Brittle-to-ductile transition temperature in indium phosphide

BRITTLE-TO-DUCTILE TRANSITION TEMPERATURE IN INDIUM PHOSPHIDE

by

LEONARDUS BIMO BAYU AJI

Submitted in partial fulfillment of the requirements

for the degree of Master of Science

Thesis Adviser: Prof. Pirouz Pirouz

Department of Materials Science and Engineering

CASE WESTERN RESERVE UNIVERSITY

January, 2006

1

TABLE OF CONTENTS

TABLE OF CONTENTS …………………………………………………… 1

LIST OF TABLES ……………………………………………………………... 3

LIST OF FIGURES ……………………………………………………………... 4

ACKNOWLEDGEMENT …………………………………………………… 10

ABSTRACT ………………………………………………………………….. 11

1. INTRODUCTION AND OBJECTIVE ………………………………… 12

1.1. Introduction ………………………………………………………… 12

1.1.1. Crystal Structure, Slip Plane and Slip System ……………… 13

1.1.2. Dislocations and Dislocation Cores in III-V Compound

Semiconductors ………………………………………………... 14

1.1.3. Stacking Faults ………………………………………………... 17

1.1.4. Dislocation Movement ………………………………………. 19

1.1.5. Surface Polarity and Symmetry in Compound Semiconductors 20

1.2. Objectives of Research ………………………………………………… 22

2. LITERATURE STUDY ……………………………………………………... 23

2.1. Griffith Theory ………………………………………………………….. 23

2.2. Dislocation - Crack Interactions ………………………………………. 27

2.3. Dislocation Velocity in Indium Phosphide …………………………….. 31

2.4. Previous Work on Plasticity of Indium Phosphide …………………… 34

2

3. EXPERIMENTAL SETUP AND SAMPLE PREPARATION …………... 40

3.1. 4-Point Bend Tests ……………………………………………………… 40

3.1.1. Sample Preparation …………………………………………….. 43

3.1.2. Technique of Introducing Precracks ……………………………… 45

3.1.3. Instron 1361 Tensile Machine …………………………………... 46

3.2. Indentation Tests …………………………………………………….... 48

3.2.1. Sample Preparation …………………………………………….. 49

3.2.2. Static Indentation Tests ………………………………………... 49

3.2.3. Dynamic Indentation Tests ………………………………………... 51

4. RESULTS AND DISCUSSION …………………………………………….. 55

4.1. 4-Point Bend Tests ……………………………………………………… 55

4.1.1. Brittle Behavior …………………………………………………. 57

4.1.2. Transition Behavior …………………………………………….. 58

4.1.3. Ductile Behavior …………………………………………………. 58

4.2. Indentation Tests ……………………………………………………… 59

4.2.1. Static Indentation Tests ……………………………………….. 59

4.2.2. Dynamic Indentation Tests ……………………………………….. 66

5. CONCLUSION …………………………………………………………… 72

APPENDIX …………………………………………………………………….. 73

REFERENCES ...………………………………………………………… 76

3

LIST OF TABLES

Table 3.1: Properties of the InP crystal used, grown by and obtained from the

Institute of Electronic Materials Technology (ITME), Warszawa, Poland

….…………………………………………………………………….. 40

Table 4.1: g b 0 analysis for Burgers vector of partial dislocations in a face-

centered cubic crystal …………………………………………….. 64

4

LIST OF FIGURES

Figure 1.1: (a) Sphalerite structure; gray and black circles are indium and phosphorus

atoms respectively (or vice versa), (b) stacking sequence of 111 planes

in the sphalerite structure. A , B , or C planes consist of indium atoms

while a , b or c planes consist of phosphorus atoms (or vice versa)

…………………………………………………………………..….... 13

Figure 1.2: Schematic showing different core structures of dislocations in compound

semiconductors……………………………………………………..... 14

Figure 1.3: Schematic of a screw dislocation viewed from top …………………. 15

Figure 1.4: Slip in face-centered cubic crystals ………………………………….. 16

Figure 1.5: Stacking sequence of 111 planes after slip of (a) a leading partial

dislocation on a plane (between C and A in this example), (b) two

partial dislocations on adjacent planes (the first between C and A , the

second between B and C ), (c) four partial dislocations on adjacent

planes (the first between C and A , the second between B and C , the

third between A and B , and the fourth between C and A )

…………………………………………………………………….… 17

Figure 1.6: Movement of dislocations by generation and motion of kinks …….. 19

Figure 1.7: (a) Polarity in the sphalerite structure, (b) the 110 directions correspond

to the interaction of 11 1 and 11 1 planes (shaded planes), which have

111 A polarity (i.e. contain all A atoms), whereas 110 directions

5

correspond to the intersection of 111 and 111 planes, which have

11 1 B polarity (i.e. contain all B atoms) …................................... 20

Figure 2.1: Plate containing an elliptical hole with semi-axes a and b subjected to a

uniform applied tension L ……………………………………..…. 24

Figure 2.2: A sharp crack with an intersecting slip plane showing the competition

between dislocation emission and cleavage propagation …………….. 28

Figure 2.3: An atomically sharp crack is blunted when a dislocation is emitted from

the tip when the Burgers vector has a component normal to the fracture

plane………………………………………………………………….... 28

Figure 2.4: Schematic illustration of dislocation nucleation at a crack tip (a) at

BDTT T , and (b) at …………………………………………… 30

Figure 2.5: (a) Velocity, v , of dislocations in undoped and S-doped n-type InP single

crystals as a function of (a) resolved shear stress, , and (b) temperature,

……………………………………………………….. 31

Figure 2.6: Velocity versus resolved shear-stress at 723 K in various indium

phosphide crystals for (a) dislocations (b) dislocations, and (c) screw

dislocations …………………………………………………….. 33

Figure 2.7: (a) Resolved shear stress versus shear strain curves for undoped InP

between 573 K and 1023 K. (b) Magnification of (a) ………………... 34

Figure 2.8: Variation of resolved shear stress at lower yield point, LYP , versus

temperature ………………………………………………………….... 36

6

Figure 2.9: Critical resolved shear stress c against temperature, . The stress denotes

the shear stress component resolved in the 101 direction on the 111

plane. Shear strain rate is 41.2 10 s-1 ……………..…….. 37

Figure 2.10: Slip lines on the side surface of InP deformed at 300 K . The slip indicates

1101 111

2 slip with frequent cross-slip …………………………. 38

Figure 2.11: TEM images of slip bands in InP deformed at 300 K . The foil was cut

parallel to the 111 slip bands. The first image is bright field exhibiting

many straight screw dislocations (shown in Fig. 2.10) are all out of

contrast in the g 202 reflection. The second image is weak beam dark

field revealing dissociation of screw dislocations…………………..… 39

Figure 3.1: Comparison of tensile stress distribution in 3-point and 4-point bend

samples. The shaded area represents tensile stress, a region ranging from

zero at the supports of the bend samples to (a) a maximum at the midspan

for the 3-point bend geometry, and (b) uniform maximum along the whole

gauge length of the samples for the 4-point bend geometry ………….. 41

Figure 3.2: Schematic of a 4-point bend test geometry. 1y and 2y are the vertical

distances between the outer rollers and inner rollers ……………….. 42

Figure 3.3: The crystallographic orientation and dimensions of a 4-point bend sample

(actual sample dimensions after polishing). …………………………... 44

Figure 3.4: A 4-point bend test sample containing five identical radial precracks,

introduced by Knoop indents spaced about 20 μm apart ……………. 45

7

Figure 3.5: (a) Photograph of the Instron 1361 tensile machine with the tensile jig and

the furnace mounted on it, and (b) schematic of the 4-point bend jig

connected to the displacement rods of the machine ………………….. 46

Figure 3.6: Schematic of indentation mechanism. P is the applied load, d is the

indentation diagonal and h is the indentation depth ……………........ 48

Figure 3.7: Schematic of indented surface in indium phosphide with a 110

orientation of indenter diagonals ……………………………………... 50

Figure 3.8: Photograph of the Nikon High Temperature Microhardness Tester model

QM ……………………………………………………………………. 50

Figure 3.9: (a) Photograph of the HTDSI apparatus, and (b) schematic diagram of the

HTDSI apparatus: (A) sample, (B) indenter, (C) sample furnace, (D)

indenter furnace, (E) capacitance displacement gauge, and (F) load

application coil ……………………………………………………….. 52

Figure 3.10: Typical load-depth plot for a material that is subject to elastic and plastic

deformation …………………………………………………………… 53

Figure 4.1: Load displacement curves for InP samples tested at , 355 C and

378 C at a strain rate of 5 12.93 10 s . At 350 C InP deforms

elastically until fracture; at 355 C InP is in the transition region, above

355 C , e.g., at 378 C , InP deforms plastically ………….………....... 56

Figure 4.2: Applied stress versus temperature for samples tested at a strain rate of

5 12.93 10 s . The brittle-to-ductile transition temperature occurs over

a very narrow temperature range of 5 , and is characterized by a sudden

increase of the applied stress ………………………………….......... 57

8

Figure 4.3: Hardness versus temperature plot for sample tested from 380 C down to

20 C , with a step size of 20 C and a 50 g indentation load ...……. 60

Figure 4.4: Indentation impressions produced by static indentation technique at (a)

123 C , (b) 263 C and (c) 320 C …….......................................... 61

Figure 4.5: Temperature dependence of the impression diameter and crack length

along 110 and 110 directions over a temperature range of 20 C to

380 C using an indentation load of 50 g . The sample was initially heated

to the highest temperature and indented. Following this, the sample was

cooled and indentations were made in a step size of 20 C until the lowest

temperature of 20 C ………………………………………………….. 62

Figure 4.6: Bright field TEM images of stacking faults in InP deformed by static

indentation technique at 320 C . Fig. 4.7(a) shows two sets of stacking

fault ribbons perpendicular to each other. One set of the stacking fault

ribbon is out of contrast in 220 and 311 reflections, as shown in figures

(b) and (c) respectively ……………………………………………... 65

Figure 4.7: Load-displacement curves obtained from dynamic indentation tests on

001 surface of InP at different temperatures: (a) 25 C , (b) 150 C , (c)

250 C , and (d) 400 C …………………………………………...... 67

Figure 4.8: Dissipated energy versus temperature plot obtained by integrating the area

under the load-displacement curves ………………………………. 68

Figure 4.9: Energy density versus temperature plot obtained by dividing the dissipated

energy with the indentation volume ……………………………..... 69

Figure 4.10: Schematic variations of stress versus temperature in a crystal .... 70

9

Figure A.1: Applied stress versus temperature for samples tested at a strain rate of

6 19.6 10 s . The brittle-to-ductile transition temperature occurs

between 374 C and 376 C ………………………………………… 73

Figure A.2: Applied stress versus temperature for samples tested at a strain rate of

5 12.88 10 s . The brittle-to-ductile transition temperature occurs over

a narrow temperature range of 10 , and is characterized by a sudden

increase of the applied stress ……………………………………...... 75

ACKNOWLEDGEMENT

10

I thank my adviser, Professor Pirouz Pirouz for his support and guidance in this work.

His vast knowledge and tremendous zeal has been a great source of inspiration for me

during this period.

I also wish to express my gratitude to Professor Peter Legerlöf and Professor John

Lewandowski for serving on my thesis committee and helping me with valuable

suggestion.

I wish to thank Paul Wesseling for training me on Nikon microhardness machine, and to

Chris Tuma for training me on INSTRON tensile machine. I wish to thank Shanling

Wang, Ming Zhang, Changrong Li and Kevin Spear for bearing my numerous questions

and their invaluable suggestions related to this work. Many thanks to Arun Reddy, Min

Huh, Meisssa, Sebastian, Yeonseop Yu and Ali Shamimi for their friendship.

I thank my parents and brother for their constant prayer and love. I dedicated this work

for them.

11

Brittle-to-Ductile Transition Temperature in Indium Phosphide

Abstract

by

LEONARDUS BIMO BAYU AJI

001 single crystals of indium phosphide were deformed by 4-point bend tests and two

types of indentation tests; static and dynamic. Temperature ranges where the material

exhibited a brittle or a ductile behavior were investigated with particular focus on the

transition from one deformation mode to another. The 4-point bend tests and the

dynamical indentation tests show that indium phosphide exhibits a sharp brittle-to-ductile

transition temperature. Static indentation tests were used to determine the dependence of

hardness on temperature, and the plastic zone produced around the indentation

impressions was characterized by transmission electron microscopy (TEM).

CHAPTER 1

12

INTRODUCTION AND OBJECTIVES

In this chapter a brief summary of the applications and properties of indium phosphide is

given, and the importance of knowing the mechanical properties of this material is

explained. Subsequently, the objectives of this thesis and the scope of the research are

discussed.

1.1 Introduction

Indium phosphide (InP) is a promising semiconducting material for a variety of practical

applications, especially for optoelectronic devices, due to its direct energy band gap. It is

used as a platform for a wide variety of fiber communication components, including

lasers, LEDs, semiconductor optical amplifiers, modulators and photo-detectors [1].

Hence, understanding the physical properties of InP, including its mechanical properties

is essential for its wider use.

A number of investigators have performed deformation tests to study plasticity and

fracture behavior of InP. It is observed that, as in other semiconductors, InP exhibits

either a brittle or a ductile behavior depending on the applied stress, temperature, strain

rate, etc. However, very few fracture studies of InP are reported in the literature

compared to plastic deformation studies. In particular, to the best of the author’s

knowledge, there has been no report on the study of the transition from brittleness to

ductility in this material.

13

1.1.1 Crystal Structure, Slip plane and Slip System

Indium Phosphide, like other tetrahedrally coordinated semiconductors, is generally

considered to be a semi-brittle material. It crystallizes in the cubic zincblende (sphalerite)

structure, which consists of two interpenetrating f.c.c. lattices, one of which is shifted by

1114

a relative to the other. The two f.c.c. lattices are occupied by two different atoms,

i.e., indium and phosphorus [1], disposed at the corners of a regular tetrahedron. The

cubic unit cell of the sphalerite structure is shown in Fig. 1.1.

(a) (b)

Figure. 1.1. (a) Sphalerite structure; grey and black circles are indium and

phosphorus atoms respectively (or vice versa), (b) stacking sequence of 111

planes in the sphalerite structure. A , B , and C planes consist of indium atoms while a , b and c planes consist of phosphorus atoms (or vice versa).

As for f.c.c. crystals, the glide system in InP is 110 1112

a, i.e., the dislocations glide

on 111 slip planes and have Burgers vectors 1

b 1102

.

1.1.2 Dislocations and Dislocation Cores in III-V Compound Semiconductors

14

There are basically three different types of dislocations, termed , , and screw

dislocations in III-V compound semiconductor crystals with a sphalerite structure. The

and dislocations can be distinguished from one another based on: (1) the species of the

atoms ending at the extra half plane, and (2) the planes between which the extra half

plane terminates (i.e., in the shuffle set or glide set). For a long time, it was believed that

slip takes place between widely-spaced planes, i.e. the shuffle set. For instance, if we

assign A , B and C planes with In atoms and a , b , and c planes with P atoms (see Fig.

1.1(b)), dislocations with their extra half plane ending with In or P atoms are called

dislocation (also denoted as A (s), B (s) or C (s)) or dislocation (also denoted as a (s), b

(s) or c (s)). However, at present most investigators [2] believe that slip actually occurs in

the narrowly-spaced planes or the glide set. In that case, dislocations previously called α

dislocation are actually a (g), b (g) or c (g) and dislocation are actually A (g), B (g),

or C (g) (see Fig. 1.2).

Figure. 1.2. Schematic showing different core structures of dislocations in compound semiconductors (After George and Rabier [3]).

15

Screw dislocations are created when the atom planes perpendicular to the dislocation are

distorted in such a way as to form a spiral ramp of atomic planes with the dislocation as

the axis of the spiral as shown in Fig. 1.3.

Figure. 1.3. Schematic of a screw dislocation viewed from top; open and closed circles are respectively atoms above and below the slip plane.

The question as to whether the slip plane in sphalerite structures is on the shuffle set or

the glide set has been rather controversial. The dangling bonds are thought to have a high

energy and are produced by movement of shuffle or glide dislocation. These dangling

bonds can lower their energy by attracting impurity atoms (e.g. hydrogen) or by

reconstruction with neighboring dangling bonds, thereby eliminating them. Considering

the position of the dangling bonds in partial dislocations in the shuffle set and glide set,

the reconstruction would be much easier for the glide set than the shuffle set, because in

the shuffle set, the dangling bonds are normal to the slip plane and the reconstruction of

the dangling bonds of neighboring atoms along dislocation line entails large bond-

bending and bond-stretching. On the other hand, in the case of glide set, the dangling

bonds make a shallow angle with respect to the slip plane and the bond-bending and

bond-stretching involved in the reconstruction is relatively small.

16

However, Shockley [5] argues that a shuffle dislocation would be preferred because its

formation would involve only one dangling bond per atom compared to three dangling

bonds per atom - a higher energy process which implies greater resistance to motion - for

a glide dislocation.

Perfect dislocations, i.e. 1

b 1102

, in the sphalerite structure can dissociate into two

Shockley partials on the close-packed 111 planes on which they glide [6,7], in this case

slip is in a 112 direction, i.e. b 1126

a . The close-packed 111 planes can be

represented by a set of hard spheres as schematically illustrated in Fig. 1.4.

Figure. 1.4. Slip in face-centered cubic crystals (After Cottrell [6]).

The atoms in the first layer are represented by full circles, A , and atoms in the second

layer rest in the sites marked B . For the two layers to shear over each other to produce a

displacement in the 110 slip direction, it is energetically more favorable for the B

atoms to move via C positions rather than over the top of A atoms. The unit dislocation

17

with Burgers vector tot

1b 110

2 therefore dissociates into two dislocations b and

according to:

totb b bt

1 1 1

101 112 2112 6 6

The subscripts and t stand for leading and trailing. The separation of the leading and

trailing partials by a distance w creates a ribbon of stacking fault of width between them

(extended dislocation).

1.1.3 Stacking Faults

Stacking faults can be described by either removal or insertion of a close-packed layer. It

can also be formed by shearing, i.e. by the propagation of partial dislocations. If ABC

represents the stacking sequence of close-packed layers of an f.c.c. structure, then any

one of the following events can take place:

1) Shear of one leading partial dislocation on one 111 plane resulting in an intrinsic

stacking fault, as represented by Fig. 1.5(a).

18

Figure. 1.5(a). Stacking sequence of 111 planes after slip of a leading partial

dislocation on a 111 plane (between C and A in this example).

2) Two shears on successive planes forming an extrinsic stacking fault, as represented

by Fig. 1.5(b).

Figure. 1.5(b). Stacking sequence of planes after slip of two partial dislocations

on adjacent 111 planes (the first between C and A , the second between B

and C ).

3) Shear with the same displacement vector on every layer forming a microtwin, as

represented by Fig. 1.5(c).

19

Figure. 1.5(c). Stacking sequence of 111 planes after slip of four partial

dislocations on adjacent 111 planes (the first between C and A , the second

between B and C , the third between A and B , and the fourth between C and A ).

1.1.4 Dislocations Movement

There are various types of obstacles to the motion of dislocations on their slip planes. The

most intrinsic is the lattice resistance and the stress required to move a dislocation

through a crystal lattice from one Peierls valley (low-energy position for the dislocation)

to the next at 0 K . This stress is defined as the Peierls stress, p . In general, the

magnitude of Peierls stress is small for materials with an f.c.c. structure compared to

directionally bonded materials such as semiconductors.

It is commonly accepted that the mobility of dislocations in semiconductor materials,

except at high temperatures, is controlled by the Peierls mechanism. There are two

processes in the Peierls mechanism: (1) formation of a kink pair, and (2) subsequent

migration of the kinks along the dislocation line. These kinks may annihilate each other

when opposite kinks meet or they may arrive at the end of the dislocation line to

constitute a unit cycle of dislocation motion [8].

20

Figure. 1.6. Movement of dislocations by generation and motion of kinks.

1.1.5 Surface Polarity and Symmetry in Polar Compound Semiconductors

Surface polarity of sphalerite and wurtzite structures materials has been reviewed by Holt

[9]. He pointed out that the 110 and 110 directions in 100 faces of III-V

compound semiconductors are not crystallographically equivalent. The asymmetry of the

two orthogonal 110 directions in 100 faces of sphalerite structures is manifested in

phenomena arising from the surface polarity differences, i.e. 111 A 1 1 1 B .

The crystallographic anisotropy in sphalerite structures is shown in Fig. 1.7. Note in Fig.

1.7(a), the top 111 surface consists of only one type of atoms (i.e. A atoms), whereas

the bottom 11 1 surface consists of only the other type of atom (i.e. B atoms).

21

(a) (b)

Figure. 1.7. (a) Polarity in the sphalerite structures, (b) the 110 directions

correspond to the intersection of 11 1 and 1 1 1 planes (shaded planes),

which have 111 A polarity (i.e. contain all A atoms), whereas the 110

directions correspond to the intersection of 111 and 1 11 planes, which

have 1 1 1 B polarity (i.e. contain all B atoms).

The A atoms are located on the lattice sites, e.g. at the origin, whereas the B atoms are at

the other sites of the bases, e.g. at 1

4,1

4,1

4 in the cubic unit cell of the sphalerite

structure. Fig. 1.7(b) schematically shows that the 11 1 and 11 1 planes (shaded

planes) contain all A atoms, whereas 111 and 111 contain all B atoms. This

anisotropy can affect the behavior of plastic deformation along 110 and 110

directions.

1.2 Objectives of Research

22

The purpose of this work is to gain a better understanding of the mechanical properties of

InP and, specifically, of temperature ranges where the material exhibits brittleness or

ductility, and the transition from one mode of deformation to another.

Focus is drawn on dislocation processes that control the brittle-to-ductile transition

(BDT) temperature in InP using different techniques. Specifically this thesis addresses

the following:

Measurement of the fracture stress and the brittle-to-ductile transition

temperature from applied stress versus displacement curves obtained by 4-

point bend tests over a temperature range of to at fixed

strain rates.

Measurement of hardness using static indentation tests over a temperature

range of to , and characterizing the plastic zone beneath the

indentation impressions produced in the tests.

Measurement of dissipated energy from load versus depth curves obtained

by dynamic indentation tests.

Finally, transmission electron microscopy (TEM) is used to study the characteristic

morphology of deformation-induced dislocations in InP.

CHAPTER 2

23

LITERATURE STUDY

2.1 Griffith Theory

An important precursor to the Griffith study [11] was the stress analysis by Inglis [12] of

an elliptical hole in a uniformly stressed plate. Inglis proposed that local stresses at a

sharp notch or a corner could rise to a level several times larger than the applied stress.

Thus it is apparent that even a small submicroscopic flaw might be a potential source of

weakness in solids resulting in its fracture and failure.

In summary, the Inglis [12] analysis assumed that Hooke’s law holds everywhere in a

plate which is under a tensile stress L , as shown in Fig. 2.1. The boundary of the hole is

stress free (a requirement for equilibrium), and the axes a and b ( a and b are crack

dimensions) are assumed to be small compared to the plate dimension. Beginning with

the equation of an ellipse,

2 2 2 2/ / 1x a y b (2.1)

The radius of curvature at point C is given by:

2 /b a (2.2)

The greatest concentration of the normal stress, , occurs at point C, and is given by:

,0 1 2 /yy La a b (2.3)

By substituting 1/2b a from Eq. 2.2 into Eq. 2.3:

24

1/2,0 1 2 /yy La a (2.4)

In the case for b a , i.e. a , 1/2/ 1a the equation reduces to

1/2,0 / 2 /yy La a (2.5)

Figure. 2.1. Plate containing an elliptical hole with semi-axes a and b

subjected to a uniform applied tension L (After Lawn and Wilshaw [11]).

The ratio in Eq. 2.5 is often referred to as the elastic stress concentration factor. It can

easily be seen that this factor can have values much larger than unity for a narrow hole.

Thus the stress concentration depends sensitively on the crack’s shape rather than its size.

Griffith’s idea was to set up a model for a crack system in terms of reversible

thermodynamic processes. Griffith recognized that a material containing a uniformly

loaded crack in equilibrium must have a maximum free energy, U . For a static crack

system Griffith proposed that the total energy is the sum of two terms:

x

y

2a

2b C

25

L E SU W U U (2.6)

The first bracketed term is the mechanical energy of the system, where LW is the work

done by the applied load and EU is the stored elastic strain energy; this term decreases as

the crack extends. On the other hand, the second term, the surface energy SU , increases

as the crack extends, since energy is required to create new fracture surfaces. Whether a

crack extends or closes up depends on whether the left-hand side of Eq. 2.6 is negative or

positive.

For a static crack, the energy would be maximum when:

/ 0dU da (2.7)

In order for the crack to extend, the free energy must decrease and therefore:

/ 0dU da (2.8)

where a is the crack length. This is known as the Griffith criteria for crack growth.

In order to calculate the energy terms in Eq. 2.6, Griffith made use of the Inglis analysis,

considering the case of a narrow elliptical `crack`. Griffith used a standard result from

linear elastic theory for a crack formed under a constant applied load given by:

2L EW U (2.9)

where, EU is calculated using the earlier work of Inglis. The related equation can be

written as:

26

2 2 /E LU a E (2.10)

where L is applied stress normal to the crack plane (see Fig. 2.1), E is Young’s

modulus, and is half of the crack length. Assuming the crack is a slit of length 2a , SU

is

simply given by:

4SU a (2.11)

where is the free surface energy per unit area. The total energy of the system thus

becomes:

2 2 / 4LU a E a (2.12)

By applying the Griffith equilibrium condition (Eq. 2.7) into Eq. 2.12, one obtains the

critical condition for fracture given by:

1/22 /F L E a (2.13)

The above equation shows that the fracture stress, F , depends both on material

properties ,E as well as the length of the crack. As it is evident from Eq. 2.13, longer

cracks will result in lower fracture stresses.

Griffith formulated his basic criterion for fracture purely in terms of thermodynamics. He

did not explicitly take into account the physical mechanism of crack extension, which is

breaking of atomic bonds. In addition, for Eq. 2.8 to be met, the theoretical strength of

the solid must be exceeded at the crack tip (thus allowing rupture of atomic bonds) as (or

before) the fracture stress given by Eq. 2.13 is reached.

27

The maximum stress, max , at the crack tip can be calculated using Eq. 2.5 as proposed

by Inglis [12]. If the crack tip is ideally sharp, the crack tip is very small 0 and

from Eq. 2.5 the stress at the crack tip, max , becomes very large. By substituting Eq.

2.13 into Eq. 2.5, the maximum stress, max , at the crack tip is given by:

1/2 1/2 1/2

max 2 2 / / 2 /c cE a a E (2.14)

From Eq. 2.14 for a sharp crack, it is found that the stress at fracture exceeds the

theoretical tensile strength and hence satisfies the Griffith criterion (as given by Eq.

2.13), i.e. max is a necessary and sufficient condition for fracture.

2.2 Dislocation – Crack Interactions

There are two general conceptual models for assessing the brittle-to-ductile transition

temperature in a crystal. The first model is based on the criterion of dislocation-emission

at the crack tip. This model proposes that if a dislocation is nucleated at the crack tip at a

lower loading level than required for brittle cleavage, the material is considered ductile.

The principle behind this model is that emitted dislocations blunt the crack, shield the

crack tip from the applied external stress and inhibit cleavage and crack propagation. The

emitted dislocations can lower the stress field around the crack and therefore increase the

critical stress for cleavage. Rice and Thomson [13] introduced the idea that competition

between dislocation emission and crack propagation determines the failure mode, as

illustrated in Fig. 2.2; if a dislocation can be emitted from the crack tip prior to the

cleavage propagation, it is considered that the material is ductile.

28

Figure. 2.2. A sharp crack with an intersecting slip plane showing the competition between dislocation emission and cleavage propagation.

Figure. 2.3. An atomically sharp crack is blunted when a dislocation is emitted from the tip when the Burgers vector has a component normal to the fracture plane (After Rice and Thomson [13]).

In order for a dislocation to blunt a crack, it must have a component of its burgers vector

normal to the crack plane, and the slip plane must intersect the crack tip along its whole

length, i.e. the crack tip must lie in a slip plane. If the crack tip intersects a dislocation, a

localized step or jog in the crack tip is formed and this jog may act as a nucleation site for

other dislocations, favoring ductile behavior [14-15]. Even if the crack tip does not fully

crack

slip plane

crack/cleavage propagation

blunt/shield dislocations

29

lie in a slip plane, it may still be blunted along its whole length either by local nucleation

events or by a screw dislocation moving around the crack profile by repeated cross-

slipping. Schematic of an atomically sharp crack blunted by one atomic plane is shown in

Fig. 2.3.

The second model is exemplified by Hirsch et al [16]. It is based on the concept of

dislocation mobility; dislocations are emitted by sources activated by high stresses near

the crack tip and the rate at which they move away from the crack tip determines the

material toughness. The emitted dislocations can also shield the crack tip and the source,

and prevent both cleavage and further emission [17]. If the emitted dislocations are

mobile, they will move away from the crack tip, and as they move away, more

dislocations can be emitted from the crack tip. The mobility of the dislocation itself is

affected by temperature; at low temperatures, dislocations tend to be less mobile, and few

or no dislocations are emitted. Therefore crack propagation is the most likely mechanism

to relieve the stress concentration at the crack tip at low temperatures. On the other hand,

at high temperatures, dislocations are generated to blunt the crack tip; these in turn move

rapidly away, and the material is ductile.

An alternative model to describe brittle-to-ductile transition temperature is proposed by

Pirouz et al [18]. This model, as illustrated in Fig. 2.4, is based on the competition

between the nucleation and propagation of leading partial dislocations versus the

nucleation and propagation of perfect (total) dislocations (i.e. trailing partial). According

to the model, if the temperature and stress are not sufficient to nucleate the trailing partial

30

(and thus the perfect) dislocations, then the increasing stress will eventually reach a

sufficient value to rupture the bonds at the crack tip, leading to its propagation [18].

Figure. 2.4. Schematic illustration of dislocation nucleation at a crack tip (a) at

BDTT T , and (b) at BDTT T (After Pirouz et al [18]).

At low temperatures, nucleation of single leading partial dislocations is not sufficient to

make the crystal ductile because, once formed, the stacking faults dragging behind the

partials prevent further nucleation events from the same sources (see Fig. 2.4(a)), i.e.,

partial dislocation multiplication from any source stops after the first leading partial is

emitted. Consequently these leading partial dislocations contribute to a very limited

extent to the straining of the crystal, and the crystal is brittle. On the other hand, at high

temperatures, full dislocations (i.e. leading and trailing partial dislocations) can be

nucleated repeatedly from the source in the crystal (see Fig. 2.4(b)) and their glide

produces large strains and causes macroscopic yielding of the crystal, and the crystal is

ductile.

crack tip

slip plane

crack tip

slip plane

(a) (b)

31

2.3 Dislocation Velocity in Indium Phosphide

Several workers have measured the dislocation velocity in InP. Nagai [19] measured

dislocation velocity in InP using the double etching technique. The author introduced

dislocations by scratching the crystal in a 110 direction and then stressing the crystal

by 3-point bend test over a range of applied resolved shear stresses, 21 kg/mm to

25 kg/mm , and over a temperature range of 523 K to 673 K . The movement of

individual dislocation was detected by the double etching technique (measuring the

distance between dislocations before and after stressing the crystal). It was found that

there is a large difference between the velocity of and dislocations. The velocity of

dislocation versus resolved stress and temperature is shown in Fig. 2.5.

. (a) (b)

Figure. 2.5. (a) Velocity, , of dislocation in undoped and S-doped n-type InP single crystals as a function of (a) resolved shear stress, , and (b) temperature, T (After Nagai [19]).

32

Yonenaga and Sumino [20] also measured the dislocation velocity in InP. In their work,

the dislocations were introduced by scratching the crystal along the 11 1 direction and

dislocation motion took place by uniaxially compressing the crystal with a constant strain

rate at various temperatures. Their results are shown in Fig. 2.6.

The temperature and stress dependence of dislocation velocity in semiconductors can be

expressed by the following equation:

/VU kTmv A e (2.15)

where is the resolved shear stress, m is the stress exponent, which depends on the

dislocation type, VU

is the activation energy for dislocation motion ( 1 2 eV for

undoped materials), and A is a pre-exponential factor which depends weakly on

temperature.

Summary from the results obtained by Nagai [19] and by Yonenaga and Sumino [20],

they concluded that, as in other semiconductors, the velocity of dislocations in InP

decreases as temperature and resolved shear stress decrease, which means that dislocation

motions becomes more difficult and sometimes immobile at low temperatures.

33

34

Fig

ure

. 2.6

. Vel

ocit

y ve

rsus

res

olve

d sh

ear

stre

ss a

t 723

K in

var

ious

indi

um p

hosp

hide

cry

stal

s fo

r (a

) α

dis

loca

tion

s (b

) β

dis

loca

tion

s, a

nd (

c) s

crew

dis

loca

tion

s. (

Aft

er Y

onen

aga

and

Sum

ino

[20]

).

(a)

(b)

(c)

2.4 Previous Works on Plasticity of Indium Phosphide

Gall et al [21] studied the plasticity of single crystal InP between 573 K and 1023 K

using uniaxial compression tests at a strain rate of 4 110 s . They compressed the

samples along the 123 axis in an Instron machine; such an orientation is most suitable

for activating a single slip system in the crystal. Their results are shown in Fig. 2.7. In

Fig. 2.7(a), the resolved shear stress, , is plotted against the plastic shear strain, p , at

various temperatures, where is the resolved shear stress in the primary 111 101

glide system. The characteristic yield drop of InP at different temperatures is observed

together with the variation of the upper yield, uys , and lower yield, lys , points. As

expected, uys lys , and uys lys decrease with temperature.

(a) (b)

35

Figure. 2.7. (a) Resolved shear stress versus shear strain curves for undoped InP between 573 K and 1023 K . (b) Magnification of (a) (After Gall et al [21]).

The magnitude of the upper yield point and the lower yield point is a sensitive function of

the strain rate, dislocation density, and temperature. The relationship between the

dislocation velocity and the magnitude of the upper yield point is given by:

mv k (2.16)

where, k is a constant of proportionality and is the stress exponent.

At low temperatures, large stresses are needed to increase the dislocation velocity.

However once the applied stress is large enough to increase the dislocation velocity (see

Eq. 2.16), the dislocation density rapidly increases due to dislocation multiplication. At

later stage, the average of dislocation velocity decreases due to dislocation-dislocation

interactions. In general, Orowan’s relation holds:

p bv (2.17)

where, p is the shear strain rate, is the dislocation density, is the Burgers vector, and is

the average dislocation velocity. Hence, there is a decrease of the applied stress down to

the lower yield stress, lys , with increasing temperature, as shown in Fig. 2.8. This is

certainly due to an increase in the dislocation mobility at higher temperatures. Therefore,

at higher temperatures smaller applied stresses are needed to create new dislocations in

order to accommodate deformation.

36

Figure. 2.8. Variation of resolved shear stress at lower yield point, , versus

temperatures (After Gall et al [21]).

From the above discussion, Gall et al concluded that:

The upper and lower yield point is a function of temperature.

In the range between 573 K to 1023 K , the p curves show three stages;

1. Dislocation multiplication.

2. Work hardening due to the interaction of dislocations.

3. Dislocation annihilation, i.e. cross-linking

However, as the temperature increases, the transition between the different stages is

indistinguishable and the curves gradually become parabolic.

InP is brittle at about 523 K .

The most important observation from their result is that at a strain rate of 4 110 s ,

InP is ductile at 573 K but is brittle at 523 K . Thus the brittle-to-ductile transition

temperature at 4 110 s lies somewhere between 523 K and 573 K .

37

Suzuki et al [22] also studied plastic deformation of single crystal InP. They investigated

plastic deformation of InP from 500 K down to 77 K under a confining pressure. Their

results are shown in Fig. 2.9. The c T relation in this figure shows that c increases to

very large values at very low temperatures.

Figure. 2.9. Critical resolved shear stress c against temperature, . The stress

denotes the shear stress component resolved in the 101 direction on the

111 plane. Shear strain rate is 4 11.2 10 s . Data of Gall et al (1987) at 4 12 10 s are shown as well (After Suzuki et al [22]).

The side surfaces of the samples deformed in the temperature range between 200 K and

400 K were subjected to observation of slip lines, as shown in Fig. 2.10. On the 143

surface, the slip lines are straight and parallel, while on the 931 surface they are not.

From the sample geometry it is obvious that slip occurs approximately on the 111

plane, but slip is not planar which indicates occurrence of cross-slipping.

38

Figure. 2.10. Slip lines on the side surfaces of InP deformed at 300 K . The

slip lines indicate 110 1 111

2 slip with frequent cross-slip (After Suzuki et al

[22]).

Transmission electron microscopy images of the sample deformed at 300 K are shown in

Fig. 2.11. The slip lines indicate 1101 111

2 slip with frequent cross-slip. The bright

field image in Fig. 2.11 shows many dislocations lying parallel to the 10 1 direction

(shown in Fig. 2.10) are out of contrast in the g 202 reflection, which means these

dislocations are predominantly screw dislocations with a Burgers vectors 1

1012 . The

weak-beam dark field image shows the dissociation of the screw dislocations. The slip

lines and transmission electron microscopy observations confirm that deformation of InP

occurs by the operation of the 1101 111

2 slip system throughout the whole

temperature range.

39

Figure. 2.11. TEM images of slip bands in InP deformed at 300 K . The foil

was cut parallel to the 111 slip bands. The first image is bright field

exhibiting many straight screw dislocations parallel to the 10 1 direction

(shown in Fig. 2.10) are all out of contrast in the g 202 reflection. The second image is weak beam dark field revealing dissociation of screw dislocations (After Suzuki et al [22]).

From these TEM observations, Suzuki et al [22] suggested that deformation of InP at low

temperatures occurs by the motion of non-dissociated shuffle screw dislocation, while at

high temperature it occurs by the motion of dissociated glide screw dislocations.

CHAPTER 3

EXPERIMENTAL SETUP AND SAMPLE PREPARATION

40

This chapter discusses the experimental setup and sample preparation techniques used in

the present work. The 001 InP crystals used in the experiments were grown by and

obtained from The Institute of Electronic Materials Technology (ITME), Warszawa,

Poland. Some data on the as-received wafer, as provided by the supplier, are shown in

Table 3.1. In this work all the tests were performed on the 001 face of InP.

UndopedType of Conductivity N

Orientation 001

Resistivity 11.89 10 cm Mobility 23300 cm / VsCarrier concentration 15 35.2 10 cm

Table. 3.1. Properties of the InP crystal grown by and obtained from the Institute of Electronic Materials Technology (ITME), Warszawa, Poland.

3.1 4-Point Bend Tests

The purpose of the present work, as described in the previous chapter, is to gain a better

understanding of dislocation processes controlling the brittle-to-ductile transition

temperature in InP by measuring its transition temperature, BDTT , as a function of the

loading rate (or, equivalently, the strain rate ). The approach is to perform a series of

identical fracture tests at different temperatures to determine the stress required for

irreversible deformation at a certain strain rate.

41

There are various techniques for measuring the brittle-to-ductile transition temperature,

BDTT , such as bend test and tension test. The bend test was selected in this work, because

the sample preparation is relatively easier and more economical compared to other

techniques. The 4-point bend test was preferred over the 3-point bend test because in the

former, the probability of a largest flaw being exposed to the peak stress is greater than

the latter; this can been seen from the stress distribution of 3-point and 4-point bend

sample shown in Fig. 3.1.

(a) (b)

Figure. 3.1. Comparison of tensile stress distribution in 3-point and 4-point bend samples. The shaded area represents tensile stress, a region ranging from zero at the supports of the bend sample to (a) a maximum at the midspan for the 3-point bend geometry (b) uniform maximum along the whole gauge length of the sample for the 4-point bend geometry.

Thus the exact position of a precrack in a 4-point bend test is not important; as long as the

precrack lie within the central portion of the beam, they will all receive an identical

tensile stress. Unlike the 4-point bend geometry, the stress distribution in the 3-point

bend geometry is very non-uniform and the central loading line should be directly above

the precrack, which means that the peak stress occurs only along a single line on the

surface of the sample. In this case, the probability of the largest flaw in the sample being

at the surface along the line of peak stress is relatively low. Therefore, it is unlikely that

42

the 3-point bend test would reveal the strength limit of the material or the flaw size that

causes fracture. The 4-point bend test geometry is shown in more detail in Fig. 3.2.

Figure. 3.2. Schematic of a 4-point bend test geometry. 1y and 2y are the

vertical distance between the outer rollers and inner rollers.

The normal stress (Pa)app applied to the end face of the sample is given by:

23 /app Pd wh (3.1)

where is the applied load (in Kg), is the sample width (perpendicular to the plane of the

paper in Fig. 3.2), h is the sample thickness, d is the bending arm, / 2d L l , is the

separation of the outer rollers, and is the separation of the inner rollers; all the spatial

dimensions are in m .

The equation for the strain in the central part of the beam is given by:

2 26 / 3 4h l L l L l h (3.2)

where 1 2y y is the vertical displacement between the outer and inner rollers; is

equal to the crosshead displacement. In general, if the separation between the inner

P/2 P/2

P/2 P/2

43

rollers is about three times the sample width 3l w , then the central portion of the

beam undergoes pure bending, and it is valid to use Eq. 3.2 [3,30,37]. However this

equation is no longer strictly valid after the onset of plasticity at higher temperatures.

An expression for the strain rate can be obtained by differentiating Eq. 3.2 with respect to

time, and is given by:

2 26 / 3 4h l L l L l h (3.3)

where is the crosshead displacement rate. In general the value of 24h in the above

equation is very small compared to the value of 23l L l L l , and thus the strain

rate is proportional and very sensitive to the sample thickness, h . Thus it is important to

ensure that all samples have the same thickness in order to have a successful series of

experiments at the same strain rate,

3.1.1 Sample Preparation

Parallelepiped samples of undoped InP single crystal with dimensions of 33 35 2 mm

were cut with a Struers Accuton- machine using a 5 in 12.7 cm diamond blade.

The samples were polished on all sides to remove surface damage and to minimize the

introduction of unwanted precracks introduced during cutting. The orientation and

dimensions of a typical sample are shown in Fig. 3.3. As mentioned in the previous

section, in order to successfully measure the brittle-to-ductile transition temperature, a

series of fracture tests at different temperatures must be performed while maintaining the

44

other parameter, such as sample geometry identical. Thus, it is essential to ensure that all

samples have the same thickness, because the applied strain rate is a sensitive function of

the sample thickness.

Figure. 3.3. The crystallographic orientation and dimensions of a 4-point bend sample (actual sample dimensions after polishing).

Batches of up to 12 samples were prepared simultaneously. All samples were

subsequently mounted on a flat glass plate using a low melting point wax and were

polished using a Buehler Automet 2 polishing machine. The polishing procedure

consisted of four steps:

Step 1. Polish with a 2400 grit SiC paper.

Step 2. Polish with a 4000 grit SiC paper.

Step 3. Polish with a 5 μm alumina slurry (alumina powder + water) on a soft

cloth.

Step 4. Polish with a 1 μm alumina slurry on a soft cloth.

The samples were polished until they showed a mirror-like surface and no sign of any

scratch on the surface under an optical microscope. On completion, the samples were

removed by soaking the glass plate in acetone for a couple of hours, until the low melting

point wax dissolved. This made sample removal quite easy without introducing scratches

45

in the samples. The samples were then cleaned using ethanol and stored, ready for

introduction of precracks.

3.1.2 Technique of Introducing Precracks

In order to ensure that fracture always initiates within the sample, precracks were

introduced in the samples and had to be the worst flaw in the samples, so that fracture

always initiates there. In this work five radial precracks were introduced in each sample

by a 50 g Knoop indentation, with the long direction of the Knoop indent parallel to

110 at the center of the 001 face of each sample, as shown in Fig. 3.4. These five

precracks were spaced far enough from each other 20 μm to ensure that there was no

interaction between the stress fields of neighboring indentations.

Figure. 3.4. A 4-point bend test sample containing five identical radial precracks, introduced by Knoop indents spaced about 20 μm apart.

A 50 g indent load was chosen because sometimes, above this load, lateral cracks

formed during indentation. If present, these lateral cracks will continue moving toward

the surface where they can break out in the form of chipping, this should be avoided in

the fracture tests.

46

3.1.3 Instron 1361 Tensile Machine

An Instron 1361 tensile machine, as shown in Fig. 3.5, was used to perform 4-point bend

experiments. In the 4-point bend tests, load-displacement curves are obtained, which can

be converted into a stress-temperature curve to determine the brittle-to-ductile transition

temperature.

Figure. 3.5. (a) Photograph of the Instron 1361 tensile machine with the tensile jig and the furnace mounted on it, and (b) schematic of the 4-point bend jig connected to the displacement rods of the machine.

Some limitations were encountered with this machine; one of them was to keep the same

constant flow rate of argon gas in every experiment, which is important because the flow

rate of argon gas can modify the temperature of the sample and the thermocouple

reading, which can cause inconsistent temperature differences between the temperature

47

controller and the thermocouple (up to ). Another parameter that can affect the

temperature reading is the position of the thermocouple with respect to the specimen

within the jig.

The 4-point bend jig is fabricated from SiC with upper and lower rollers made from

molybdenum due to its smooth surface; reliable data were not obtained using alumina

rollers. These molybdenum rollers were obtained from Goodfellow Metals, Co. In order

to achieve a good surface finish, these rollers were electropolished in a solution of 25%

sulphuric acid, 75% methanol with a stainless steel cathode with a voltage of 10 V

applied for about 5 minutes. This technique produced an optically smooth surface finish

for the rollers.

The 4-point bend jig was then placed in the furnace tube, argon gas flow started and the

jig heated up while high purity argon gas continued flowing to avoid thermal

decomposition or oxidation of the sample. In each case, the sample was annealed at

for about one hour before initiation of deformation. Following the annealing step,

the desired temperature was set and the test conducted in the displacement mode with a

constant crosshead speed (i.e., a constant strain rate, ). Each test was continued until the

sample either fractured or deformed plastically.

3.2 Indentation Tests

48

Indentation is a popular technique to characterize the mechanical properties of materials,

such as their resistance to plastic deformation (hardness) and their resistance to cracking

(fracture toughness). In indentation tests, an indenter is forced into the surface of the

sample under a fixed load, as schematically illustrated in Fig. 3.6, for certain duration of

time.

Figure. 3.6. Schematic of indentation mechanism. is the applied load, is the indentation diagonal and h is the indentation depth.

There are three processes that can take place when the indenter is forced into a crystal.

The crystal initially deforms elastically and subsequently either fractures or deforms

plastically (or a combination of the latter). At low temperatures, in the brittle regime of

the solid, the predominant mode of accommodating the indenter is by fracturing of the

sample. On the other hand, at high temperatures, in the ductile regime of the solid, the

sample deforms plastically to accommodate the indenter.

Using such an indentation test, the hardness value of the sample can be estimated. This is

determined by the length of the diagonal of indentation impression or by the indentation

depth. The indentation microhardness (HV) was calculated using the following standard

equation:

21854.4 /HV P d (3.4)

49

where P is load in g , and d is the mean diagonal of an indent in μm .

3.2.1 Sample Preparation

Parallelepiped samples of InP with dimensions of 33 5 2 mm were cut with a Struers

Accuton- machine using a 5 in 12.7 cm diamond blade such that the large

23 3 mm faces were parallel to the 001 plane. The 001 face was then polished in

order to remove surface damage and to minimize the introduction of unwanted precracks

introduced during cutting. For this purpose, the sample was mounted on a flat glass plate

using a low melting point wax and polished using a Buehler Automet 2 polishing

machine. The polishing procedure was identical to that of the 4-point bend samples (see

section 3.1.1).

3.2.2 Static Indentation Tests

Static indentation tests were performed on the 001 face of InP with a Nikon high

temperature microhardness indenter. A diamond Vickers indenter (a square-based,

pyramidal indenter with a 136 angle) was used for indentations. In these tests, the

sample was aligned such that its 110 and 110 directions were parallel to the indenter

diagonals, as shown in Fig. 3.7. Note that the 110 directions correspond to intersection

of 111 slip planes with the 001 sample surface. The indenter was left for 15 seconds

50

on the sample before it was raised up, in this way plastic impression was observed on the

sample surface.

The tests were conducted in the temperature range of to , starting from the

highest temperature and going down gradually to in a step size of . Five to

eight indentations were made at each temperature. The load, on the indenter was 50 g .

After the indentation, the sample was etched in a HCL:H3PO4 solution for about 10

seconds and the length of the diagonals of the indentation impression were measured.

Figure. 3.7. Schematic of indented surface in InP with a 110 orientation of

indenter diagonals.

Figure. 3.8. Photograph of the Nikon High Temperature Microhardness Tester model QM.

51

Specimens for transmission electron microscopy were prepared by polishing the back

side of the indented sample to a thickness of approximately using SiC paper. The

specimen was then dimpled using diamond paste to obtain a thickness of

approximately . The specimen was then loaded into a PIPS (Precision Ion Beam

Polishing System) for ion beam thinning using double modulator at energy and an

incident beam angle of to obtain a large thin area for imaging (to make the specimen

electron transparent). Transmission electron microscopy was carried out using a Philips

CM20 TEM, operated at .

3.2.3 Dynamic Indentation Tests

Dynamic indentation tests were performed on the face of InP with a high-

temperature depth-sensitive indenter. Fig. 3.9 shows a photograph and schematic diagram

of the high-temperature depth-sensitive indentation (HTDSI) equipment.

A conventional Vickers diamond indenter is used in this machine. A current-controlled

electromagnetic moving coil is used to apply the load, which enables a wide range of

displacement rates and a maximum load up to [26]. A capacitance displacement

gauge is used not only to determine the position of indenter but also to detect the instant

when the indenter touches the sample surface prior to indentation, as well as to track the

movement of the indenter during indentation. In this machine, the sample and indenter

are heated separately in vacuum to prevent oxidation of the furnace heating element and

52

the diamond indenter. During our tests the indenter and the sample were kept at the same

temperature as close as possible

Figure. 3.9. (a) Photograph of the HTDSI apparatus, and (b) schematic diagram of the apparatus: (A) sample, (B) indenter, (C) sample furnace, (D) indenter furnace, (E) capacitance displacement gauge, and (F) load application coil (After Kim and Heuer [26]).

The basis of the depth-sensitive indentation (DSI) technique is similar to the conventional

microhardness test, the major difference being that instead of measuring the impression

diagonal after indentation, this technique monitors the penetration depth as a function of

the applied load as the indenter is driven into the material and withdrawn from it. In the

DSI test, a load-depth plot is obtained, which can be used to calculate the energy

consumed in making an indent at a fixed temperature.

A typical load-depth plot obtained from a test is shown in Fig. 3.10. The displacement of

the indenter in the vertical direction is along the x-axis and the load is along the y-axis.

Such a plot typically consists of a loading curve and an unloading curve that form a loop

showing hysteresis. Thus, in Fig. 3.10, the path OA is the loading cycle, which increases

53

continuously with the applied load. At A, the load reaches its maximum value and then

stays constant while the depth increases to B. BC corresponds to the unloading cycle

where the load gradually decreases to zero. The area bound by OABD is the total energy,

, expended by the indenter to impress into the material. This energy consists of two

parts: (1) elastic energy, , and (2) work done, , to produce a permanent

impression. The latter can be plastic deformation required to produce the impression as

well as the surface energy produced by cracking. If the material was purely elastic, the

paths OA and BC would overlap and there would be no hysteresis, i.e. , since the

elastic energy is fully recovered during the unloading path. On the other hand, if the

material is purely plastic, the path would be OABD and there would be no elastic

recovery.

54

Figure. 3.10. Typical load-depth plot for a material that is subject to elastic and plastic deformation.

Fig. 3.10 is a typical plot for a material that shows an elastic/plastic behavior. As shown

in this figure, after unloading, the depth displacement does not go back to zero, because

the material has undergone some plastic deformation. Consequently, the area under

OABC is related to the plastic energy dissipated in the volume of indentation, i.e. energy

expended to create and move dislocations during indentation process and surface energy

from any crack produced. Since the area under OABD gives the total energy, , which

consists of the plastic energy, , and the elastic energy, . The elastic energy,

is the area under CBD.

Tests were performed using a load in the temperature range between and

(the machine can in fact produce indentations over the temperature range between

and ). In each case, the indentations were started from the highest

temperature gradually decreasing to the lowest temperature at in step size of .

The indenter was left for seconds on the sample before it was raised up. Moreover

eight to ten indentations were made at each temperature.

55

CHAPTER 4

RESULTS AND DISCUSSIONS

This section presents the results of mechanical testing of InP from all the experiments

conducted in the present study. First, the results of 4-point bend tests are presented and

discussed. This is followed by indentation tests including statical indentation tests with

the Nikon high temperature microhardness indenter model QM and dynamical

indentation tests with the high-temperature depth-sensitive indentation machine.

4.1 4-Point Bend Tests

The purpose of these experiments is to identify the basic characteristics of the brittle-to-

ductile transition in InP, such as the temperature range over which transition occurs and

the form of stress versus temperature curves.

A series of tests were carried out at a crosshead displacement rate of

, which correspond to strain rate of . The variation

56

of the sample thickness in these tests was . The samples were tested over a

temperature range of to . Load-displacement curves (as plotted by the

Instron chart recorder) of a sample tested at three different temperatures at a strain rate of

are shown in Fig. 4.1.

Figure. 4.1. Load displacement curves for InP samples tested at ,

and at a strain rate of . At InP deforms elastically until fracture; at InP is in the transition region; above , e.g., at , InP deforms plastically.

The complete results from a series of tests at different temperatures are presented in Fig.

4.2, in the form of applied stress to deform the crystal versus temperature. The plot

consists of two parts: (1) up to about 350°C, all the samples underwent elastic

deformation and then fractured by cleavage in a brittle fashion at an approximately

constant applied stress of 90 MPa, and (2) above 355°C all the samples exhibited

plastic deformation.

57

Figure. 4.2. Applied stress versus temperature for samples tested at a strain rate of . The brittle-to-ductile transition temperature occurs over a very narrow temperature range of , and is characterized by a sudden increase of the applied stress.

4.1.1 Brittle Behavior

At and below, the applied load versus displacement curves were linear up to the

point where the samples broke (see Fig. 4.1(a)), indicating that the material exhibited

elastic behavior until it fractured. The samples fractured catastrophically at an applied

stress at about .

Samples tested in this regime show roughly a constant fracture stress value; the

variability of fracture stress arises because most samples did not break at the introduced

precrack which resulted in higher fracture stress than if fracture had initiated at a pre-

crack. For instance at two tests were conducted, each giving a different fracture

stress value: when the sample broke catastrophically at the introduced precracks

58

and when it did not (see Fig. 4.2). Larger indentation loads, up to were

tried to produce larger precracks and to overcome this problem, but still only very few of

the samples broke at the introduced precracks.

4.1.2 Transition Behavior

At the load-displacement curve was still linear, but at the curve exhibited

a small deviation from linearity before it broke (see Fig. 4.1(b)). This deviation indicates

the start of plasticity. As shown in Fig. 4.2, there is a rapid rise in the applied stress

between and . In that stage, the dislocations start emitting from the crack

tip, thus blunt and also shield the crack tip from the applied stress. Consequently a larger

applied stress is needed to break the sample. The temperature at which the rapid rise takes

place corresponds to the brittle-to-ductile transition temperature.

4.1.3 Ductile Behavior

Above , the samples were no longer cleaving in a brittle manner but rather, they

deformed plastically until fractured in a ductile manner (i.e. by necking). Fig. 4.1(c)

shows that the samples at exhibit yielding (ductility) followed by fracture. In the

later stages of deformation, necking occurred: beginning at the maximum load point, the

sample cross section rapidly decreased at some point until it was no longer able to

support the load, and ultimately broke. The stress needed to plastically deform InP in the

ductile regime decreases as the temperature increases. The reason for this is that

dislocation mobility increases with temperature and makes plastic shearing of the crystal

easier as temperature increases.

59

From the applied stress versus temperature plot, it is certain that the brittle-to-ductile

transition is characterized by a sudden increase of the applied stress to shear the samples.

In this work the brittle-to-ductile transition temperature occurs in a very narrow

temperature range, , between the highest temperature where the sample deforms in a

completely brittle manner and the lowest temperature where the sample yields. At a strain

rate of , the highest temperature at which the sample deforms in a

brittle manner is and the lowest temperature at which the sample deforms

plastically is .

The brittle-to-ductile transition temperature range itself is also affected by variations

between individual samples. In general, despite the fact that chipping starts to appear

with higher indentation loads, larger precrack sizes result in a narrower transition

temperature range giving a sharper applied stress versus temperature plot.

4.2 Indentation Tests

4.2.1 Static Indentation Tests

Static indentation test was another technique employed in this study to understand the

mechanism of plastic deformation of InP. In this work besides measuring the temperature

dependence of the hardness, fracture and plastic behavior of InP subjected to indentation

was also investigated.

60

The hardness and the strain rate values were extracted from the measured indentation

impression diagonals (shown in Fig. 4.4). The roughly calculated strain rate in this static

indentation test was . The temperature dependence of the hardness of

undoped InP is shown in Fig. 4.3; as the temperature increases, the sample hardness

rapidly decreases until a temperature is reached where the dislocation mobility becomes

high, yield strength becomes very low and hardness approaches a constant value.

Figure. 4.3. Hardness versus temperature curve for sample tested from down to , with a step size of and a indentation load.

61

In addition to the indentation diagonals, the temperature dependence of the length of

radial cracks emanating from the indent corners (recall that the indentation diagonals

62

Fig

ure

4.4

. In

dent

atio

n im

pres

sion

s pr

oduc

ed b

y st

atic

ind

enta

tion

tec

hniq

ue a

t (a

) 12

3°C

, (b

) 26

3°C

, an

d (c

) 32

0°C

. T

hese

fig

ures

sho

w t

hat

the

sam

ple

hard

ness

dec

reas

es w

ith

incr

easi

ng t

empe

ratu

re d

ue t

o hi

gher

dis

loca

tion

mob

ilit

y at

hi

gher

tem

pera

ture

s. I

t is

als

o ca

n be

see

n th

at c

rack

sta

rt e

man

atin

g fr

om t

he i

nden

t co

rner

s at

263

°C, a

t th

is t

empe

ratu

re

crac

k st

art t

o pr

opag

ate

from

the

inde

nt c

orne

rs a

s sh

own

in (

b).

(a)

(b)

(c)

were along two orthogonal directions) was also measured. The temperature

dependence of and crack lengths are shown in Fig. 4.5.

Figure. 4.5. Temperature dependence of the impression diameter and crack

length along and directions over a temperature range of to

using an indentation load of . The sample was initially heated to the highest temperature and indented. Following this, the sample was cooled and indentations made in step size until the lowest temperature of .

The indentation brittle-to-ductile transition (IBDT) temperature was determined from the

disappearance of radial cracks from the corners of the indentation impression. Two

values were obtained: and . Note that

the indentation brittle-to-ductile transition temperature for cracks is slightly lower

than that for cracks, showing the asymmetry of the two directions in a polar

63

crystal. This asymmetry also affects its mechanical properties along and

directions, i.e. the crack length along and directions are not the same at any

temperature below (see Fig. 4.5). This behavior, previously reported for III-V

compound semiconductors, can be explained on the basis of crystallographic anisotropy

in sphalerite structures (see section 1.1.4).

The TEM images of the sample deformed by the static indentation technique at

are shown in Fig. 4.6. Fig. 4.6(a) shows two sets of stacking fault ribbons perpendicular

to each other, when viewed along the direction. These two sets are formed on

different slip planes. One set of stacking fault ribbons is out of contrast under

and reflections (as indicated in Fig. 4.6(b) and 4.6(c), respectively). Using the

analysis (see Table. 4.1), we conclude that the partial dislocations have the same Burgers

vector inclined to the surface. These TEM observations show that plastic

deformation of InP occurs by the operation of the slip system with

dislocations belonging to this system dissociating into two partial dislocations.

64

Table. 4.1. analysis for Burgers vector of partial dislocations in a

face-centered cubic crystal (black and white regions correspond to

(dislocations in contrast) and (dislocations out of contrast)).

65

66

Fig

ure

4.6

. B

righ

t fi

eld

TE

M i

mag

es o

f st

acki

ng f

ault

s in

ind

ium

pho

sphi

de d

efor

med

by

the

stat

ic i

nden

tati

on t

echn

ique

at

320˚

C.

Fig

. 4.

5(a)

sh

ows

two

sets

of

stac

king

fau

lt r

ibbo

ns p

erpe

ndic

ular

to

each

oth

er.

One

set

of

the

stac

king

fau

lt r

ibbo

ns i

s ou

t of

con

tras

t in

220

and

311

re

flec

tion

s, a

s sh

own

in f

igur

es (

b) a

nd (

c) r

espe

ctiv

ely.

(a)

(b)

(c)

4.2.2 Dynamic Indentation Tests

As mentioned in 3.2.3, this test is basically the same as the conventional static

indentation test, but instead of measuring the impression diagonal after an indenter

penetrates a crystal to obtain its hardness value, the impression depth is monitored as a

function of the applied load to obtain a load-depth plot. This plot can subsequently be

used to calculate a dynamic hardness value. The area under the load-displacement curve

is related to the total energy dissipated in the impression volume produced by the

indentation.

Load-displacement curves at different temperatures on surface of InP are shown in

Fig. 4.7. For these tests, at every temperature, a load of was gradually applied to

the indenter to penetrate into the InP crystal with a strain rate of . The

duration of each test was seconds, after which the load was maintained for seconds

before unloading. Fig. 4.7(a) shows that there is considerable elastic recovery at low

temperatures, however as temperature increases the indenter penetrates further into the

sample, indicating softening with increasing temperature; the indentation penetration

depth increases and elastic recovery reduces, e.g. Fig. 4.7(d).

67

Figure 4.7. Load-displacement curves obtained from dynamic indentation tests on

surface of indium phosphide at different temperatures: (a) , (b) , (c)

, and (d) .

68

(a)

By integrating the area under the load-displacement curves in Fig. 4.7, we obtained a plot

of energy versus temperature for the indentation load, as shown in Fig. 4.8.

Figure. 4.8. Dissipated energy versus temperature plot obtained by integrating the area under the load-displacement curves in Fig. 4.6.

The principal mechanism of plastic deformation in a crystal is by fracture or sliding (slip)

between planes of atoms and the latter occurs in an incremental manner due to dislocation

motion. These dislocations blunt the crack tip and decrease the stress concentration at the

crack tip. Thus, with increasing temperature, the contribution of fracture to the dissipated

energy decreases, and that of shear deformation increases. Since the volume of

indentation produced by shearing increases with temperature, the energy dissipated also

increases with temperature.

We assume here that the volume of indentation produced is a perfect square base pyramid

with an angle of between opposite planes. The indentation impression volume is

69

then , where is the indentation depth. We can now estimate the energy density,

by dividing the dissipated energy, by . A plot of versus indentation

temperature is shown in Fig. 4.9.

Figure. 4.9. Energy density versus temperature plot obtained by dividing the dissipated energy with indentation volume.

Fig. 4.9 shows that the energy density, , stays constant up to about and decrease

as the temperature increases. At , the sample is deformed by fracture in a

brittle manner (which involves rupturing of atomic bonds). Since the bond energy does

not vary much with temperature, the applied stress needed to break the sample is

expected to be constant. Above the energy density declines smoothly due to

increasing dislocation mobility with temperature. We define the inflection point in the

plot as the indentation brittle-to-ductile transition (IBDT) temperature. In the

70

present case, InP exhibits a transition temperature at about . Above this

temperature the sample deformed plastically by shearing and the sample deformed by

fracture in a brittle manner below transition temperature. Fig. 4.8 looks very similar with

the schematic variation of the proposed by Pirouz et all [27], shown in Fig. 4.10.

Figure. 4.10. Schematic variations of stress versus temperature in a crystal. (After Pirouz et all [27]).

The curve in Fig. 4.10 shows temperature dependence of the resolved shear stress, ,

needed for plastically deforming crystal at a constant strain rate. If a crystal loaded with

an increasing applied stress , then below transition temperature, reaches before

reaching and the crystal fracture, i.e. represents brittle regime. On the

other hand, above transition temperature, reaches first and the crystal yield

plastically, i.e., represents ductile regime. The brittle-to-ductile transition

temperature is defined from the intersection of the shear stress, and fracture stress,

71

curves. It can be seen that the curve in Fig. 4.10 is actually the same curve

as shown in Fig. 4.9.

CHAPTER 5

CONCLUSION

Experiments have been performed in this work to determine the basic characteristics of

brittle-to-ductile transition (BDT) temperature in single crystal InP using three

techniques; 4-point bend tests and indentation tests (static and dynamic). All three

techniques show that InP exhibits a sharp brittle-to-ductile transition temperature:

4-point bend tests ( ): between and .

Static indentation tests ( ): .

Dynamic indentation tests ( ): .

Of course the different techniques do not give absolutely identical values, since the

deformation mode is not identical for the different techniques. In particular, in the

indentation test, the presence of a hydrostatic pressure shifts the transition temperature to

a lower value, i.e. , in general.

At low temperatures, below , InP deformed (fractured) in a brittle manner at an

approximately constant stress. At the transition temperature, the deformation mode

changes and a higher stress is needed to break the crystal. As the temperatures increases

above , InP deformed plastically but the yield stress is lower and hence a lower

72

applied stress is required. This is because dislocation mobility increases with

temperature, and makes plastic shearing of the crystal easier.

TEM observations of InP sample indented by static indentation machine at

showed that plastic deformation of InP occurs by the operation of the slip

system.

73

APPENDIX

A series of tests were conducted to see how the transition temperature varies with the

strain rate. Such tests shed light on the correlation between dislocation mobility and the

transition temperature. This correlation has been previously reported for silicon [35]. As

described in section 3.1.1, in this series of tests, all the samples were prepared in one

batch to minimize variation between individual samples. Fig. A.1 shows the applied

stress versus temperature plot for tests performed at a strain rate of .

Figure. A.1. Applied stress versus temperature for samples tested at a strain rate of . The brittle-to-ductile transition temperature occurs between and .

74

It can be seen that at lower strain rate, the brittle-to-ductile transition temperature falls

between and . This result is unexpected; because the smaller the strain

rates the lower should be the brittle-to-ductile transition temperature. In other words, the

faster the crystal is loaded, the wider should be the temperature regime over which it

behaves in a brittle manner.

It was decided to re-determine the brittle-to-ductile transition temperature at a strain rate

of . The same precautions were taken in preparing the samples for these

tests. However, a small number of samples were used in this series of tests, because the

re-runs were simply a crosscheck to verify the validity of the previous results. Actually,

the strain rate used was close to, but not exactly . It was in fact

. The results are presented in the form of an applied stress versus

temperature plot in Fig. A.2.

This time the brittle-to-ductile transition temperature falls between and .

This result is about higher than the previous set of experiments, which could be due

the fact that these measurements were made at different times using samples taken from

different batches. Besides, the details of an experiment also affect the result: such

parameters include the flow rate of the argon gas, or the distance between the

thermocouple and the sample jig. Both parameters can affect the temperature reading.

Based on the re-run tests done above, we feel that only the first set of measurements, i.e.

those performed at a strain rate of are reliable.

75

Figure. A.2. Applied stress versus temperature for samples tested at a strain rate of . The brittle-to-ductile transition temperature occurs over a narrow temperature range of , and is characterized by a sudden increase of the applied stress.

The fact that the brittle-to-ductile transition temperature determined at a strain rate of

is higher than the brittle-to-ductile transition temperature at a strain rate

of , is not yet understood. However, in order to clarify this, more

experiments are required in particularly at low strain rates.

76

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