ ring effects and zone axis ne structure, and provides

a framework for more quantitative analysis of BKPs (see Fig. 2.8). Recent

additional work by Winkelman (2010) suggests that the depth-distribution

of backscattered electrons should also be taken into account in quantitative

descriptions of Kikuchi pattern formation.

Although dynamic scattering models for BKPs assume quasi-elastic

scattering (Omoto et al., 2002; Winkelmann et al., 2007; Winkelmann,

2010), there is experimental evidence showing that electrons which lose

up to 20% of the incident beam energy still participate in the formation of

the Kikuchi pattern (Deal et al., 2008). Went et al. (2009) recently showed

spectroscopic evidence that in BKPs there is an elastic peak that is separated

from the loss distribution. They also found that electrons with less than

2.5 eV of energy loss, expected for the case of thermal diffuse scattering

and still within the elastic peak, provide the most contrast. In essence, the

experimental pattern should be considered as a sum of different patterns,



44 In situ characterization of thin ﬁlm growth

(a)

(b)

2.8 BKP of GaN 0001 at 20 kV: (a) experimental pattern; (b) dynamical

simulation. In area B, attention is drawn to the HOLZ ring at

approximately two-thirds of the radius of the area. The ﬁne structure

in areas A and C is strikingly similar in the two patterns. Reprinted

with permission (Winkelmann, 2010).



45Inelastic scattering techniques for in situ characterization

each calculated for a specic energy loss, but strongly weighted towards

quasi-elastic scattering.

As mentioned earlier, ECPs and BKPs are considered to be reciprocal

measurements, and the general forms of the two patterns are indeed very

similar. However, ECPs tend to show much more detail than the BKPs. This

difference is a result of the much larger energy spread of electrons involved

in the multi-step BKP pattern formation, as compared with the well-dened

energy of the incident beam that generates the ECPs (Wilkinson and Hirsch,

1997).

As an alternative to a fully dynamic simulation, Zaefferer (2007) argues

that the limited resolution of most cameras, and the different coherent

scattering path lengths for all the electrons, lead to a blurring of the dynamical

diffraction effects, resulting therefore in the appearance of bands of average

intensities. Zaefferer showed that a signicant improvement in the intensity

calculations for BKPs over intensities that are proportional to the square of

the structure factor, i.e. kinematic intensities, can be achieved by applying a

relatively simple correction function to the kinematical intensities, originally

proposed by Blackman (1939). This correction is appropriate only outside

principal zone axes; nevertheless that accounts for a signicant portion of

the BKPs and therefore this approach may be a quick starting point for

comparing experimental patterns to possible structures.

2.8 Epitaxial ﬁlm structure determination

As discussed earlier, Wilkinson demonstrated that it is possible to obtain

sensitivity to strains of approximately 0.02% on thick Si

1–x

epitaxial layers

grown on planar Si substrates (Wilkinson, 1996). The method used – analysis

of interzonal angles – is limited to strains that distort the shape of the unit

cell. However, unit cell distortion is of primary interest in understanding

the tetragonal distortion that can occur with epitaxial growth; therefore

interzonal angles are one method for tracking epitaxially driven changes to

the structure of thin lms.

Another approach to exploring possible symmetry changes caused by epitaxy

is highlighted by Baba-Kishi’s comparison of ZnS and CuFeS

(Baba-Kishi,

1992, 2002). ZnS is cubic and CuFeS

is tetragonal with a doubled ZnS-type

structure. The symmetry features of BKPs in the cubic ZnS and those of the

tetragonal CuFeS

are very similar, since the tetragonal distortion in CuFeS

is very small. However, it is possible to distinguish subtle changes to the

BKP. The Kikuchi lines from CuFeS

that intersect within the Kikuchi bands

generated from the (024) plane highlight the slight tetragonal distortion.

These Kikuchi line intersections are slightly offset from the center of the

Kikuchi bands (see Fig. 2.9) and indicate that for CuFeS

these planes are

not mirror planes, as they would be for the cubic ZnS structure.



46 In situ characterization of thin ﬁlm growth

Changes in the atomic positions within a unit cell may not be readily

detected by these analysis techniques. Therefore it may also be of interest

to look at the differences in the intensity of specic Kikuchi bands as a

route to explore other epitaxially inuenced changes in the structure of thin

lms. To sort out what to look for in the experimental Kikuchi pattern in

order to help distinguish possible changes in the crystal structure of a lm

due to effects of epitaxy, a simulation is needed. If changes to the patterns

can be found away from principal zone axes, then the corrected kinematic

simulation scheme proposed by Zaefferer (2007) (and discussed above) may

be an appropriate starting point.

An example of a possible epitaxial inuence on the structure of a grown

lm is the potential buckling of the Cu–O planes in the high-pressure phase

of SrCuO

when grown with compressive strain. SrCuO

is the end member

(n = ∞) of the homologous high-pressure series Sr

n−1

n+1

(Hiroi et al.,

1991). Owing to the simplicity of the crystal structure and the planar nature

of its Cu and O ordering, it is often called the parent compound of the high-

temperature superconductors (Jorgensen et al., 1993) and is considered to be

a two-dimensional quantum magnet (Yasuda et al., 2005). An extremely large

change in the c-axis of this material was seen when it was grown by epitaxy

with reduced a and b lattice parameters (Ingle et al., 2002). One possible

explanation for this anomalous expansion in the c-axis is the buckling of the

Cu–O planes, suggested by Vailionis et al. (1997). The proposed buckling of

2.9 Kikuchi lines from CuFeS

intersecting within the Kikuchi band

formed from the (024) plane, showing a shift towards the right with

respect to the large arrow which points to the center of the band.

This shift at the intersection point originates from the tetragonal

structure of CuFeS

. Inset: lines drawn over the Kikuchi lines to help

indicate the asymmetry of the intersections with respect to the large

black arrow. Reprinted with permission (Baba-Kishi, 2002).



47Inelastic scattering techniques for in situ characterization

the Cu–O planes occurs by the motion of just the oxygen atoms, and as such

it is extremely hard to see in x-ray diffraction. However, Kikuchi diffraction

may be an ideal tool to look at the potential of an epitaxially driven change

in the dimensionality of the Cu–O planes.

Figure 2.10 shows several changes in the Kikuchi pattern that are expected

between planar and buckled Cu–O planes in SrCuO

, as simulated using the

corrected kinematic scheme described by Zaefferer (2007). These Kikuchi

patterns are centered around the (130) zone axis and indicate several possible

changes in the pattern if the Cu–O planes were to buckle by the oxygen

atoms moving in and out of the a–b plane by 10% of the c lattice constant

(Fig. 2.10(b)) in contrast to a planar Cu–O structure (Fig. 2.10(a)). In this

part of the Kikuchi pattern buckling causes an increase in intensity of the

scattering from the {224} planes, indexed according to the enlarged unit cell

required to describe buckling and highlighted in Fig. 2.10(b). Furthermore,

there is also signicant reduction in intensity expected for the (001) and

(003) planes, as well as for the cubic-indexed {204} planes from the buckled

structure (highlighted in Fig. 2.10(a)).

[–130]

[1–10]

[–130]

[1–31] [1–31]

(00n)

(002)

(224)

(2–2–4)

(20–4)

(024)

(a) (b)

2.10 The calculated Kikuchi patterns, and structures, of the high-

pressure phase of SrCuO

without buckled Cu—O planes (a), and

with buckled Cu—O planes (b). The light and dark lines at the top

and bottom of the image are guides to the eye of the respective

excess and deﬁcient lines that deﬁne the edges of the Kikuchi bands

that change between the two images. Reprinted with permission

(Ingle et al., 2010).



48 In situ characterization of thin ﬁlm growth

There are a number of other expected changes in the Kikuchi pattern for

the buckling of the Cu–O plane in SrCuO, but these are primarily in the

high-index planes. While high-index planes are present in the image, they not

only have an inherently lower intensity but they are also overlaid with the

more intense low-index planes, and locations in the pattern are not always

present that allow them to be seen. However, these simulations suggest

that even subtle changes in the structure of epitaxially grown lms might

be quite distinguishable in an in situ and real-time dual-screen RHeeD/

Kikuchi pattern collection set-up. In addition, the ability to collect a Kikuchi

pattern from a well-characterized substrate just prior to the growth of a lm

provides a remarkable opportunity to minimize unknown experimental and

geometrical effects in the patterns and to clarify the signicant aspects of

the simulations. This affords a tremendous advantage to the nal analysis

and interpretation of the Kikuchi patterns collected from an epitaxial lm.

The use of more recent multi-beam dynamic models by Wilkelmann et al.

(2007), which include improvements in the handling of inelastic scattering

processes and the description of the excitation process, can provide much

more detailed simulations. These models, along with continual improvements

in hardware (Day, 2008) and software that are being applied to EBSD in

SEMs, may allow a much more accurate and ne-grained approach to look

for subtle changes in the atomic structure by inspecting and understanding

the experimental Kikuchi patterns collected from thin epitaxial lms.

2.9 Conclusion

The use of grazing incidence high-energy electrons during the growth of

epitaxial lms not only generates RHEED patterns from the elastically

scattered electrons, but also generates Kikuchi patterns at larger scattering

angles from the inelastically scattered electrons. These Kikuchi patterns can

be analyzed to obtain an abundance of information about the crystallographic

structure of the lm. Of particular relevance to epitaxial lm growth, the

effects of strain and more generally the changes in space group and atomic

positions of thin lms can explored. These Kikuchi patterns can be collected

in real-time, and simultaneously with the RHeeD data with a dual-screen

RHEED/Kikuchi collection set-up. The SEM-based EBSD community can

provide a wealth of experience and has laid down a substantial amount of

ground work that the lm growth community can immediately use to help

collect, analyze, and simulate Kikuchi patterns. In combination with standard

RHeeD analysis, the inelastically scattered electrons allow a remarkably

complete set of data which help elucidate the full crystallographic structure

of the potentially novel structures that can be formed by the inuence of

epitaxy on the growth of thin lms.



49Inelastic scattering techniques for in situ characterization

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