deformation structure induced by indentation in gaas and si single crystals
DESCRIPTION
http://www.me-journal.org/paperInfo.aspx?ID=7503 Investigations conducted by the authors into the plasticity, damage, phase transformation and fracture induced by micro-indentation are critically reviewed. The materials used in this study are Si and GaAs single crystals. The principal findings are the following: (a) Micro-indentation may induce a transition from crystalline to nano-crystalline and amorphous structure. There is a critical stress for occurrence of the transition. The shear stress, rather than hydrostatic stress is proposed to be attributed to this transition. (b) The atomic-scale structures ahead of the crack-tip are extended and successfully screened by a high-resolution electron microscope (HREM) using both plane view and cross-sectional view. It is found that the crack tip is not atomically sharp, dislocations produced during indentation lead to the crystal lattice distortion and even to a transition from crystalline lattice to disordered structure resulting inTRANSCRIPT
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
doi: 10.14355/me.2014.0301.03
13
Deformation Structure Induced by
Indentation in GaAs and Si Single Crystals Y.B. Xu 1, Z.C. Li 2, Y.Q. Wu 3
1 Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences,
Shenyang 110016, China 2 School of Materials Science and Engineering, Central South University, Changsha 410083, China 3 Ames Laboratory, Iowa State University, Ames, IA 50011, USA
1 [email protected]; 2 [email protected]; 3 [email protected]
Abstract
Investigations conducted by the authors into the plasticity,
damage, phase transformation and fracture induced by
micro‐indentation are critically reviewed. The materials used
in this study are Si and GaAs single crystals. The principal
findings are the following: (a) Micro‐indentation may induce
a transition from crystalline to nano‐crystalline and
amorphous structure. There is a critical stress for occurrence
of the transition. The shear stress, rather than hydrostatic
stress is proposed to be attributed to this transition. (b) The
atomic‐scale structures ahead of the crack‐tip are extended
and successfully screened by a high‐resolution electron
microscope (HREM) using both plane view and
cross‐sectional view. It is found that the crack tip is not
atomically sharp, dislocations produced during indentation
lead to the crystal lattice distortion and even to a transition
from crystalline lattice to disordered structure resulting in an
amorphous band with a width of 1‐2 nm ahead of the crack
tip. The crack propagates along the amorphous band rather
than sequential rupture of cohesive bonds. (c) The results of
fast Fourier transformation and corresponding inverse‐fast
Fourier transformation fringe images from different lattice
planes reveal that deformation around the crack‐tip is
anisotropic. The lattice fringes along ( 111 ) plane are not changed and the atom arrangement on this plane is still
essentially ordered, and serious lattice distortion occurs on
the planes of (001) and ( 111 ). (d) In‐situ observations by
HREM show that there is a critical current density for the
crystalline nucleation in amorphous area stimulated by an
electron beam, and the crystalline nucleation is not related to
the irradiation‐induced temperature rise.
Keywords
Micro‐indentation, HREM; Amorphization, Crack‐tip Structure,
Crystallization, Fast Fourier Transformation and Inverse‐fast
Fourier Transformation
Introduction
Mechanical damage, including deformation, phase
transformation, and micro‐fracture induced by contact
stress in the semiconductor materials is an important
topic of both technological and fundamental interests.
The influence of the mechanical damage on the
properties of the semiconductors is crucial in the
design and fabrication of nano‐scale microelectonic
and optoelectronic devices. In this case, micro‐ and
nano‐indentations have been widely used as the most
common and the simplest technique both to assess
mechanical properties and induce mechanical
deformation damage. The entire brittle materials such
as silicon and gallium arsenide have been shown to be
a various kinds mechanical damages including slip,
twin and phase transformation as well as cracking at
ambient temperature. The phase transformation
induced by indentation has been reported by using
transmission electron microscopy (TEM) and high
resolution electron microscope (HREM) in Si. In
contrast with Si, however, there is no evidence of the
phase transformation induced by indentation to be
observed in GaAs, where slip and twinning had been
suggested to be a major deformation mode.
A number of studies of the entirely semiconductors
appear to be characteristic discontinuities on the
indentation load‐displacement curves, which is called
“pop‐in”. It is proposed that this kind of event is
caused by the generation of discrete dislocation loops
or the phase transformation under contact stress.
Although the mode of deformation induced by
indentation has been extensively investigated in Si and
Ge, but there has been little report on the
microstructure evolution induced during indentation
in compound semiconductors, especially, in GaAs.
In this article, we will give a review of the
microstructural aspects of the damage and fracture
generated under the contact loading at ambient
temperature, and even the electron‐beam‐induced
crystallization in amorphous semiconductor resulting
from researches carried out by the authors over the
past 20 years. The emphasis is placed on the direct
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
14
observations, carried out by TEM and HREM, of the
microstructure evolution, including deformation,
phase‐transformation, and in particular deformation‐
behavior ahead of the crack‐tip in silicon and gallium
arsenide single crystals.
Materials and Experimental Procedures
The <110> oriented Si and GaAs single crystals were
selected for the studies. The Si has a diamond‐type
lattice structure as shown in Fig. 1a, and GaAs has a
sphalerite‐type lattice structure, which is similar to the
diamond lattice structure as shown in Fig. 1b. The
difference between the Si lattice structure and the
GaAs lattice structure is four atoms located at the <1/4
1/4 1/4>. In the GaAs, these four atoms are Ga‐atoms
and the rest are As‐atoms. Both of them are typical
brittle materials at ambient temperature.
For plane‐view samples, 3 mm diameter discs with
(110) orientation surface were ultrasonically cut,
mechanically ground and polished to a thickness of
about 300 μm. Vickers indentations were conducted on
the polished surface by using a Vickers
super‐microindenter (CHX‐1000, Shanghai) with
different loads, 0.0049 N, 0.049 N, 0.098 N and 0.147 N,
respectively, in air at ambient temperature. The
diagonal of indenter is selected to parallel to a certain
direction as shown in Fig. 2. In order to increase
success rate for TEM observation of the indentations,
400 impresses were generally made in the surface for
plan‐viewed samples. The indented specimens were
mechanically thinned to approximately 80 μm and
dimpled to a thickness of about 20 μm from the side
opposite indentations. The dimpled side was ion‐beam
thinned to perforation. Finally, a further 5 min
thinning was performed on both sides with ion‐beam
thinning to remove the materials deposited on the
surface. The structures were characterized by TEM
(JEM‐2000FXII, Japan) and HREM (JEM‐2010, Japan).
FIG. 1 ILLUSTRATION OF CRYSTALLINE STRUCTURES FOR
CRYSTALS, (a) Si, (b) GaAs
For the cross‐sectional view, sandwich method was
used as shown in Fig. 3. A plate‐like specimen (about
0.5 mm thickness) of [001] single‐crystal silicon was
selected. Vickers indentations were formed with a load
of 0.049 N at ambient temperature. The sample was
oriented in such a way that the diagonals of the
indentation impression were aligned along <110>
directions in the (001) plane. A cross‐sectional sample
was prepared in a sandwiched way. The specimen was
ion‐beam thinned. In order to obtain electron‐
transparent sections in the whole indented region,
further low‐angle ion‐beam thinning of very short
duration (3~5 min) was carried out during intervals of
HREM observations, allowing the whole amorphized
region (from top‐side to bottom) near the interface to
be observed clearly by HREM (JEOL 2000EXII, Japan).
FIG. 2 ILLUSTRATION OF SPECIMEN FOR INDENTATION TEST
FIG. 3 SCHEMATIC DIAGRAM OF THE SANDWICH METHOD
FOR CROSS‐SECTIONAL OBSERVATION
As discussed in the studied results, amorphous phase
can be induced in both Si and GaAs crystals under
indentation, the related electron‐beam induced
crystallization in GaAs with amorphous phase induced
by indentation was in‐situ investigated to study the
nucleation and growth processes by using a JEM 2010
HREM operating at 200 kV. The current densities of
the electron beam were selected to be 93, 74 and 50
pA/cm2, respectively.
Results and Discussion
Deformation Structures Induced by Indentation
1) Deformation Dislocations
Fig. 4a shows a plane‐viewed bright‐field
observation of an indentation on the (110) Si surface.
A great deal of tangled dislocations distribute
around the periphery of the indentation. The
dislocations are bended into contours and ended in
the same place as shown in a dark‐field in Fig. 4b. It
can be seen that the indented region is
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
15
characterized by a devoid of crystallographic
contrast. A selected area electron diffraction (SAED)
taken from the indented region consists of diffused
rings (insert in Fig. 4a), indicating that a transition
from crystal lattice to amorphous structure occurs.
This kind of result is confirmed further by HREM
observations that will be discussed later.
FIG. 4 PLANE‐VIEW OBSERVATIONS OF AN INDENTATION ON
(110) Si, (a) BRIGHT‐FIELD IMAGE, (b) DARK‐FIELD IMAGE
TAKEN FROM THE PERIPHERY OF THE INDENTATION
Fig. 5 is a cross‐sectional bright‐field image taken
from the edge of an indenter marked by A. It is
interesting to note that an amorphous region,
shaped as an inversed triangle, which is absent
from the crystalline lattice. This will be discussed in
detail later. Under the indentation, some groups of
dislocations, marked by B, C, D and E, can be
observed. It is reasonable to propose that the
dislocations belong to different kinds of
characteristics. It is clear that the distribution of the
dislocations around the indenter is inhomogeneous
and they have different natures. This is confirmed
further by the observation in GaAs.
FIG. 5 CROSS‐SECTIONAL TEM IMAGE TAKEN FROM A
REGION NEAR BY AN INDENTATION ON (001) Si
FIG. 6 DEFORMED STRUCTURE INDUCED BY AN
INDENTATION WITH A LOAD OF 0.049 N
Fig. 6 shows a plane‐viewed TEM bright‐field
micrograph of an indentation produced with a load
of 0.049 N in GaAs single crystal at room
temperature. It is shown clearly that tangled
dislocation distribution around the vicinity of the
indentation is inhomogeneous, and appears to be
the fourfold symmetry of the rosette, consisting of
four‐set long arms, and four‐set short arm
dislocations. This observation is similar to the
earliest finding by Warren et al. as shown in Fig. 7.
Meanwhile, Bourhis and Patriarche have studied
the nanoindentation structures achieved at room
temperature on (001) GaAs with either n‐ or p‐type
doping, and found that GaAs with n‐doped shows
partial dislocations in the form of both long‐ and
short rosette arms as shown in Fig. 8.
FIG. 7 FOUR‐FOLD SYMMETRY ROSETTE PATTERN AROUND
{001} SURFACE INDENTATIONS, (a) INTRINSIC Ge, (b) GaAs
FIG. 8 TEM PLANE VIEW OF AN INDENTATION IN GaAs
UNDER VARIOUS CONTRAST CONDITIONS
Fig. 9 shows the schematic diagrams of the possible
slip geometry in a (110) GaAs crystalline thin film.
It can be seen that there are six possible slip planes.
Four of the slip planes, (1 1 1 ), ( 1 1 1 ), ( 1 11)
and (1 1 1), are shown in Fig. 9a, and other two,
( 1 1 1) and ( 1 1 1 ), are shown in Fig. 9b. The
analysis of dislocations which are shown in Fig. 6,
reveals that the short rosette‐arm dislocations are
parallel to the direction [ 1 12] or [1 1 2], and they
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
16
glide on the planes of (1 1 1 ), ( 1 1 1 ), ( 1 11) and
(1 1 1) in (110) GaAs crystalline thin film.
FIG. 9 SCHEMATIC DIAGRAM OF THE POSSIBLE SLIP
GEOMETRY IN (110) GaAs CRYSTALLINE THIN FILM
Fig. 10 shows TEM observations of two fields near
an indentation, showing the long‐rosette arm
dislocations. It consists of the high dense
dislocation structure near the center of indentation.
The half‐loop shape of the dislocations and long
and straight dislocations along [ 1 10 ] direction
glide on ( 1 1 1) or ( 1 1 1 ) plane as shown in Fig.
9b. This observation is similar to the earliest study
of Warren et al., who attributed to the different
nobilities of α and β dislocations, and was verified
further by Bourhis and Patriarche.
FIG. 10 TEM IMAGES OF THE LONG‐ROSETTE ARM
DISLOCATIONS AROUND AN INDENTATION
In order to determine the rosette‐dislocation nature,
the diffraction contrast analysis has been made into
one of the fields observed at present study. Fig. 11
shows a bright‐field TEM image taken from one
corner of the indentation and the related SAED
pattern. It is found that these dislocations glide
along three sets of directions of [ 1 1 0], [ 1 1 2 ] and
[1 1 2 ], respectively, during indentation induced
deformation. The dislocations which are parallel to
[1 1 0] direction glide along ( 1 11) or ( 1 1 1 ) plane.
They are referenced to be α‐type dislocation. The
other two sets of dislocations lying on the planes of
( 111 .111 .), ( 111) and (111), as shown in Fig. 9,
with the dislocation line directions of [ 112 ] and
[ 112 ], consisting of the short rosette arm
dislocations, are proposed to be the β‐type
dislocations.
The characteristic of the dislocations shown in Fig.
11 were analyzed under different diffraction
conditions as shown in Fig. 12. By using a
diffraction condition of g=[ 111 ], only the
dislocations along [1 10 ] direction were detectable
as shown in Fig. 12a. When g is [ 004 ], only the dislocations along [112 ] were visible (see in Fig.
12b). Fig. 12c was imaged using g=[113 ], it can be
seen that only the dislocations along [112 ] were
visible and those along [1‐10] were slightly
detectable. When g=[ 220 ], the dislocations were
not detectable besides those along [110 ] direction as shown in Fig. 12d. According to g∙b=0, the
Burgers vectors can be determined to be of 1/2[110]
for short‐rosette arm dislocations and 1/2[1 10 ] for long‐rosette arm dislocations. The former is a
mixed type dislocation and the later is pure‐screw
one. The related results are listed in Table 1. The
distribution of dislocations induced by an
indentation in silicon single is much similar to that
in GaAs.
FIG. 11 THREE‐SET DISLOCATION STRUCTURE TAKEN FROM A
CORNER OF AN INDENTATION AND THE RELATED SAED
FIG. 12 DISLOCATION ANALYSIS BY VARIOUS DIFFRACTION
CONDITIONS, (a) g=[111] , (b) g=[ 004 ], (c) g=[113] , (d) g=[ 220]
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
17
TABLE 1 DIFFRACTION CONTRACT ANALYSIS OF THE LONG‐ AND SHORT‐ROSETTE ARM DISLOCATIONS
Fig. No. g b (±1/2) visible or not
[110] [1 1 0] [101] [10 1 ] [011] [01 1 ] [1 1 0] [1 1 2 ] [ 1 1 2 ]
12a [1 1 1 ] 0 1 0 1 ‐1 0 visible missing missing
12b [004] 0 0 2 ‐2 2 ‐2 missing visible missing
12c [1 1 3 ] 0 1 ‐1 2 ‐2 1 missing visible missing
12d [2 2 0] 0 2 1 1 ‐1 ‐1 visible missing missing
TABLE 2 CONTRAST ANALYSIS OF STACKING FAULTS AS SHOWN IN FIG. 14
Figure
number g
b (±1/2) Visible or not
[110] [110] [101] [10 1] [011] [ 011] Ld* Trl** SFF***
14a 111 0 0 0 ‐1/3 2/3 ‐1/3 visible visible visible
14b 111 2/3 ‐1/3 ‐1/3 0 2/3 0 missing missing visible
14c 220 2/3 ‐1/3 ‐1/3 ‐1/3 2/3 ‐1/3 visible missing missing
14d 113 ‐1/3 2/3 ‐1/3 1 ‐1 0 missing visible missing
* Leading dislocations, ** Trailing dislocations, *** Stack‐fault fringes
2) Stacking Faults
As shown in Fig. 13, two‐kind of morphologies of
the stacking faults had been observed in GaAs
induced by indentation with a large load of 0.147 N.
Fig. 13a is a plane‐viewed TEM bright‐field image
of one kind of stacking fault. It is seen clearly that
the trace of the stacking fault is parallel to [ 220 ]
and they are in ( 1 11 ) or ( 111) planes. Diffraction contrast analysis of the partial dislocations by using
different diffraction conditions are shown in Fig. 14
and the results are listed in Table 2. When the
g=[ 111 ] is used to imaging, the stacking faults and
partial dislocations at both ends of the stacking
faults were visible (Fig. 14a). The stacking fault
fringes were visible, and the partial dislocations at
the end of the stacking faults disappeared when
g=[ 111 ] was used to image (Fig. 14b). However,
when g=[ 220 ] and [ 113 ] were used to image (Figs.
14c and d), only leading (Fig.14c) and trailing (Fig.
14d) dislocations are visible respectively. Therefore,
the Burgers vectors of the partial dislocations can
be determine to be 1/6[ 112 ] and 1/6[ 121 ],
respectively.
Fig. 13b shows another type of stacking faults
occurred in GaAs crystal during indentation.
Contrast analysis shows that this kind of stacking
faults are composed of the partial dislocations
which are parallel to each other and have the
Burgers vectors of 1/6[ 112 ].
FIG. 13 STACKING FAULTS OBSERVED NEAR AN
INDENTATION INDUCED WITH A LOAD OF 0.147 N IN GaAs
FIG. 14 CONTRAST ANALYSIS OF A SERIES OF PARTIAL
DISLOCATIONS IN STACKING FAULTS, (a) g=[ 111] , (b) g=[ 111 ],
(c) g=[ 220 ], and (d) g= [ 113 ]
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
18
3) Deformation Twins
In addition to the dislocations and stacking faults
formed during indentation, and twinning is also
one of the important modes of deformation. As
shown in Fig. 6, two‐fold‐symmetry deformation
bands distribute around the indentation. An SAED
as shown in Fig. 15a were taken from the region
marked by a circle in Fig. 6. The typical diffraction
spots reflecting twinning can be seen obviously, the
diffraction spots locate at the positions of ±1/3{111}
of that from the GaAs crystal. The analysis shows
that the twinning plane is {111} and its direction is
<112>. These indicate that the two‐fold‐symmetry
deformation bands have a typical twining
characteristic. The twins distributing around the
indentation looks like a rhomboid as shown
schematically in Fig. 15b.
FIG. 15 SAED ANALYSIS OF TWINS AROUND THE
INDENTATION, (a) SAED PATTERN TAKEN FROM THE AREA
MARKED BY A CYCLE IN FIG. 6, (b) SCHEMATIC DIAGRAM FOR
THE TWIN DISTRIBUTION AROUND INDENTATION
Fig. 16a presents a typical HREM image of the
twins. It can be found that each piece of twins is
consisted of multi‐micro‐twins, and the twin plane
is a stacking fault plane. This is seen more clearly
from Fig. 16b, where two stacking faults in the
original location of the twins are shown. This
implies that the formation of the twin is related to
the production of stacking fault closely.
FIG. 16 HREM IMAGES OF TWINS (a), AND TWINING
INITIATION REGION (b)
Indentation‐induced Phase Transition
1) Single Crystal to Poly‐crystal Transition
A great number of investigations have been made
since the first observation of high‐pressure induced
phase transition by Minomura and Drickamer.
Many of those studies focused on the phase
transformation in Si and Ge, but there has been
little report on the pressure induced phase
transition in GaAs.
Fig. 17 shows a TEM investigation of an indentation
induced with a load of 0.0049 N in GaAs. Fig. 17a is
a TEM bright field image of an indentation region.
Different diffraction contrasts, which can be
reduced to grey and bright contrasts, can be seen in
the indentation region. The related contrast
distribution in the indentation region is illustrated
in the schematic diagram in Fig. 17b. SAEDs taken
from the areas as indicated by A and C in Fig. 17b
are shown in Fig. 17c and Fig. 17d, respectively. It is
found that the 4 zones along diagonals as marked
by A in Fig. 17b have the similar contrast that
changes while tilting the sample in TEM. The
electron diffraction from these areas reveals
polycrystalline characteristic with diffraction
speckles as shown in Fig. 17c, implying that a
transition from single crystal to polycrystal or
microcrystal has occurred during indenting. A
further detail can be obtained from the HREM
observation as displayed in Fig. 18, where many
nano‐grains (marked by n) with a size of about 10
nm can be observed. These nano‐grains, among
which is amorphous structure, have different
crystalline orientations. However, the SAED taken
from other areas as marked by B and C in Fig. 17b
are slightly elongated speckles, indicating that
these zones are deformed slightly although they
still keep single crystalline nature. Fig. 19 shows a
HREM image taken from the indentation center,
many dislocations (marked by D) and stacking
faults (denoted by SF) can be detected.
FIG. 17 PLANE‐VIEWED TEM INVESTIGATION OF AN
INDENTATION INDUCED WITH 0.0049 N, (a) BRIGHT‐FIELD
IMAGE OF THE INDENTATION, (b) SCHEMATIC DIAGRAM OF
THE CONTRAST DISTRIBUTION IN THE INDENTATION
REGION, (c) SAED TAKEN FROM THE AREAS AS MARKED BY A
IN (b), (d) SAED TAKEN FROM THE AREAS AS MARKED BY C IN
(b)
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
19
FIG. 18 HREM IMAGE TAKEN FROM A REGION IN THE
INDENTATION AS INDICATED BY A IN FIG. 17B
FIG. 19 HREM IMAGE TAKEN FROM INDENTATION CENTER,
SHOWING DISLOCATIONS MARKED BY D AND STACKING
FAULTS DENOTED BY SF
2) Indenter‐induced Amorphization
FIG. 20 BRIGHT‐FIELD TEM IMAGE TAKEN FROM AN
INDENTATION INDUCED WITH A LOAD OF 0.049 N, THE
INSERT IS A SAED FROM THE INDENTATION CENTER
It is interesting to find that a transition from
crystalline lattice to amorphous structure occurred
during indentation with the load of 0.049 N in
GaAs. Fig. 20 shows a plane‐viewed bright‐field
TEM image and related SAED (see insert) of an
indentation. The SAED consists of two diffusion
rings. The SAED analysis reveals that the rings in
the SAED are from the (111) and (220) or (113)
crystalline planes and belong to the one from
amorphous GaAs. This is confirmed further by
HREM observation as shown in Fig. 21, where a
completely disordered lattice area marked by
‘amorphous zone’ can be seen obviously, indicating
that a transition from crystalline lattice to
amorphous structure occurred under the
indentation. This is a surprising finding and is, to
the authors’ knowledge, the first observation of a
crystalline lattice to amorphous transition in GaAs
single crystal under indentation. It is also noted, as
shown in Fig. 21, that there are many
disordered/amorphous clusters (marked by *) with
1‐2 nm in size, and nano‐grains (denoted by nano)
with different orientations and dislocations (by D)
distributing along the interface between the
amorphous and crystalline lattice zones. It is
reasonable to propose that the crystalline to
amorphous transition may go through a crystalline
lattice deformation and distortion, rather than
lattice abrupt collapse.
FIG. 21 HREM IMAGE OF THE INTERFACE REGION BETWEEN
CRYSTALLINE AND AMORPHOUS PARTS IN A 0.049 N LOAD
INDUCED INDENTATION
It is surprising to note that deformation behavior in
silicon induced by indentation is much similar to
those in GaAs single crystal. Fig. 22 is a typical
TEM observation of an indenter made on (110)
silicon single crystal. As the same that seen in Fig.
20, the diffusion diffraction rings taken from the
center of the indenter, shown inserted in Fig. 22,
indicate that the amorphization took place as that
in GaAs. This can also be further verified by HREM
observation as shown in Fig. 23, where two regions
the amorphous region at the lower part are marked
by a‐Si and the crystalline one at upper part is
marked by c‐Si.
FIG. 22 PLANE‐VIEW TEM IMAGE OF AN INDENTED REGION
ON (110) Si SURFACE, AND THE INSERT SAED IS TAKEN FROM
THE INDENTATION CENTER
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
20
FIG. 23 HREM IMAGE TAKEN FROM AN INDENTATION
CENTER IN Si SINGLE CRYSTAL, SHOWING THE
PHASE‐TRANSFORMATION TAKEN PLACE FROM
CRYSTALLINE LATTICE TO AMORPHOUS STRUCTURE
In contrast with the crystalline region, the
disordered lattice and amorphous region is a strong
evidence for the occurrence of the transition from
crystalline to amorphous in silicon. From uneven
interface between the two regions of c/a Si, and a
great deal of defects such as micro‐twins, clusters
with lattice disorder marked by the arrows,
indicating again that this kind of transition goes
through middle severe lattice deformation stage,
rather than crystalline lattice sudden collapse.
In order to verify the amorphous matter
underneath the indenter produced by the
indentation rather then by TEM specimen
preparation process, A GaAs thin foil with
indentations induced with the load of 0.049 N was
annealed at 500°C for 60 min, and then TEM film
was prepared. The observations are shown in Fig.
24. It is found that microcrystalline grains appear
inside the indentation in the annealed sample. The
SAED (see insert in Fig. 24a) taken from the
indenter shows polycrystalline rings with some
diffraction spots instead of amorphous ones,
implying that recrystallization took place inside the
indentation where amorphous characteristic were
observed as shown in Figs. 20 and 21. HREM image
(see Fig. 24b) taken from the indenter in Fig. 24a
demonstrates that there are many nano‐grains in
the indented region.
FIG. 24 MICROSTRUCTURES OF AN INDENTATION SUBJECTED
ANNEALING AT 500 °C/60 MIN OBSERVED BY, (a) TEM, (b)
HREM
Electron‐beam‐induced Crystallization
1) In‐situ Observation
The several mechanisms for electron‐beam‐induced
crystallization have been proposed by some
researchers and are involved: elastic‐ collision‐
driven recrystallization, plastic‐interaction
promoted defect motion and electron‐ beam‐
induced induced recrystallization. Jenčič et al have
considered that crystallization is a plastic or
ionization process which is a cut and recombination
of the atomic bonds. Narayan has proposed that the
matter migration occurred at interface between the
crystalline and amorphous as the crystallization.
However, there have been fewer in‐situ
observations of the nucleation and growth of
recrystallization induced by electron‐beam,
especially, in amorphous GaAs.
Fig. 25 shows TEM images and corresponding
SAED taken from the same fields (marked by a
arrow) before (Fig. 25a) and after (Fig. 25b)
electron‐beam irradiation. It can be seen that the
diffusion rings before electron‐beam irradiation
(Fig. 25a) becomes typical polycrystalline rings with
diffraction spots (Fig. 25b), implying that
recrystallization occurred in this field after
electron‐beam irradiation. This can be also
confirmed by the changes of the diffraction
contrast.
FIG. 25 TEM OBSERVATIONS OF ELECTRON‐BEAM INDUCED
STRUCTURE CHANGE OF AN AMORPHOUS REGION SUBJECTED
TO AN IRRADIATION WITH CURRENT DENSITY OF 73 pA/cm2, (a)
BEFORE IRRADIATION, (b) AFTER IRRADIATION
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
21
Fig. 26 shows a series of in‐situ HREM observations
of the electron‐beam‐irradiation crystallization in
an amorphous GaAs induced by indentation. The
same region was investigated after various
electron‐beam‐irradiation time. Fig. 26a shows an
amorphous region induced by indentation in GaAs
single crystal, showing a typical amorphous
structure. Fig. 26b shows a HREM image of the
same field as shown in Fig. 26a after irradiation for
10 min. One can see that there are several clusters
(marked by arrows) with atomic scale appeared.
After irradiation for 30 min, these clusters become
the nano‐grains with a certain crystallographic
orientation as shown in Fig. 26c. As the increasing
irradiation time, nano‐grains with random
orientations increase as shown in Figs. 26d, 26e and
26f. When irradiation for 120 min (see in Fig. 26e),
this region appears many nano‐grains. And after
180 min irradiation, the whole area becomes
crystalline zone as shown in Fig. 26f.
FIG. 26 IN‐SITU HREM OBSERVATIONS OF THE
CRYSTALLIZATION OF AMORPHOUS GAAS WITH DIFFERENT
IRRADIATION TIME, (a) 0 MIN, (b) 10 MIN, (c) 30 MIN, (d) 60 MIN,
(e) 120 MIN, (f) 180 MIN
2) Crystallization Mechanism
It is believed that the electron‐beam irradiation can
result in the temperature rise of the samples.
According to the calculated temperature rise for
Fe78Si12B10 of 557°C induced by electron‐beam
irradiation, Fisher and Liu et al. proposed that the
crystallization induced by electron‐beam
irradiation is the result of the temperature rise.
The temperature rise at the center of the specimen
induced during electron‐beam irradiation is
expressed by
ΔT=4
I
ke(
E
d
)(γ+2
b
a) (1)
where, e is electron charge, γ is a Euler constant
(0.5772), a is Gaussian width of the beam (effective
diameter of the beam), b is the radius (equal to
diameter of the specimen), k is thermal conductivity
coefficient (is 44 Wm‐1K‐1 for GaAs), I is the beam
current rate, and ΔE is the loss of energy of an
electron crossing the distance d in the specimen.
The Eq. (1) is modified as following when the
specimen has a hole at the center:
ΔThole=I
ke(
E
d
)ln
0
b
r (2)
where, r0 is effective diameter of the current beam.
If the loss in energy is small relative to initial
energy, ΔE/d becomes dE/dx (stopping power).
Therefore, it is found:
–dE
dx=
4
2 2
r e
m c
[ln2 2
2
mc
I
+F(β)] (3)
where,
F(β)=21
2
+
2
1
2( 1) [
2
8
‐(2 +1)ln2] (4)
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
22
here, e is electron charge, n is the density of the
target material, m is the electron mass, c is the light
speed, β=v/c, v the electron speed, τ is the radio of
the electron energy to dynamic energy (E/mc2). The
temperature rise in GaAs induced by electron‐beam
irradiation at 300 keV is 7.0°C by using Eqs. (3) and
(4).
According to Eqs. (1) and (2), the temperature rise
in GaAs during irradiation with acceleration
voltage of 200 keV and the beam current density of
94 pA/cm2 was calculated to be about 10.8°C. While
the parameters were selected as following: the
radius b (equal to diameter of the specimen) is 1.5
mm, the width of the specimen d is 20 nm. Table 3
lists the temperature rise of some materials induced
during electron‐beam irradiation collected from the
references. It can be found that the temperature
rises of all materials listed in Table 3 are much
lower for them to reach their recrystallization
temperatures. Although the calculated temperature
rises of the GaAs at 200 keV are different between
the present work and that by Jenčič et al. for the
different effective diameters r0 of the current beam
and the beam current rates, both of which are not
large enough for obtaining the recrystallization
temperature of GaAs (300°C). Therefore, it is
reasonable to propose that the crystallization in
GaAs induced during irradiation is related to the
electron‐beam current density, rather than the rise
in temperature.
On the other hand, Meldrum found that the
crystallization occurred when both the phosphate
glass and amorphous fluorapatite in liquid nitrogen
were irradiated. Jenčič et al also found that
crystallization can still occurred when both Si and
GaAs were irradiated by electron beam under 30 K.
All these indicate that the irradiation‐crystallization
is independent of temperature rise. Meanwhile, the
present study shows that the electron‐beam
irradiation could not induce crystallization of
amorphous GaAs even for a long time, e.g. 120 min,
until the beam current is larger than 50 pA/cm2.
This implies that there is a critical electron‐beam
current to be required for occurrence of the
crystallization induced by electron‐beam
irradiation.
On the other hand, there are a number of models to
describe the interracial growth of crystallization
Jenčič et al reported that crystallization occurs at
electron‐beam energy of 50 keV (acceleration
voltage of 50 kV) in Si, Ge, GaP and GaAs, and the
higher the electron‐beam energy is, the lower the
growth rate of crystallization is.
Jenčič et al also found that the growth rate of
crystallization is the lowest when the electron
energy is near the threshold value for atom
displacement. Therefore, inelastic energy loss
mechanism is responsible for the crystallization and
growth under low electron‐beam irradiation (< 100
keV). However, when the electron‐beam energy is
high, for example, higher than 100 keV, the elastic
energy is proposed to promote the motion and
rearrangement of the atoms or defects at the
interface between the amorphous and crystalline
(a/c) regions, implying that the elastic energy, on
one hand, may induce production of the defects in
crystalline materials, on the other hand, can make
the crystalline growth at the a/c interface.
TABLE 3 THE PARAMETERS OF THE TEMPERATURE RISE FOR VARIOUS MATERIALS INDUCED DURING ELECTRON IRRADIATION
Electron
Energy (keV)
Temperature rise (°C)
Si† Ge† GaP† GaAs† GaAs§ LaPO4‡ Zircon‡ ScPO4‡
50 0.2 0.6 0.4 0.9 7.1 6.6
100 0.5 1.8 1.3 2.7 11.9 10.9
150 0.8 2.6 1.9 3.8 19.1 17..4
200 0.3 0.9 0.7 1.4 10.8 41.1 19.0 40.0
250 0.4 1.3 0.9 1.9
300 1.4 4.8 3.5 7.00
Note: † from refs. 30 and 31; ‡ from ref. 37; § from this work
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
23
The present in‐situ HREM observation shows that
the crystallization of the amorphous GaAs is
related closely to the electron‐beam current density.
The larger the electron‐beam current results in the
larger the energy (ΔE) obtained in an irradiated
zone in per area per time. When the energy (ΔE)
reaches a critical value, it may excite the fracture
and re‐arrangement of the atomic bonds, leading to
nucleation and growth of the crystalline. On the
other hand, when the beam‐current density is lower
than 50 pA/cm2 in present work, the energy carried
by electrons is not large enough to make the
re‐arrangement of the atomic bond in the irradiated
zone. However, the larger beam‐current density,
for example, 74 pA/cm2, can obviously make the
occurrence of crystallization, and as the increase in
the beam‐current density (93 pA/cm2), the rate for
nucleation and growth of crystallization increase in
the amorphous GaAs.
Sutton et al. also found that crystallization is an
instantaneous process, where a weak ordered
structure in the amorphous zone is as the precursor
of crystallization, and then this kind of weak
ordered structure may transfer the ordered
crystalline. Obviously, the weak‐ordered structure
is similar to the atomic clusters observed in the
present work. It is found that the clusters with a
size of nano‐scale occurred when the irradiation
reached 10 min as shown in Fig. 26b, and this kind
of clusters may act as the nuclei of crystallization.
And as increasing irradiated time, the nuclei grow
gradually at the amorphous and crystalline nuclei
interface. So it is reasonable to propose that the
crystallization may involve two processes: the
atoms in the amorphous zone ahead of the cluster
form a new ordered cluster by diffusion, and then
these clusters growth into the nucleus of the
crystalline grains.
Deformation and Cracking Ahead of Crack‐tip
The brittle fracture of structural materials has been the
project of numerous theoretical and experimental
investigations since the earliest explanations
developed by Inglis and Griffith, but the basic
mechanism of the phenomenon has hitherto been
unclear. The major reason for this is that the structure
and deformation behavior at the crack tip under stress
is not well understood at present. The structure at the
crack tip induced by stress is the so called “black box”,
although some models had been developed as shown
in Fig. 27. Continuum media mechanics is shown to
have intrinsic limitation in its capacity to deal with the
structural change that occurs in the “black box” at the
atomic scale. Hockey and Lawn have investigated the
fracture behavior of the brittle materials Si, Ge and SiC.
They suggested that the crack tips are atomically sharp
and there is no evidence for dislocation activity or
plasticity associated with crack propagation at room
temperature. Their atomically sharp model is in fact in
agreement with the earlier idea of the lattice‐trapped
theory and cohesive force theory. Evidence supporting
the concept of an atomically sharp crack mainly came
from the earlier TEM studies of crack tips, and that
was verified later by HREM and high‐voltage electron
microscope (HVEM) studies. Those studies commonly
showed that there was no evidence of micro‐plasticity
near the crack tips, and successive debonding between
two adjacent lattice planes was the basic fracture
model in the covalent crystals. Recent observations by
HVEM and atomic force microscopy (AFM) have,
however, indicated that dislocations might be emitted
from a crack tip induced by indentation in silicon
when the temperature was raised to higher than 552°C
to activate dislocation sources. The key to
understanding the structure and deformation behavior
of a crack tip in a brittle material is to make a crack
with a very sharp tip, and then to make direct
observations at the atomic scale.
FIG. 27 ILLUSTRATION OF VARIOUS CRACK TIP MODELS, (a)
ATOMICALLY SHARP CRACK MODEL, (b)
QUASI‐ONE‐DIMENSIONAL MODEL OF A SHARP CRACK,
WITH NONLINEAR CHARP‐TIP BOND EMBEDDED IN A
LINEAR “LATTICE”, (c) DUGDALE‐BARENBLATT MODEL OF
THE CRACK‐TIP
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
24
Fig. 28 shows bright‐field TEM images of the cracks
induced by Vickers indentation with a load of 0.049 N
on the surface of (110) Si and GaAs. It is interesting to
find that the mircocracks appear at the intersections
between the slip bands, rather than at the corners of
the indenter as shown in Fig. 28c.
To explore the origin and nature of the cracks, an
observation ahead of the crack‐tip was made on the
diffraction contrast scale as the first step. Fig. 29 shows
a image at a crack tip induced by indentation in single
crystal Si. It was found that the crack tip can emit
several groups of dislocations which can interact to
form the dislocation network. This implied that the
crack tip appears plastic behavior.
FIG. 28 TEM BRIGHT‐FIELD IMAGE, SHOWING A SMALL
CRACK WITH A VERY SHARP TIP APPEARED AT THE
INTERSECTION BETWEEN SLIP BANDS, (a) IN Si, (b) IN GaAs,
AND (c) SCHEMATIC DIAGRAM OF THE CRACK PRODUCTION
FIG. 29 CROSS‐SECTION IMAGE OF DISLOCATION EMISSION
FROM THE CRACK‐TIP IN SILICON SINGLE CRYSTAL
DEFORMED UNDER INDENTATION
Fig. 30 is a group of HREM images taken from the
crack tip in Fig. 28b. Fig. 30a shows in detail the crack
tip structure induced by an indentation with a load of
0.049 N. It is fascinating to find that a series of
amorphous clusters (indicated by “a”) about 2‐3 atoms
in width are separated by areas of crystalline fringes
(indicated by “c”), and they are distributed alternately
between the crack walls. As the indentation load
increases to 0.098 N, an amorphous band of 1‐2 nm
width forms between the crack‐walls and the crack
propagates along the amorphous band as shown in Fig.
30b, which is a magnified HREM image taken from the
left part of the Fig. 30a. The process of the transition
from a crystalline lattice to a disordered structure
along the propagation direction of the crack tip and the
fact that the disordered regions between the crack
walls (Fig. 30a) are connected to form an amorphous
band (Fig. 30b) can be clearly seen. The displacement
in atomic arrangement between both sides of the crack
(indicated by FD in Fig. 30b) and dislocations indicated
by D is apparent (Fig. 30b). Electron diffraction
analysis shows that the three group of atomic planes
are (001), ( 111) and ( 111 ), respectively, and the extent
of the atomic disorder is quite different in these three
planes as shown in Fig. 30b. The lattice disordered
extent is the lightest in ( 111), and the most severe in
( 111 ), in which the atom arrangement is completely
disordered.
FIG. 30 HREM IMAGES TAKEN FROM A REGION AHEAD OF A
CRACK TIP, (a) A SERIES OF CLUSTERS WITH DISORDERED
LATTICE MARKED BY “A” BETWEEN THE CRACK WALLS, (b) A
MAGNIFIED HREM IMAGE TAKEN FROM THE CRACK TIP,
SHOWING AMORPHOUS BAND WITH 1‐2 NM IN WIDTH,
DISLOCATIONS (DENOTED BY D), AND DISPLACED LATTICE
(DENOTED BY DL) AHEAD OF THE CRACK TIP
In order to confirm further the results obtained by
HREM observations mentioned above, fast‐Fourier
transformation (FFT) and Inverse‐fast Fourier
transformation (IFFT) were performed on areas
selected near the crack tip. Fig. 31 shows an HREM
image of a crack tip, and the FFT results (denoted as
FFT‐SAED) from two selected regions marked by the
squares I and II are inserted, respectively. According to
the FFT‐SAED, IFFT transition was performed to get
the corresponding IFFT fringe images for the three
planes of ( 111), (001) and ( 111 ), respectively. Figs.
32a, 32b and 32c present the IFFT fringe images
resulting from the related FFT‐SAEDs ( 111), (001) and ( 111 ), respectively, corresponding to the region II as
shown in Fig. 31. It is fascinating to find that the
fringes are not changed on the ( 111) plane, and the atom arrangement is still essentially ordered (Fig. 32a).
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
25
However, the lattice arrangement ahead of the crack
tip is distorted seriously on the (001) and ( 111 ) planes
and dislocations occurring on the (001) and ( 111 )
planes as shown by arrows in Figs. 32b and 32c.
Similar results were obtained from square I in Fig. 31.
As shown by arrows in Figs. 32d, 32e and 32f, the
fringes keep a normal arrangement essentially on the
( 111) plane, serious lattice distortion occurs on ( 111 ),
and dislocations appear in both (001) and ( 111 ) planes.
All these results observed in GaAs single crystal are
surprisingly similar to those obtained by HREM for Si
single crystals.
FIG. 31 HREM IMAGE OF A CRACK TIP, AND FAST FOURIER
TRANSFORMATION (FFT) RESULTS FROM TWO SELECTED
SQUARES MARKED BY I AND II ARE SHOWN, RESPECTIVELY
So far, one may still argue that the amorphous regions
between the crack walls observed ahead of the crack
tip in this study could probably be introduced by
specimen preparation such as grounding or ion‐beam
thinning. In order to rule out these possibilities, an
EDX determination of the chemical composition in an
amorphous band was performed using a
field‐emission gun TEM 2000 (FEG TEM‐2000) with an
electron beam spot 1 nm in diameter. The result shows
that in addition to Ga and As, there are no impurities
to be detected inside the amorphous band, and the
chemical composition of the amorphous band is
completely the same as that from a region of the matrix
far away from the crack tip. This implies that the
amorphous band between the crack walls ahead of the
crack tip could not have been introduced by either
impurities or contamination during specimen
preparation. To confirm this point further, the
specimen with an amorphous band ahead of the crack
was annealed at 500°C for 60 min, as described in Fig.
24. It was found that the amorphous band disappeared
and recrystallized grains appeared along the band
ahead of the crack tip. These recrystallized grains had
the same lattice structure as the matrix, although their
size is slightly larger than the width of the amorphous
bands. This is probably to be attributed to the growth
of the grains during annealing.
FIG. 32 FFT‐SAED AND CORRESPONDING IFFT FRINGES FROM
DIFFERENT LATTICE PLANES IN SELECTED SQUARE II (a, b,
AND c) AND SQUARE I (d, e AND f), RESPECTIVELY
All the observations reported above provide new
insights into the possible structure at the crack tip and
the fracture mechanism in highly brittle crystalline
materials such as GaAs single crystal. Deformation
along different crystalline planes ahead of the crack tip
is anisotropic and the crack tip induced during
indentation at room temperature under stress is not
atomically sharp. Dislocations are produced, leading to
crystal lattice distortion, and even a transformation
from a crystalline lattice to a disordered structure
ahead of the crack tips. The crack propagation is
proposed to be a result of decohesion by the
amorphous band, rather than the sequential rupture of
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
26
cohesive bands.
Conclusions
(1) Rosette dislocations occurred and inhomogenously
distributed around an indentation in the ambient‐
temperature brittle materials such as Si and GaAs
single crystals. The short‐rosette arm dislocations with
the Burgers vector of 1/2[110] belong to β‐type mixture
dislocations, and the long‐rosette one with Burgers
vector of 1/2[1 1 0] belong to the α‐type screw
dislocations. Twins and stacking faults are also the
parts of crystal deformation.
(2) Transition from crystal lattice to nanocrystalline
and amorphous structure took place in silicon and
gallium arsenide single crystals under indentation. The
shear stress rather than hydrostatic pressure is
proposed to attribute to the transition, and there are
critical shear stresses for the transitions.
(3) The atom‐level structure ahead of the crack‐tips has
been successfully captured by using the HREM
observations with both plane‐ and cross sectional
views. The crack tips are not atomically sharp. The
dislocations can be emitted from the crack tip during
indentation, leading to crystal lattice distortion and
even to a transition from a crystalline lattice to
disordered structure, forming an amorphous band
with a width of 1‐2 nm. The crack propagates along the
amorphous band, rather than the sequential rupture of
cohesive bonds.
(4) The analysis of fast Fourier transformation
(FFT)‐SAED and corresponding inverse‐fast Fourier
transformation (IFFT) fringe images of different lattice
planes shows that deformation around the crack tip is
anisotropic. The lattice fringes along ( 111) plane does not change and the atom arrangement on this plane is
still essentially ordered, and serious lattice distortion
occurs on the planes of (001) and ( 111 ).
(5) In‐situ observations by HREM show that there is a
critical electron‐beam current density, instead of the
irradiation‐induced temperature rise, for the crystalline
nucleation during crystallization process. Critical
electron‐ beam current density for the crystalline
nucleation is 50 pA/cm2. The larger the current density
is, the faster the crystallization rate is.
REFERENCES
A. Kailer, Y.G. Gogotsi, K.G. Nickel, “Phase transformations
of silicon caused by contact loading”, J. Appl. Phys., vol
81, pp. 3057‐3063. April, 1997.
A. Meldrum, L.A. Boatner and R.C. Ewing,
“Electron‐irradiation‐induced nucleation and growth in
amorphous LaPO4, ScPO4, and zircon”, J. Mater. Res.,
vol 12, pp. 1816‐1827. July, 1997.
A.A. Griffith, “The phenomena of rupture and flow in
solids”, Phil. Trans. R. Soc., Lond. A, vol 221, pp. 163‐198.
October, 1920.
A.B. Mann, D. Van Heerden, J.B. Pethica and T.P. Weihs,
“Size‐dependent phase transformations during point
loading of silicon”, J. Mater. Res., vol 15, pp. 1754‐1758.
August, 2000.
A.L. Ruoff and T. Li, “Phase transitions in III‐V compounds
to megabar pressures”, Annu. Rev. Mater. Sci., vol 25, pp.
249‐271. August, 1995.
B.J. Hockey and B.R. Lawn, “Electron microscopy of
microcracking about indentations in aluminium oxide
and silicon carbide”, J. Mater. Sci., vol 10, pp. 1275‐1284.
August, 1975.
B.R. Lawn, “Physics of fracture”, J. Am. Ceram. Soc., vol 66,
pp. 83‐91. February, 1983.
B.R. Lawn, B.J. Hockey and S.M. Wiederborn, “Atomically
sharp cracks in brittle solids: an electron microscopy
study”, J. Mater. Sci., vol 15, pp. 1207‐1223. May, 1980.
C. St John, “The brittle‐to‐ductile transition in pre‐cleaved
silicon single crystals”, Phil. Mag., vol 32 pp. 1193‐1212.
December, 1975.
C.E. Inglis, “Stresses in a plate due to presence of cracks and
sharp corners”, Trans. Inst. Naval. Archit., vol 55, pp.
219‐241. March, 1913.
D.L. Davidson and J. Lankford, “Fatigue crack growth in
metals and alloys: mechanisms and micro‐ mechanisms”,
Int. Mater. Rev., vol 37, pp. 45‐76. January, 1992.
D.R. Clarke, M.C. Kroll, P.D. Kirchner, R.F. Cook and B.J.
Hockey, “Amorphization and conductivity of silicon and
germanium induced by indentation”, Phys. Rev. Lett., vol
60, pp. 2156‐2159. May, 1988.
E. Le Bourhis and G. Patriarche, “Structure of
nanoindentations in heavily n‐ and p‐doped (0 0 1)
GaAs”, Acta Materialia, Vol. 56, pp. 1417‐1426, April,
2008.
E.R. Weppelmann, J.S. Field and M.V. Swain, “Influence of
spherical indentor radius on the indentation‐induced
transformation behaviour of silicon”, J. Mater. Sci., vol 30,
pp. 2455‐2462. May, 1995.
Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org
27
F. Spaepen and D. Turnbull, “Laser annealing of
semiconductors”. New York: Academic Press; 1982. F.
Spaepen and D. Turnbull, in Laser Annealing of
Semiconductors, edited by J. M. Poateand J. W. Mayer
(Academic, New York, 1982).
G. Michot and A. George, “Dislocation emission from
cracks‐observations by x‐ray topography in silicon”,
Script Matell., vol 20, pp. 1495‐1500. November, 1986.
G. Patriarche and E. Le Bourhis, “In detph deformartion of
InP under a Vickers indentor “, J. Mater. Sci.‐Mat.
Electronics, vol 36, pp. 1343‐1347. March, 2001.
G.I. Bareblatt, “The mathematical theory of equilibrium
cracks in brittle fracture”, Adv. Appl. Mech., vol 7, pp.
55‐129. 1962.
H. Saka and G. Nagaya, “Plane‐view transmission electron
microscopy observation of a crack tip in silicon”, Phil.
Mag. Lett., vol 72, pp 251‐255. October, 1995.
H. Saka and S. Abe, “FIB/HVEM observation of the
configuration of cracks and the defect structure near the
cracks in Si”, J. Electron Microscopy, vol 46, pp. 45‐57.
January, 1997.
H. Tanaka and Y. Bando, “Atomic crack tips in silicon
carbide and silicon crystals”, J. Am. Ceram. Soc., vol 73,
pp. 761‐763. March, 1990.
H. Tanaka, Y. Bando, Y. Inomata and M. Mitimi, “Atomically
sharp crack in 15R‐sialon”, J. Am. Ceram. Soc., vol 71, pp.
C32‐33. January, 1988.
H.R. Hoche and J. Schreiber, “Anisotropic deformation
behaviour of GaAs”, Phys. status. Solidi A, vol 86, pp.
229‐236. Novembor, 1984.
I. Jenčič and I.M. Robertson, “Low‐energy electron beam
induced regrowth of isolated amorphous zones in Si and
Ge”, J. Mater. Res., vol 11, pp. 2152‐2157. September,
1996.
I. Jenčič, M.W. Bench and I.M. Robertson,
“Electron‐beam‐induced crystallization of isolated
amorphous regions in Si, Ge, GaP, and GaAs”, J. Appl.
Phys., Vol 78, pp. 974‐82, February, 1995.
I. Suni, G. Goltz, M.A. Nicolet and S.S. Lau, “Effects of
electrically active impurities on the epitaxial regrowth
rate of amorphized silicon and germanium”, Thin Solid
Films, vol 93, pp. 171‐178. July, 1982.
J. Narayan, “Interface structures during solid‐phase‐epitaxial
growth in ion implanted semiconductors and a
crystallization model”, J. Appl. Phys., vol 53, pp.
8607‐8614. December, 1982.
J.E. Bradby, J.S. Williams, J. Wong‐Leung, S.O. Kucheyev,
M.V. Swain and P. Munroe, “Spherical indentation of
compound semiconductors”, Phil. Mag. A, vol 82, pp.
1931‐1939. July, 2002.
J.E. Bradby, J.S. Williams, J.W. Leung, M.V. Swain and P.
Munroe, “Transmission electron microscopy observation
of deformation microstructure under spherical
indentation in silicon”, Appl. Phys. Lett., vol 77, pp.
3749‐3751. December, 2000.
J.S. Li, Z.C. Li, L. Liu and Y.B. Xu, “Stacking‐fault structure
induced by indentation in GaAs”, Chinese J. Mater. Res.
Vol 17, pp. 359‐364. August, 2003. (in Chinese)
J.S. Williams, Y. Chen, J. Wong‐Leung, A. Kerr and M.V.
Swain, “Ultra‐micro‐indentation of silicon and
compound semiconductors with spherical indenters”, J.
Mater. Res., vol 14, pp. 2338‐2343. June, 1999.
K. Wasmer, M. Parlinska‐Woitan, R. Gassilloud, C. Pouvreau,
J. Tharian, and J. Micher, “Plastic deformation modes of
gallium arsenide in nanoindentation and
nanoscratching”, Appl. Phys. Lett., Vol 90, pp. 031902.
January, 2007.
L. Csepregi, R.P. Kullen, J.W. Mayer and T.W. Sigmon,
“Regrowth kinetics of amorphous Ge layers created by
74Ge and 28Si implantation of Ge crystals”, Solid State
Commun., vol 21, pp. 1019‐1021. March, 1977.
M. Liu, L.Y. Xu and X.Z. Lin, “Heating effect of electron
beam bombardment”, Scanning, vol 16, pp. 1‐5.
January‐February, 1994.
M. Sutton, Y.S. Yang and J. Mainville, “Observation of a
precursor during the crystallization of amorphous
NiZr2”, Phys. Rev. Lett., vol 62, pp. 288‐291. January,
1989.
P.D. Warren, P. Pirouz and S.G. Roberts, “Simultaneous
observation of α‐ and β‐dislocation movement and their
effect on the fracture behaviour of GaAs”, Phil. Mag. A,
vol 50, pp. L23‐L28. May, 1984.
R. Nowak, T. Sekino and K. Niihara, “Surface deformation of
sapphire crystal”, Phil. Mag. A, vol 74, pp. 171‐194. July,
1996.
R. Thomson, “Brittle fracture in a ductile material with
application to hydrogen embrittlement”, J. Mater. Sci.,
vol 13, pp. 128‐142. January, 1978.
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014
28
R.F. Cook and G.M. Pharr, “Direct observation and analysis
of indentation cracking in glasses and ceramics”, J. Am.
Ceram. Soc., vol 73, pp. 787‐817. April, 1990.
R.M. Thomson, C. Hsieh and V. Rana, “Lattice trapping of
fracture crack”, J. App. Phys., vol 42, pp. 3154‐3160. July,
1971.
S. Johansson and J.A. Schweitz, “Contact damage in
single‐crystalline silicon investigated by cross‐sectional
transmission electron microscopy”, J. Am. Ceram. Soc.,
vol 71, pp.617‐623. August, 1988.
S. Minomura and H.D. Drickamer, “Pressure induced phase
transitions in silicon, germanium and some III‐V
compounds”, J. Phys. Chem. Solids, vol 23, pp. 451‐456.
May, 1962.
S.B. Fisher, “On the temperature rise in electron irradiated
foils”, Radiat. Eff., vol 5, pp. 239‐243. January, 1970.
S.M. Wiederhorn, “Brittle fracture and toughening
mechanisms in ceramics”, Ann. Rev. Mater. Sci., vol 14,
pp. 373‐403. August, 1984.
S.M. Wiederhorn, B.J. Hockey and D.E. Roberts, “Effect of
temperature on the fracture of sapphire”, Phil. Mag., vol
28, pp. 783‐796. October, 1973.
S.O. Kucheyev, J.E. Bradby, C. Jagadish, M. Toth, M.R.
Phillips and M.V. Swain, “Nanoindentation of epitaxial
GaN films”, Appl. Phys. Lett., vol 77, pp. 3373‐3375.
November, 2000.
S.S. Chiang, D.B. Marshall and A.G. Evans, “The response of
solids to elastic/plastic indentation, II. Fracture initiation”,
J. Appl. Phys., vol 53, pp 312‐317. January, 1982.
T. Page, W.C. Oliver and C.J. McHargue, “Deformation
behavior of ceramic crystals subjected to very low load
(nano)indentations”, J. Mater. Res., vol 7, pp. 450‐473.
Feburary, 1992.
T. Suzuki, T. Yasutomi, T. Tokuoka and I. Yonenaga, “Plastic
deformation of GaAs at low temperatures”, Phil. mag. A,
vol 79, pp. 2637‐2654. November, 1999.
T.F. Page, L. Riester, S.V. Hainsworth, “The plasticity
response of SiC and related isostructural materials to
nanoindentation: slip vs. densification”, in Fundamentals
of Nanoindentation and Nanotribology, Mat. Res. Soc.
Symp. Proc., vol 522, pp. 113‐118. April (MRS Spring
Meeting), 1998.
X.S. Zhao, Y.R. Ge, J. Schroeder and P.D. Persans,
“Carrier‐induced strain in Si and GaAs Nanocrystals”,
Appl. Phys. Lett., vol 65, pp. 2033‐2035. October, 1994.
Y.B. Xu, “Indentation‐induced plasticity, damage and
fracture in Si and GaAs single crystals”, J. Inorganic
Mater., vol 24, pp. 1081‐1089. November, 2009. (in
Chinese)
Y.G. Gogotsi, V. Domnich, S.N. Dub, A. kailer and K.G.
Nickel, “Cyclic nanoindentation and Raman
microspectroscopy study of phase transformations in
semiconductors”, J. Mater. Res., vol 15, pp. 871‐879. April,
2000.
Y.Q. Wu and Y.B. Xu, “Direct evidence on microplastic
fracture in single‐crystal silicon at ambient temperature”,
Phil. Mag. Lett., vol 78, pp. 9‐13. July, 1998.
Y.Q. Wu and Y.B. Xu, “Lattice‐distortion‐induced
amorphization in indented [110] silicon”, J. Mater. Res.,
vol 14, pp. 682‐687. March, 1999.
Y.Q. Wu, X.Y. Yang and Y.B. Xu, “Cross‐sectional high
resolution electron microscopy observation on the
amorphized indentation region in [001] single crystal
silicon”, Acta Mater., vol 47, pp. 2431‐2436. June, 1999.
Y.Q. Wu, Y.B. Xu and X.Y. Yang, “An HREM study of a
lateral microcrack beneath indentation of [001] silicon”,
Acta Metall. Sinica (English Letters), vol 11, pp. 342‐346.
October, 1998.
Z.C. Li, H. Zhang and Y.B. Xu, “Direct observation of
electron‐beam‐induced nucleation and growth in
amorphous GaAs”, Mater. Sci. in Semicond. Proc., Vol 7
pp. 19–25, January, 2004.
Z.C. Li, L. Liu, L.L. He and Y.B. Xu, “Shear‐activated
indentation crack in GaAs single crystal”, J. Mater. Res.,
Vol 16, pp.2845‐2849, October, 2001.
Z.C. Li, L. Liu, X. Wu, L.L. He and Y.B. Xu, “Indentation
induced amorphization in gallium arsenide”, Mater. Sci.
Eng. A, Vol 337, pp. 21‐24, January, 2002
Z.C. Li, L. Liu, X. Wu, L.L. He and Y.B. Xu., “TEM
observation of the phase transition in inverted GaAs”,
Mater. Lett., vol 55, pp. 200‐204. July, 2002