Deformation Structure Induced by Indentation in GaAs and Si Single Crystals

Journal of Metallurgical Engineering (ME) Volume 3 Issue 1, January 2014 www.me‐journal.org

doi: 10.14355/me.2014.0301.03

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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

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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


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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


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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]


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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 ]


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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)


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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


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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


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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)


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


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


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).


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


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.

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Deformation Structure Induced by Indentation in GaAs and Si Single Crystals

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