# Brittle fracture studied by ultra-high speed synchrotron X-ray diffraction
imaging

Antoine Petit<EMAIL_ADDRESS>Univ. Grenoble Alpes, CEA, LETI, MINATEC
Campus, F-38054 Grenoble, France  Sylvia Pokam  Univ. Grenoble Alpes, CEA,
LETI, MINATEC Campus, F-38054 Grenoble, France  Frédéric Mazen  Univ. Grenoble
Alpes, CEA, LETI, MINATEC Campus, F-38054 Grenoble, France  Samuel Tardif
Univ. Grenoble Alpes, CEA, IRIG-MEM-NRS, F-38000 Grenoble, France  Didier
Landru  SOITEC, Parc Technologique des Fontaines, 38190 Bernin, France  Oleg
Kononchuk  SOITEC, Parc Technologique des Fontaines, 38190 Bernin, France
Nadia Ben Mohamed  SOITEC, Parc Technologique des Fontaines, 38190 Bernin,
France  Margie P. Olbinado  ESRF – The European Synchrotron, 71 avenue des
Martyrs, F-38043 Grenoble, France  Alexander Rack  ESRF – The European
Synchrotron, 71 avenue des Martyrs, F-38043 Grenoble, France  François
Rieutord  Univ. Grenoble Alpes, CEA, IRIG-MEM-NRS, F-38000 Grenoble, France

###### Abstract

Ever since the very first human-made knapped tools, the control of fracture
propagation in brittle materials has been a vector of technological
development. Nowadays, a broad range of applications relies on crack
propagation control, from the mitigation of damages, e.g., from impacts in
glass screens or windshields, to industrial processes harnessing fracture to
achieve clean cuts over large distances. Yet, studying the fracture in real
time is a challenging task, since cracks can propagate up to a few km/s in
materials that are often opaque. Here, we report on the in situ investigation
of cracks propagating at up to 2.5 km/s along a (001) plane of a silicon
single crystal, using X-ray diffraction megahertz imaging with intense and
time-structured synchrotron radiation. The studied system is based on the
Smart Cut™ process, where a buried layer in a material (typically Si) is
weakened by micro-cracks and then used to drive a macroscopic crack
($10^{-1}$m) in a plane parallel to the surface with minimal deviation
($10^{-9}$m). The results we report here provide the first direct confirmation
that the shape of the crack front is not affected by the distribution of the
micro-cracks, which had been a postulate for previous studies based on post-
fracture results. We further measured instantaneous crack velocities over the
centimeter-wide field-of-view, which had only been previously inferred from
sparse point measurements, and evidence the effect of local heating by the
X-ray beam. Finally, we also observed the post-crack movements of the
separated wafer parts, which can be explained using pneumatics and elasticity.
Thus, this study provides a comprehensive view of controlled fracture
propagation in a crystalline material, paving the way for the in situ
measurement of ultra-fast strain field propagation.

††preprint: APS/123-QED

##  I Introduction

Fracture dynamics and crack propagation in brittle materials are of paramount
importance in fields ranging from geology to civil engineering or
technological materials science. Frequently, experimental in situ studies
represent a challenge, in particular in opaque materials, and one is often
limited to a post mortem analysis [1]. Indeed, the spatial extension of the
crack in a brittle material is small, with very rapidly varying strain and
stress fields near the crack position. In addition, the crack propagation
velocity is very high, typically of the order of the Rayleigh velocity or the
sound velocity in the material (several km/s). Hence, obtaining a
submillimeter resolution without motion blur requires exposure times much
below the microsecond. These stringent requirements can only be met using
bright synchrotron radiation: the pulsed source enables snapshot images with
nanosecond exposure time and hence, freeze ultra-fast motion in the images.

X-ray scattering, and in particular X-ray diffraction, is a powerful technique
whenever crystalline materials are to be studied. The materials penetration
properties of X-rays are also well suited to investigate phenomena occurring
in the bulk. Diffraction-based imaging, i.e., X-ray (Bragg) topography, takes
advantage of the contrast stemming from defects in single crystals to image
them in real space, yielding quantitative information, as recently reviewed by
[2]. In the field of fracture mechanics, X-ray topography has proven to be an
efficient tool to investigate cracks in single crystal [3, 4, 5, 6, 7].
Numerous studies have been conducted to measure the strain and estimate the
stress near crack tips, but they usually only dealt with static or quasi-
static distributions of strain and stress, as discussed in an extensive review
[8]. Combined with hard synchrotron radiation, X-ray topography can be
performed in real-time [9, 10], under mechanical [11, 12] or thermal loading
[13, 6]. More recently, some of the present authors have shown that thermally
induced crack propagation could be followed in situ using X-ray imaging, both
in transmission and diffraction conditions, with peak velocities observed on
the order of a few m/s [14]. We show in this report that synchrotron X-ray
diffraction imaging can actually be fast enough for the real time and real
space study of fracture mechanics near the sound velocity, providing
unprecedented direct observations of crack propagation and a wealth of
information at different time and length scales, otherwise inaccessible.

This report focuses on single crystal silicon, the most common substrate for
the microelectronics industry. In particular, our test vehicles are assemblies
of silicon wafers prepared with the Smart Cut™ technology. This process is
widely used to transfer thin single crystal layers to a different substrate by
fracturing in a controlled manner an implanted interface [15]. The transfer
can be done on any substrate and this technology is currently used for the
mass production of Silicon On Insulator (SOI) substrates [16, 17]. The full
workflow of the technology is described elsewhere and can be summarized as
follows. First, a high dose of light ions, typically hydrogen [15, 18], or a
mixture of hydrogen and helium [19, 20], is implanted in a silicon substrate.
This results in the formation of a buried weakened layer within the substrate.
By bonding a stiff substrate on the surface of the implanted wafer (e.g., an
“acceptor” wafer), the implantation-related defects grow in-plane under
annealing, forming a network of pressurized microcracks [21, 22]. The size of
these microcracks depends on the annealing conditions and the nature and
amount of implanted gases. A typical image obtained by infrared (IR) confocal
microscopy is shown in Figure 1b, showing an assembly of flat microcracks with
typical sizes in the few µm range after few hours of annealing at 375°C. Once
the surface coverage of the microcracks is large enough, a manually generated
or naturally occurring fracture propagates through the weakened layer and
effectively transfers the surface film to the acceptor [15].

Before the fracture, the system is in a metastable state where the interface
is internally loaded by the distribution of pressurized microcracks. Each
microcrack is in pseudo-equilibrium, as its evolution is very slow and the
equilibrium state can be described using the standard Griffith argument, where
the energy release rate is equal to the surface energy [23]. The internal load
on the microcrack faces is due to the inner pressurized gas, which has
precipitated from the implanted material layer. The pressure load is
compensated by the elastic deformation of the material and the surface
opening. The implanted dose is usually around $10^{16}$ $at/cm^{-2}$,
therefore the pressure in a micrometer-sized crack is on the order of 100 MPa,
and the corresponding microcrack height is in the nanometer range. A crude
description of each microcrack is the so-called penny-shape crack model that
can be found in standard textbooks [24].

Upon fracture, the crack front propagates in the microcracks layer, akin to a
2-dimensional pre-perforated material. The crack propagation plane is close to
the middle of the 2 × 775 µm thick silicon wafer assembly, parallel to the
wafer external surfaces, i.e., in the so-called strip geometry. It has been
shown that in this case, the crack velocity reaches rapidly an asymptotic
velocity close to the Rayleigh velocity [25] which prevents a deflection of
the front [26]. The crack front emits acoustic waves and the feedback of those
acoustic waves on the propagating crack front causes small deviations of the
fracture plane [27, 28]. This translates into periodic patterns of roughness
modulations on the surfaces obtained after splitting [25, 29]. Similar results
have also been found in asperity-free silicon samples [30]. Therefore, the
study of the propagation is key to understand the dynamic brittle fracture in
such structures and its impact on the morphology of the separated surfaces.

As mentioned earlier, the in situ experimental study of crack propagation is
difficult in opaque, brittle materials. Infrared lasers have been used to
measure the crack velocity [25] and crack opening displacement [29], but this
technique only gives a point measurement at the laser spot position. To the
best of our knowledge, no direct imaging of the crack front propagation at
Rayleigh velocity in silicon substrates has been reported so far. Here, we
fill this gap by presenting an original approach taking advantage of short
X-ray synchrotron pulses and an ultra-high-speed X-ray detector to illuminate
the Si crystal in diffraction conditions and consequently, image the crack at
different steps of its propagation. Our direct observation of crack
propagation provides measurements of both the crack front shape and velocity,
together with post-split wafer deformation.

##  II Methods

###  II.1 Experimental setup

For this experiment, ultra-high speed diffraction imaging is deployed at the
ID19 beamline at the ESRF, as shown in Figure 1a [31, 32]. The X-ray setup
details of the ID19 beamline follow a protocol for high-speed diffraction
imaging of wafer fracture [14]. The beamline undulators were optimized for 20
keV photon energy, the impinging radiation on the wafer was basically white
with only a diamond and an aluminum attenuator in the beam. We could
illuminate a wide area of the sample with a large and parallel size beam
thanks to the long distance between the source and sample (150 m). The typical
beam size at the sample position was a rectangle of 21 mm * 12.5 mm. For the
experiment, the ESRF operated in the so-called timing mode 4-bunch where 4
highly populated electron bunches (10 mA) are stored equidistantly in the
storage ring (100 ps pulse duration, 704 ns pulse period [33]).

Figure 1: (a) Top view of the imaging experiment setup used at ID19 beamline,
the ID19 pink beam illuminate the sample (bonded wafers) in diffraction
condition, and high-speed camera connected to an image intensifier records the
diffracted image on the scintillator. The motorized tip is used to
mechanically initiate the fracture, which is detected by the infra-red laser,
which in turn is used to trigger the camera. The zoom at the center of the
sample shows the fracture propagation through the pressurized micro-cracks
layer. (b): Top view of the pressurized micro-cracks layer, made by
implantation-related defects after a few hours of annealing. (c, d): 3D
representation of the strip and wafer samples, respectively. The red dot
represents the IR laser.

Two types of samples were used. The starting material was assemblies of two
[001]-oriented 300 mm diameter, 775 µm thickness silicon wafers, prepared by
implantation of hydrogen and helium at doses around $10^{16}$ $at/cm^{-2}$,
direct bonding and annealing to form a buried layer of micro-cracks (Figure
1b). They were then either cut along the radius in 20 mm-wide strips, with
their length along [110] or [100] (Figure 1c), or used as they were (Figure
1d).

The samples were mounted vertically on a rotation stage such that their [110]
or [100] direction (i.e. their length for the strip samples) was horizontal.
They were then rotated around a vertical axis to bring the (220) or (400)
planes in diffraction condition in the horizontal scattering plane, in the so-
called Laue transmission geometry. For the full wafer sample, the 220
diffraction was chosen.

Initially, the intensity received on the detector is constant since the two
wafers are still bonded and do not move. When the crack front crosses the
beam-illuminated area, the transmitted intensity changes due to the assembly
opening following the crack front, thus imaging the crack front. The scattered
X-ray beam image is converted into visible light using a combination of a
scintillator and an X-ray image intensifier [34]. The image was recorded using
an ultrafast camera type HPV-X2 (Shimadzu Corporation, Japan) [35], placed 170
cm downstream from the sample, and offset by the scattering angle ($\approx$
18.6° for 220, 26.4° for 400). The camera can acquire 256 frames at a rate up
to 10 MHz and exposure time down to 50 ns (depending on the acquisition mode).
Here, thanks to the stroboscopic nature of the incident radiation, the
effective exposure time is given by the bunch length and not by the
integration window of the camera, provided that the integration window is
equal or larger than the pulse period (so-called single bunch imaging). We
thus used the camera either in 1 MHz mode or 1.4 MHz mode (700 ns and 400 ns
integration time, respectively). The effective pixel size of the detector
(camera coupled with X-ray image intensifier) is either 300 µm or 165 µm,
depending on the magnification ratio selected.

The triggering of the camera was performed using the optical setup described
hereafter. An infrared laser beam is directed to an InGaAs IR photodiode
through the sample in such a way that the fracture front crosses the laser
beam before the X-ray illuminated area. The photodiode signal is recorded by
an oscilloscope and a trigger threshold can be set on the transmitted
intensity, as the latter changes sharply when the crack front crosses the
laser beam. The time delay between the trigger signal and the camera can be
adjusted according to the distance between the IR laser spot and the X-ray
illuminated region and to the crack velocity. In addition, the crack opening
following the crack front creates air wedge interference fringes, which are
visible in the transmitted signal from the IR photodiode. These signals can be
used for dynamic measurement of the crack velocity and give detailed
information on the vibrations of the wafers associated to the crack front
propagation, including acoustic (Lamb) waves [25, 29]. Finally, in our
experiment, the samples were pre-annealed to develop microcracks up to desired
microcrack surface coverage and a motor-driven blade was used to mechanically
induce the fracture at room temperature. The motorized blade was slowly
inserted in the beveled edge of the wafers until the fracture occurs.

##  III Results and discussion

###  III.1 Crack front shape

The evolution of the diffracted signal (220 or 400 Bragg reflection) recorded
by the camera when the crack crossed the field of view is shown in Figure 2
for the different types of samples. Figure 2a,b shows the crack propagation in
strip samples, while Figure 2c shows the propagation in a full assembly of 300
mm wafers. For the two types of samples, the first image is taken few
microseconds before the crack front reaches the illuminated area. Then, the
following images are taken at regular interval, in a stroboscopic manner (for
clarity, we only show every other image). The comparison of the different
delayed images evidences the crack front propagation. As we will show after,
the enhanced scattered intensity at the crack front is due to an overlapping
of the diffraction of the strongly curved region at the crack front. Thanks to
the wide incidence spectrum, the tilted crystal regions around the crack front
are still in diffraction condition. Thus, the crack front can be directly
visualized as an intense signal line visible at the center of the diffracted
area on the images of the Figure 2. The very short illumination due to a
single bunch provides a snapshot of the crack front shape with negligible
blurring due to crack movement during exposure. For all the samples, the crack
front has a smooth circular shape, within the resolution of our setup, which
experimentally confirms for the first time what was previously a working
hypothesis for the analysis of the crack propagation [28].

Figure 2: X-ray diffraction imaging of the crack front in silicon (a)
[110]-strip, (b) [100]-strip and (c) full 300 mm wafers. The time $t_{0}$
indicates the entry time of the crack front in the field of view. The scale
bar is 10 mm.

###  III.2 Crack front velocity

Interestingly, the fracture speed does not seem to depend strongly on the
crystal orientation, as the topographs from Figure 2a and Figure 2b seem to be
quite synchronized. Knowing the size of the illuminated area (21$\pm$ 1 mm)
and the travel time for the crack front through this area (9$\pm$ 1 µs) for
Figure 2a and Figure 2b, the crack front velocity can be estimated to about
2.4$\pm$0.4 km/s for both strip samples. The part of the signal behind the
crack front presents several stripes due to the afterglow of the scintillator
associated with the pulsed time structure of the X-ray beam in the 4-bunch
mode filling pattern of the ESRF storage ring. Indeed, the scintillator is
often responsible of a deleterious background intensity between bunches [33].
Here, we harnessed this time structure to obtain a more accurate instantaneous
crack velocity. To do so, we compute a max-filtered image for each sample by
taking the maximum value observed at any time for every pixel of our set of
images. This is somewhat akin to a “bulb exposure” photograph, showing in a
single image all the maximum intensities seen by the camera (Figure 3, top
row). We then extract a line profile perpendicular to the crack front, showing
the peaks due to every single bunch. As mentioned before, the time separation
of the bunches is well-known and fixed by the storage ring filling pattern. To
quantify their space separation, we fitted each peak locally by a Gaussian
function to extract the peak position with sub-pixel resolution (Figure 3,
middle row). We could thus compute the instantaneous crack velocity for each
bunch (Figure 3, bottom row).

The crack velocity is slightly higher for the strip sample along [100] than
for the strip along [110] (2.2 km/s to 2.4 km/s and 2.0 km/s to 2.15 km/s,
respectively). This can be explained in the context of dynamic crack
propagation, where the asymptotic crack velocity v is proportional to the
Rayleigh wave velocity $v_{R}$ [36] :

$v=v_{R}\left(1-\frac{\Gamma}{G}\right)$ (1)

with $\Gamma$ the fracture energy, related to the area between the microcracks
where the fracture must break the material, and G the energy release rate,
i.e. the internal elastic energy recovered when the material is cracked, here
directly related to the pressure inside the microcracks [25]. Since the strip
sample along [110] and along [100] have been cut out from the same wafer, the
microcracks are identical (density, internal pressure) and thus $\Gamma$ and G
should identical as well. The Rayleigh velocity depends however on the
propagation direction, from 4.90 km/s along [100] to 5.06 km/s along [110]
[37]. Thus, the observation of a faster crack propagation along [100] is not
consistent with this description. We also note that the instantaneous velocity
for the 300 mm wafer sample is significantly lower. Both of these results are
explained hereafter.

The crack velocity is noticeably higher near the center of the X-ray
illuminated area for each strip sample: 2.41 km/s (2.13 km/s) at the center vs
2.24 km/s (1.97 km/s) at the edge of the [100]-strip sample ([110]-strip
sample). This can actually be explained by the local heating of the sample due
to the intense X-ray beam. As mentioned before, the energy release rate G is
proportional to the pressure in the microcracks, and thus to the temperature.
The relation $1-v\textfractionsolidus v_{f}=A/T$, where A is a constant, was
already experimentally verified in a previous study [25]. Therefore, the
observed 8 % velocity increase at the center of the field of view for both
samples corresponds to a 5% to 6% temperature increase. This would amount to a
$\Delta T=$15 K to 25 K around room temperature (300 K to 400 K).

Similarly, a different average sample temperature over the field of view can
explain the discrepancy in the numerical values between the dynamic model
($v_{110}\textfractionsolidus v_{100}=1.03$) and the experimental value
($v_{110}\textfractionsolidus v_{100}=0.90\pm 0.01$). The faster crack
velocity along [100] would correspond to a $13\pm 1\%$ temperature increase
compared to the [110]-strip, i.e. the [100]-strip sample was about 40 K to 50
K hotter. A longer alignment time for the first [100]-strip sample would have
resulted in an increased exposure to the beam, and therefore in the increased
heating before the fracture was triggered. We note that the samples were too
hot to be touched bare handed right after the measurement, indicating
temperatures typically above 340 K.

Using the same approach, comparing the 300 mm wafer sample and the strip
samples, the respective velocities indicate an average temperature about 30%
higher in the strip samples. This indicates that the strip samples were about
100 K hotter than the wafer sample, which is consistent with their much
smaller heat capacity and heat dissipation.

Figure 3: (top) single image of all the maximum intensities seen by the camera
for the different strip samples and full 300 mm wafers. The center of the
X-ray illuminated area is represented by a red cross, the orange line
indicates the position of the line profile extracted below. (center) line
profile perpendicular to the crack front. Each peak is due to a single bunch.
Space-wise, the exact location of each peak is obtained by a gaussian fit and
indicated by a green triangle. Time-wise, each bunch is 704 ns after the
previous one. (bottom) evolution of crack front velocity in the X-ray
illuminated area, as calculated from the peaks space-time positions.

###  III.3 Post crack oscillations

As shown in Figure 2, we observe a signal modulation in the wake of the crack
front. This is particularly visible on the edges of the beam footprint. The
detector image actually shows the superimposition of two scattered images of
the incident beam, with a time-dependent shift. These two images are the
scattered images by the two arms of the crack opening. The crack opening
angular displacement can thus be obtained from the analysis of the diffracted
image motions. Given the beam divergence (21 mm over 150m) and bandwidth
($\lambda/\Delta\lambda$=100), we estimate from the Du Mond diagram for the
220 (400) reflection that sample rotations up to about 0.8 (1.1) mrad can
still be imaged (Supplementary Information). This is larger than the typically
deflection that we have previously measured using optical reflection [38],
indicating that the full movement of the two sample plates after the fracture
can be captured.

To analyze the post-crack sample movement, we extract the center line of the
diffracted image (averaged over 5 pixels) and plot it as a function of time in
Figure 4. The facture propagation from one side to the other is clearly seen
as the intense diagonal line with slope $v_{f}$. The crack opening is directly
visible in the wake of the crack front. Shortly after the crack front
crossing, the two separated plates can be seen as the half-intense areas at
each extremity, where only one of the two plates contributes to the
diffraction. Note that small similar shadows could be observed on each side
before the crack apparition, simply due to a slight misalignment of the
crystal planes in the two bonded wafers. The angular separation just behind
the crack indicates a “wedge” shape of the crack opening. This is consistent
with infrared interferometry measurements of the crack opening [25] and
optical reflection measurements [38]. From linear elastic fracture mechanics,
the profile is parabolic in the close vicinity of the crack front, as strain
varies as K/$\sqrt{x}$, with K the stress intensity factor. At larger
distances, a regular beam bending strain should be expected. The wedge shape
is probably due to the transition between these two regimes with opposite
curvatures and a convolution by the experimental resolution. The later
oscillatory shape finally indicates a back-and-forth movement of the plates.

In order to go further in the analysis, we simulated the diffracted images
using the following approach. The IR laser signal to trigger the high-speed
camera also provides an indirect measurement of the gap profile behind the
crack front. The method is described elsewhere [25] and can be summarized as
follows. The opening of the crack creates two partially reflecting surfaces.
The transmission through this gap is thus a function of the gap opening, with
maxima every $\lambda$/2, resulting in fringes in the detected signal as a
function of time. It is not directly possible to know if the gap is opening or
closing by this quantified amount at each fringe, but it is reasonable to
assume that a maximum in the delay between two successive fringes (vanishing
speed) indicates a reversal of the motion. We thus obtain the local discrete
profile $\zeta(t)$ of the gap at the location of the IR laser, where each
plate is deformed by $\pm\zeta(t)$/2 (see Supplementary information). Assuming
that the profile is invariant by translation, i.e., the sample deformation
behind the crack is the same throughout the crack propagation,
$\zeta(t)=\zeta(-x/v_{f})$. The angle of the surfaces can then be computed as:

$\alpha=\pm\frac{1}{2}\frac{\partial\zeta}{\partial
x}=\pm\frac{1}{2v_{f}}\frac{\partial\zeta}{\partial t}$ (2)

The corresponding diffraction image can be simulated using a simple ray-
tracing approach. For a time step t, a length of 21 mm of the deformation
profile is illuminated by parallel rays every 10 µm. Each ray is then
deflected by $\pm 2\alpha$, where $\alpha$ is the local sample rotation
defined above. The rays propagate over d=1.7 m and hit the detector where all
the resulting positions are binned according to the pixel size. The initially
illuminated area is shifted for the next time step $t+\Delta t$ by
$v_{f}\Delta t$. The resulting simulated image is shown in Figure 4 as well.
The main features are well captured by the simulation, confirming that our
description is correct. The observed back-and-forth motion of the two plates
visible on the edges (x=$\pm$10 mm) is actually due to pneumatic oscillations,
as described before [25]. Small discrepancies can be observed for the later
times, which may indicate that the deformation profile is not exactly
invariant by translation, probably because of the finite size of the sample
and/or local temperature changes. Finally, back propagating waves are observed
in the experimental data as slightly more intense lines with a negative slope
in Figure 4, yet they are not reproduced by our simple simulations. These
waves could actually be flexural waves, recently observed using optical
reflection measurements [38].

Figure 4: Diffracted intensity for the [110]-strip sample as a function of
time and position along the length x (i.e. along [110]), taken at center y
position, (top) experimental data, (bottom) simulated data considering the
propagation of the gap opening profile.

##  IV Summary and outlook

As it had previously been foreseen [14], X-ray diffraction imaging using a
large parallel synchrotron beam as proven to be a unique tool for real-time
dynamic fracture studies, thanks to the high-flux and temporal resolution of
synchrotron illumination, coupled with high-speed cameras. Here, we showed
that synchrotron X-ray diffraction imaging can be fast enough for the in-situ
study of fracture mechanics in a brittle material, at speed over few km/s. We
harnessed this technique to tackle the industrially-relevant problem of the
fracture propagation in the Smart Cut™ technology and to obtain otherwise
inaccessible data. In particular, both real-space and real-time images of the
crack front propagating in single crystal Si at speed near the Rayleigh
velocity were acquired for the first time. This direct visualization of the
crack front shape experimentally confirmed the homogeneous propagation of the
fracture, which was previously only a working hypothesis for the fractography
analysis of post-split surfaces. Thanks to the time structure of the
synchrotron source, the local crack velocity could be measured and compared to
point measurement using infra-red laser transmission. While the average
velocity value is consistent with IR measurements, the effect of increased
velocity near the image center could be interpreted as a local heating due to
the intense X-ray beam, in agreement with previous studies [25, 28]. Finally,
the post-split images showed the movements of the separated wafers and
confirmed the importance of the pneumatic oscillations in the wake of the
fracture. Additional back-propagating waves were also observed, reminiscent of
flexural waves and requiring further analysis. These results open a vast
avenue of future potential studies. For example, it could be very interesting
to trigger the fracture thermally using the X-ray heating of the sample, to be
as close as possible to the phenomenon occurring in the annealing furnace, and
thus observe the very first stages of fracture initiation. A more detailed
stress and strain description at the crack tip is now probably at reach, using
e.g., a larger sample to detector distance, combined with the improved
brilliance of the new ESRF source. Also, coupling high-speed diffraction
imaging (few MHz) with more conventional yet fast optical imaging (10 kHz to
100 kHz) could provide a full understanding of the fracture propagation, the
related acoustic waves emission and their intimate interplay. Finally, our
approach here is not limited to silicon and can be extended to any crystalline
material of interest that can be transferred using the Smart Cut™ technology,
such Ge, GaAs or SiC.

###### Acknowledgements.

We thank the staff of the ESRF beamlines ID19 and BM32 for dedicated technical
assistance setting up and running the experiment. Beam time allocation is
acknowledged. The support of the FRAINDY project from the French national
research agency under No. ANR-18-CE08-0020 is acknowledged.

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