Microscopie de biréfringence et caractérisation de matériaux à grand gap

Wide band gap WBG semiconductor materials such as Silicon Carbide SiC and Diamond have outstanding material properties.. Extended defects in 6H-SiC wafer and diamond materials were chara

THÈSE

Pour obtenir le grade de

DOCTEUR DE L’UNIVERSITÉ DE GRENOBLE

Spécialité : « Matériaux, Mécanique, Génie Civil et Électrochimie »

Arrêté ministériel : 7 aỏt 2006

Présentée par

Thi Mai Hoa LE

Thèse dirigée par «Thierry OUISSE»

préparée au sein du «Laboratoire des Matériaux et du Génie Physique (LMGP) »

dans l'École Doctorale « Ingénierie – Matériaux, Mécanique, Énergétique, Environnement, Procédés (IMEP-2) »

Microscopie de biréfringence et caractérisation de matériaux

à grand gap Thèse soutenue publiquement le « Mars 2014 »,

devant le jury composé de :

Monsieur, Thanh Vinh LE

Professeur, Université d’Aix-Marseille, (Rapporteur)

Monsieur, Efstathios POLYCHRONIADIS

Professeur, Université Thessaloniki, (Rapporteur)

Monsieur, Jocelyn ACHARD

Professeur, Université Paris 13, (Président)

Monsieur, Didier CHAUSSENDE

Chargé de recherche CNRS, ( Membre )

Monsieur, Thierry OUISSE

Professeur, Grenoble INP, ( Directeur de thèse)

TABLE OF CONTENTS

Abstract i

Acknowledgments iii

Chapter 1 General introduction Foreword……… ……… 2

1 A brief review of Silicon Carbide (SiC)……… … ………5

1.1 Structure and properties of Silicon Carbide…… ……… ……… 5

1.1.1 Crystal structure… ……… ……… 5

1.1.2 Properties of Silicon Carbide… ………… ………… …… 7

1.2 Crystallographic defects in SiC material and their characterization… ….9

2 A brief review of Diamond……….… …… ………14

2.1 Structure and properties of Diamond……… …… … 14

2.1.1 Crystallographic structure……… ……… 14

2.1.2 Properties of diamond……… …… …15

2.2 Crystallographic defects in Diamond and their characterization… 17

3 About the necessity of studying crystallographic defects 20

4 About the necessity of developing non-destructive characterization techniques 22

5 Layout of the thesis 23

References……… …… ……… 24

Chapter 2 Birefringence and rotating polariser method 1 Introduction 32

2 Birefringence or Double refraction 32

2.1 The dielectric tensor and the refractive index 32

2.2 Birefringence 36

3 Elasticity 39

3.1 Stress and strain 39

3.1.1 Stress 39

3.1.2 Strain 41

3.2 Hooke’s law 42

3.3 Relation between compliance and stiffness 43

3.4 The matrix and tensor notations 43

3.5 Transformation rule of the stress tensor 44

4 Stress- induced birefringence 47

5 Birefringence microscopy 49

5.1 Introduction 49

5.2 Conventional set-up for birefringence measurements 51

5.2.1 The nature of light 51

5.2.2 Linear and circular polarized light 52

5.2.3 Quarter-wave plate 53

5.2.4 Plane polariscope 54

5.2.5 Circular polariscope 55

5.3 Experimental setup of the rotating polarised method 56

6 Birefringence modelling 59

6.1 Birefringence images of a dislocation in 6H-SiC crystals 59

6.1.1 Introduction 59

6.1.2 Birefringence modelling 60

6.1.3 The calculation of the residual stress field and birefringence image 62

6.2 Birefringence images of a dislocation in diamond 65

6.2.1 Introduction 65

6.2.2 The calculation of the birefringence image of a dislocation in Diamond 65

References 70

Chapter 3 Birefringence microscopy study of dislocations in SiC substrates

1 Introduction 75

2 Experimental birefringence image of dislocations in Silicon carbide 76

2.1 Introduction 76

2.2 Sample and experimental method 76

2.3 Results and discussion 77

3 Comparison between experiment and theory 80

3.1 Introduction 80

3.2 Sample and experimental method 81

3.2.1 Sample 81

3.2.2 Experimental method 82

3.3 Results and discussion 82

4 The influence of the residual stress upon the birefringence pattern 87

4.1 Introduction 87

4.2 Results and discussion 87

5 Observing dislocations with a small component of the Burgers vector in the basal plane 90

5.1 Introduction 90

5.2 Results and discussion 91

6 Experimental and simulated birefringence patterns induced by dislocations with different Burgers vectors 92

6.1 Introduction 92

6.2 Results and discussion 93

7 Dependence of the birefringence pattern on the dislocation length along the z axis 96

7.1 Introduction 96

7.2 Results and discussion 97

8 Comparison between birefringence and KOH etching 100

8.1 Introduction 100

8.2 Experimental method 101

8.3 Results and discussion 101

9 The correlation between the birefringence and the substrate thickness 111

9.1 Introduction 111

9.2 Sample and experimental method 114

9.3 Results and discussion 115

10 Conclusion 122

References 123

Chapter 4 Birefringence microscopy study of dislocations in Diamond 1 Introduction 131

2 Birefringence patterns due to dislocations and inclusions in diamond 133

2.1 Samples and experimental method 133

2.1.1 Samples 133

2.1.2 Experimental method 133

2.2 Results and discussion 134

3 Identification of the dislocations in single crystal CVD diamond by combining experiment and simulation 143

3.1 Experimental method 143

3.2 Results and discussion 144

4 Dependence of the birefringence pattern on the dislocation length along the z-axis 152

4.1 Introduction 152

4.2 Results and discussion 152

5 Investigation of the characteristic of the HPHT substrate before and after chemical vapour deposition (CVD) growth 158

5.1 Introduction 158

5.2 Results and discussion 158

6 Investigation of the dislocation propagation from the HPHT substrate into the CVD layer 161

6.1 Introduction 161

6.2 Samples and experimental method 161

6.3 Results and discussion 162

7 Conclusion 167

References 167

General conclusion. 174

Wide band gap (WBG) semiconductor materials such as Silicon Carbide (SiC) and Diamond have outstanding material properties Many applications can benefit from WBG semiconductors In order to improve material quality as well as to increase the range of technological applications of the WBG semiconductor materials, it is necessary to decrease or minimize the number of extended defects

This research work deals with the assessment, modelling and development of analytical techniques based upon the use of optical microscopy The thesis dedicated

to the identification of structural defects in Silicon Carbide (SiC) and diamond materials Extended defects in 6H-SiC wafer and diamond materials were characterized by birefringence microscopy The measured birefringence patterns of individual dislocations modelled

In the case of SiC, a good agreement is obtained between theory and experiment, which led to the proper determination of the Burgers vector values and background residual stress All observed dislocations were almost vertical dislocations with a mixed character Sometimes, their orientation changes resulting in the observation of a faint birefringence pattern We compared birefringence data with etch pits formed after KOH etching Combining both techniques is a method to discriminate between pure screw dislocations and mixed or pure edge dislocations

Typical dislocations in single crystal CVD diamond were determined by birefringence measurement and quantitatively modelled Although the simulated images only approximate the experimental ones, the individual dislocations are determined to be threading edge or mixed dislocations with a possible Burgers vector a/2(011) or a/2(110) Sometimes, the vertical dislocations can convert to a horizontal

or slightly tilted line and then turn vertical again resulting in the observation of two separated birefringence patterns The dislocation propagation from the HPHT substrate into the CVD layer has been investigated by simultaneously analysing the HPHT substrate and the CVD layer in the same sample region

Keywords: Birefringence microscopy, crystallographic defects, Diamond, Silicon

Carbide, Chemical Vapour Deposition

Les matériaux semi-conducteurs à large bande interdite (WBG) tels que le carbure de silicium (SiC) et le diamant ont des propriétés matérielles exceptionnelles De nombreuses applications peuvent bénéficier des semi-conducteurs WBG Afin d'améliorer

la qualité de ces matériaux, ainsi que pour augmenter leur gamme d'applications technologiques, il est nécessaire de diminuer ou réduire au minimum le nombre de défauts étendus

Ce travail de recherche a porté sur l'évaluation, la modélisation et le développement

de techniques d'analyse s’appuyant sur l'utilisation de la microscopie optique La thèse s’est focalisée sur l'identification des défauts structurels dans le carbure de silicium (SiC)

et le diamant Les défauts étendus dans des substrats 6H-SiC et du diamant ont été caractérisés par microscopie de biréfringence et les figures de biréfringence des différentes dislocations mesurées ont été modélisées

Dans le cas du SiC, un bon accord est obtenu entre théorie et expérience ce qui a amené à la détermination valide des vecteurs de Burgers et contraintes résiduelles d’arrière-plan Presque toutes les dislocations observées étaient des dislocations verticales

à caractère mixte Parfois, leur orientation change résultant dans l'observation d'un motif

de faible biréfringence Nous avons comparé les données de biréfringence avec les gravures formées après attaque KOH La combinaison des deux techniques est une façon

de discriminer entre les dislocations vis pures et les dislocations mixtes ou coins

Les dislocations typiques dans du diamant monocristallin CVD ont été déterminées par mesure de biréfringence et quantitativement modélisées Bien que les images simulées soient des approximations des observations expérimentales, les dislocations individuelles apparaissent comme étant des dislocations coins ou mixtes avec un possible vecteur de Burgers a / 2 (011) ou a/ 2 (110) Parfois, les dislocations verticales peuvent se transformer en ligne horizontale ou inclinée, puis revenir à nouveau à la verticale résultant dans l'observation de deux figures de biréfringence séparées La propagation de dislocations à partir du substrat HPHT dans la couche CVD a aussi été étudiée en analysant simultanément le substrat HPHT et la couche CVD dans la même région de l'échantillon

Mots-clés: Microscopie de biréfringence, défauts cristallographiques, diamant, carbure

de silicium, dépôt vapeur en phase chimique CVD

This research work has been achieved at the Laboratory of Materials and Engineering Physics (LMGP) and financially supported by both the Vietnamese and French Governments

I wish to express my deep gratitude to my advisor Prof Thierry OUISSE, of Grenoble INP, for giving me the opportunity to complete this thesis, for his excellent support in all situations, for his helpful discussions concerning both experiment and theory, and for kindly spending a lot of time in discussing and correcting my dissertation His wide knowledge, mentorships and encouragements throughout my entire study make this thesis possible I am proud of my mentor and exemplary teacher

I would like to thank Bernard CHENEVIER, Director of LMGP, Dr Didier CHAUSSENDE, the SPCS group members as well as all members of LMGP for their great help during my research

Particularly, I would like to acknowledge Prof Jocelyn ACHARD, Dr Alexandre TALLAIRE and the LSPM group members for kindly supplying the Diamond samples

I also would like to thank all the dissertation committee members and their valuable advice

Specially, I am thankful to my parents Vũ Thị Yến and Lê Đức Mậu, my sister and my brother for their love and endless encouragement

Many thanks to all my friends from Vietnam, France, Thailand, Korea, Germany and many other countries in the world for their friendship and provided when the support writing this thesis

France, December 2013

Chapter 1

General introduction

Foreword……… 2

1 A brief review of Silicon Carbide (SiC)……… ………5

1.1 Structure and properties of Silicon Carbide……… ……… 5

1.1.1 Crystal structure……… ……… 5

1.1.2 Properties of Silicon Carbide……… ……… 7

1.2 Crystallographic defects in SiC material and their characterization………….9

2 A brief review of Diamond……….… ………14

2.1 Structure and properties of Diamond……… … 14

2.1.1 Crystallographic structure……… ……… 14

2.1.2 Properties of diamond……… ………15

2.2 Crystallographic defects in Diamond and their characterization……… 17

3 About the necessity of studying crystallographic defects 20

4 About the necessity of developing non-destructive characterization techniques 22

5 Layout of the thesis 23

References……… ……… 24

Foreword

It is known that about 50-60% of all energy consumption comes under the form of electrical energy, and this percentage will increase in the future [1] Therefore, power electronic devices play a very important role in order to save, share and deliver energy There have been substantial research efforts aimed at developing high frequency power devices over the last few years With a promising potential for applications in power electronics, Silicon Carbide (SiC), Gallium Nitride (GaN) and Diamond (C) are competitive materials Due to its relative maturity, SiC might finally be the most realistic choice for the future very high power applications The excellent electronic and physical properties of diamond and SiC make them one of the materials best suited to the fabrication of high power electronic devices [2] Besides, many other applications could benefit from SiC and Diamond development, such as high frequency, high temperature and hostile environment operating devices [3] However, a major difficulty with SiC and Diamond materials has been the presence of crystal defects It has been demonstrated that they can produce premature electrical failures in most power electronic devices [4, 5] The development of SiC or diamond based devices at a commercial level is strongly dependent on the substrate quality A total elimination of extended defects has not yet achieved It is also well recognized that a precise determination of the nature of crystal defects is very important in order to understand their mechanism of creation and consequently to improve materials quality by a better control of the growth conditions Reducing production costs while improving materials quality should thus provide the breakthrough needed to ensure a definitive economic supremacy

Although many techniques have been used to identify crystal defects in wide band gap semiconductor materials [6-9], it is highly desirable to develop fast and low cost characterisation techniques for materials defect identification The research topic of this

thesis deals with the development of analysis techniques based upon the use of optical microscopy The choice of using birefringence microscopy is due to the fact that it is a non-destructive method and that is involves only a low-cost equipment, as compared to other techniques [10] It relies on the fact that the refractive index is a function of materials stress, so that the observation of the birefringence around dislocations can provide useful information about the related stress field and dislocation characteristics [11] Although the dislocation core is quite small, the associated stress field can sometimes be sensed over hundreds of micrometers, and thus the technique can reveal various defects In ref [12], dislocations induced birefringence in SiC materials has been already reported and modelled, but the analysis was restricted to the case of micropipes

It thus needed to be extended to and modelled in the case of smaller and even unit dislocations, and to other wide band gap semiconductors such as Diamond

The work of this thesis is essentially dedicated to the identification of crystal structural defects The main purpose is to provide further understanding of the characteristics as well as the source of extended defects in SiC and Diamond materials This thesis thus provides a detailed discussion of birefringence characterization problems related to SiC and diamond materials, so as to assess the dislocation density and its distribution, the residual stress, and identify the nature of these dislocations

The thesis is divided into three parts In the first part, we describe the theoretical background and the practical details useful for understanding the method of birefringence microscopy In a third part we present and discuss the results obtained from birefringence microscopy applied to dislocations in SiC substrates Results about diamond are presented in chapter 4 before we give a general conclusion

This research work has been achieved at the Laboratory of Materials and Engineering Physics (LMGP), Grenoble INP, France

1 A brief review of Silicon Carbide (SiC)

Silicon carbide (SiC) is a wide band gap semiconductor material with unique physical properties In a semiconductor technology based on silicon carbide substrates, the excellent properties of the SiC material make it suited for a large number of applications This section gives a brief introduction about the structure, properties and crystallographic defects of the SiC material

1.1 Structure and properties of Silicon Carbide (SiC)

1.1.1 Crystal structure

• Basic structure

Figure 1.1 The tetrahedron of SiC [1]

The unit structure of silicon carbide is illustrated in Figure 1.1 It is described by a

tetrahedron in which each silicon atom is surrounded by four carbon atoms [13] The distance between the carbon atoms is determined to be 3.08 Ǻ and the SiC bond length is equal to 1.89Ǻ [13] Reciprocally, each carbon atom is also surrounded by four silicon atoms in a similar tetrahedral structure The way these tetrahedrons are combined to form the SiC lattice is described below

• Polytypism

SiC crystals exist in the form of about 250 polytypes, each with a different crystal structure They are characterized by a different stacking sequence of the Si-C layers [13-15] To describe the polytypes of SiC, three notational systems are used: notation of Ramsdell, notation of Jagodzinski and the ABC description, but the most common used notations is the Ramsdell notation [13]: a number is used, which corresponds to the number of bilayers in a unit cell, and a letter indicates the structure of the crystal: C for cubic, H for hexagonal, and R for rhombohedral [13-15]

Figure 1.2(a) Stacking sequence of packed close

The stacking sequence is described as follows: each bilayer is formed by a set of adjacent

Si and C atoms with a bond direction parallel to the c-axis Then, to construct the lattice, each couple of Si-C atoms so defined are assimilated to a sphere, and the lattice is obtained by the classical rules which dictate a compact, hexagonal stacking of spheres: The first layer is called the A layer and the spheres are positioned at A sites In the second

layer the sites can be either of the B type, or of the C type (see Fig.1.2 (a)) In Figure

1.2(a), the sites A, B and C are projected in the basal plane Every layer, occupied in one

of the three positions A, B or C, creates the closed packed stacking [50, 51] For instance,

the only cubic, periodic stacking sequence is A B C A B C and the simplest hexagonal

sequence is A B A B A B [50, 51]

Among the 250 polytypes of SiC actually known, only a few of them, such as the 3C, 6H and 4H polytypes, are the subject of intensive research and development By using a classical ABC notation, the stacking sequence of the cubic polytype 3C-SiC is ABC The stacking sequences of the two important polytypes, 6H-SiC and 4H-SiC, are ABCACB

and ABCB…, respectively [14, 15, 62, 53] Figure 1.2(b) shows the stacking sequence of

the 3C, 6H and 4H shown in the [112�0] zone axis [16]

Figure 1.2 (b) The three most common polytypes SiC viewed in the [ 112�0] zone axis [16]

1.1.2 Properties of Silicon Carbide

Some electronic properties of silicon carbide are compared with those of other

semiconductor materials in Table 1.1

• Band gap

Silicon carbide is a wide band gap semiconductor material This property makes SiC suited for high temperature applications, since the intrinsic regime is repelled at very high temperatures Depending on the polytype, the band gap of SiC varies between 2.39 eV to 3.33 eV [13, 17]

Table 1.1 Some electronic properties of silicon carbide in comparison with those of other

semiconductor materials [13, 17]

Properties 3C-SiC 4H-SiC 6H-SiC Si GaAs Diamond Band gap (eV) at T < 5K 2.40 3.26 3.02 1.12 1.43 5.5 Electrical breakdown field

Physical stability Excellent Excellent Excellent Good Fair Very good

• Breakdown electric field strength ( critical field )

The critical electric field is one of the most important properties for power device applications Due to its wide band gap, the breakdown field of SiC is 10 times that of Si [13, 17]

• Saturated drift velocity

A saturated drift velocity is an important property for high frequency devices The saturated drift velocity of SiC is two times higher than that of Si [13, 17]

The relation between the critical field and saturated drift velocity is described by the

Johnson’s Figure of Merit, as shown by the following equation [13, 17]:

𝐽𝐹 = 𝐸𝐵4𝜋2𝑣𝑠𝑎𝑡22 (1.1) where 𝐸𝐵2 and 𝑣𝑠𝑎𝑡2 are the breakdown field and saturated drift velocity, respectively

1.2 Crystallographic defects in SiC and their characterization

In SiC material, the most common crystallographic defects are extended defects They include micropipes (hollow-core dislocation), closed-core screw dislocations, threading edge dislocations, grain boundaries, etc [18-20]

The two major types of dislocations in hexagonal SiC are dislocations with the direction

of dislocation line along [0001] (threading type) and [112�0] (basal plane type) In references [60, 61], the authors indicated that the slip plane of all the hexagonal SiC polytypes is the (0001) basal plane and the Burgers vector of the dislocations is b = a/3(21�1�0) These dislocations are dissociated into two partials with Burgers vectors b = a/3(11�00) and b = a/3(101�0) The Burgers vectors of closed-core dislocations are 1c or 2c for 4H-SiC and 1c for 6H-SiC (c is the lattice constant along the [0001] growth axis, c

≈ 10A° for 4H and c ≈ 15A° for 6H) [18, 19])

Among various defects appearing in SiC wafers, micropipes and closed-core screw dislocations are of particular interest because they are one of the major factors limiting the application of SiC [21] Many methods are used to characterize defects in SiC

material, such as synchrotron white beam X-ray topography (SWBXT) [6, 7, 9], atomic force microscopy (AFM) [19], scanning electron microscopy (SEM), transmission electron microscopy (TEM) [22, 8, 24], scanning laser microscopy (SLM) and infrared light-scattering tomography (IR-LST) [25], deep-level photoluminescence (PL) [26], etching in molten potassium oxide (KOH) [23, 25, 27, 28], polarized light microscopy (PLM) or birefringence topography [11] Among the various characterization methods, X-ray topography is a very powerful technique to observe crystal defects in SiC

X Ma [19] investigated superscrew dislocation structure in silicon carbide using a combination of polarized light microscopy (PLM) and atomic force microscopy (AFM)

He has demonstrated that this method can precisely determine the magnitude and the sign

of Burgers vector for each dislocation or micropipe [19] Careful AFM study indicated that in high quality commercial 6H-SiC wafers, most micropipes are 4c or larger, and

none of 2c dislocations are open-core [19] Figure 1.3 shows AFM images of different

defect structures around 1c, 2c or 3c screw dislocations [19]

Figure 1.3 AFM images of different defect structures around 1c, 2c and 3c screw

dislocations [19]

Transmission electron microscopy (TEM) is suitable for the quantitative analysis of the dislocation structure However, the conventional TEM technique, such as a weak-beam

dark-field (WBDF) method has some limitation when the Burgers vector b needs to be

accurately determined Y Sugawara et al [29] developed a TEM sample preparation technique for a low dislocation density of 4H-SiC wafer by combining the KOH+Na2O2etching and the focused ion beam (FIB) technique W.M Vetter and M Dudley [24, 33]

have directly determined the magnitude of the Burgers vector by using synchrotron white beam x-ray topography (SWBXT)

Figure 1.4 shows such back-reflection topography of a small area of a 6H-SiC wafer In

the image, the dislocations induce white circles They suggested that the smallest of the white circles represent the 1c dislocations In recent years, the birefringence technique has become an important method to visualize the residual stress and to characterize the type of defects present in transparent crystals This method was initially studied by Ma et

al [18, 19] in the case of silicon carbide As shown in Figure 1.5, the birefringence

method can be used to reveal and map the defects in silicon carbide (SiC) wafers [21] By this method, micropipes are usually detected because they induce butterfly patterns

Figure 1.4 The back-reflection topography of a 6H-SiC wafer The dislocations appear as

white circles [33]

Figure 1.5 The birefringence image recorded from a 6H-SiC wafer [21]

Defect etching of SiC in molten potassium hydroxide (KOH) is a very common method

to detect dislocations S A Sakwe et al have developed a KOH etching procedure for silicon carbide In their opinion, etching time and temperature are of primary importance during KOH defect etching of SiC [30] Optimization of KOH etching parameters was carried out by analyzing a series of etching experiments for p-type SiC wafers (See

Figure 1.6) [30]

Figure 1.6 Optical microscope images of the etched p-type 6H-SiC wafers used for

determination of optimum etching conditions [30]

Several publications reported on the etching behaviour of SiC [28, 30, 31, 32] B Kallinger et al have studied the etching behaviour of threading dislocations in n- and p-type 4H-SiC substrates by KOH etching and synchrotron X-ray topography [31] They concluded that KOH etching does not provide full information about the dislocation

structure Figure 1.7 shows a comparison of etch pits with X-ray topography Recently,

Y Yao et al have reported a novel etching technique using KOH+Na2O2 to reveal dislocations in n-type 4H-SiC (n > 1019 cm-3) ( see Figure 1.8) [23] In their study, X-ray

topography (XRT) has been used to examine the accuracy of KOH+Na2O2 (KN) etching and to identify dislocation types in n-type 4H-SiC As a result, KN etching is a more reliable method than KOH etching [23]

Figure 1.7 Comparison of etch pits (a) with X-ray topography (b) for n-type 4H-SiC

substrate with n > 2x10 18 cm -3 [31]

Figure 1.8 Optical microscope images of the Si-face of n-type 4H-SiC: (a) after the first-time

KOH etching at 510 °C for 4 min, (b) after the second-time KN etching at 510°C for 4 min

Pits revealed as threading screw dislocations (TSDs) by KN etching are labelled with “S” [23]

A one-to-one correlation has been found between large hexagonal pits and XRT contrast

of threading screw dislocations, and between small hexagonal pits and small dot like

XRT contrast of threading edge dislocations [23] Figure 1.9 shows a comparison

between the KN etched Si-face and XRT image [23]

Figure 1.9 (a) Optical microscope image of the Si-face of n-type 4H-SiC after KOH+Na 2 O 2

etching (510 °C, 4 min), (b) Grazing incidence mode synchrotron monochromatic-beam X-ray

topography (SMBXT) image taken from the same sample area before etching [23]

2 A brief review of Diamond

Diamond is one of the most promising semiconductor materials, due to its excellent intrinsic properties Most notable are its extreme hardness and thermal conductivity as well as its wide band gap This section provides the reader with a brief review of Diamond The review focuses on the structure and properties of diamond, crystallographic defects and their characterization

2.1 Structure and properties of Diamond

2.1.1 Crystallographic structure

The unit structure of cubic diamond is illustrated in Figure 1.10 It is described by two

face-centred cubic (FCC) lattices shifted from one another by a quarter of the diagonal of the conventional lattice cell The lattice dimension is about 0.3567 nm The C-C bond length is 0.154nm [36]

Figure 1.10 Unit cell of the cubic diamond

2.1.2 Properties of diamond

The properties of diamonds have been reported by several authors [36-39] Some of the

excellent properties of diamond are presented in Table 1.2 [38]

Table 1.2 Some of the excellent properties of diamond [38]

Fracture toughness (MPa V-1 m-1) 5.5

Coefficient of thermal expansion (ppm K-1) 1.2

- Diamond has high refractive indices in the UV of the spectrum with n = 2.60 at 266nm and n = 2.46 at 405 nm [36, 38] This means that pure diamonds should be

transparent and colourless

- Diamond is an optically isotropic material due to its cubic symmetry

The optical properties of diamond have been reviewed by Zaitsev [36]

• Thermal properties

Diamond is a good heat conductor because of the strong covalent bonding, and in spite of its semiconducting or insulating character Heat transport is ensured by the phonons The thermal conductivity of pure diamond is higher than that of any other materials The thermal conductivity of diamond is measured to be about 3000 Wm-1K-1 at room temperature [37, 38]

• Electrical properties

Diamond is a wide band gap semiconductor with a band-gap of about 5.47 eV [38]

It is known that there are two kinds of diamonds: synthetic and natural diamonds Synthetic diamonds are grown by high-pressure high-temperature (HPHT) or Chemical Vapour Deposition (CVD) methods [36, 37] They are fabricated in a laboratory and often exhibit a yellow colour due to nitrogen impurities Natural diamonds are formed by geological processes under the Earth’s surface [37] Because synthetic diamonds are

cheaper than natural diamonds, they are widely used Table 1.3 presents a comparison of

properties of natural and synthetic diamond [37]

In general, diamonds are divided into types Ia, Ib, IIa and IIb depending on the type of impurities and on their concentrations [37, 39] Type I diamonds contain nitrogen as the main impurity Due to the presence of nitrogen, they absorb in both the infrared and ultraviolet regions [37, 39] The difference between type Ia and Ib is the content of nitrogen impurities Type Ia diamonds contain more nitrogen impurities than that of type

Ib Almost all synthetic diamonds are of type Ib

Contrary to type I diamonds, type II diamonds contain only a very low amount of nitrogen impurities They absorb in a different region of the infrared and transmit in the ultraviolet below 225nm [37, 39]

Table 1.3 Some properties of natural and synthetic diamonds [37]

Property (typical values)

Type Nitrogen content

(ppm) Colour

Thermal conductivity (Wm -1 K -1 ) (300K)

Dislocation density

IIa natural < 10 Brown/ colourless 1800-2200 108-109cm-2

2.2 Crystallographic defects in Diamond and their characterization

Diamonds contain various types of defects such as inclusions, twins, stacking faults, dislocations, etc [43-46] Dislocations are very common defects in both natural as well as

synthetic diamonds [44] As shown in Table 1.3, in general the dislocation density of

diamond is about 104-106 cm-2 [38] However, the type IIa natural diamond contains relatively high densities (up to 108-109 cm-2)

Because the synthetic high-pressure, high-temperature (HP-HT) type IIa diamond does not contain as many detectable nitrogen or other impurities, it is expected to be a suitable substrate for CVD layers to be grown on it P M Martineau et al [44] have reported the results of X-ray topography of both high-pressure high-temperature (HP-HT) and

chemical vapour deposition (CVD) synthetic diamond The results suggested that a high quality HPHT type IIa synthetic diamond offers significant advantages over type Ib

material for growing homoepitaxial diamond (see Figure 1.11) [44].

Figure 1.11 Four {111} X-ray projection topographs of a single crystal CVD diamond layer

on its type IIa HPHT synthetic diamond substrate [44]

H Umezawa et al [46] have reported the characterization of crystallographic defects in CVD epitaxial film grown on a HP-HT type Ib single crystal substrate The results of X-ray topography indicated that the dislocation types were determined to be edge or mixed

dislocations (see Figure 1.12) [46] Y Kato et al elucidated the nature of the dislocations

in type IIa single crystal diamond using X-ray topography (XRT) [49] They indicated that almost all dislocations in the observed sample are edge dislocations and mixed 45°

dislocations with Burger vector a/2[011] [49] (see Fig 1.13).

Figure 1.12 (a) XRT image of g = [404], (b) higher magnification image of g = [404] at the

low density defect region [46]

Figure 1.13 XRT of type IIa diamond: (a) XRT image (g = [1-13]), (c) XRT image (g =

substrates Figure 1.14(a) is taken from their work and represents transmission X-ray

topography of the diamond (220) plane using Mo-Kα radiation According to the (220) diffraction image, the density of defects is determined to be 3.5 x103cm-2 As shown in

Figure 1.14(b), the cross-section image indicated that most of line defects along the

(001) growth direction seem to be generated at the interface between the film and the

substrate As shown in Figure 1.15, X-ray topography of (220), (-220) and (400)

diffraction plane suggest that the dominant defects are most likely mixed dislocations

Figure 1.15 X-ray topography of (a) (220), (b) (-220) and (c) (400) diffraction planes using

Mo-K α radiation [50]

Table 1.4 summarizes the experimental and analyzed results of the dislocation studies

using X-ray topography

Table 1.4 Burgers vector and dislocation type in diamond

Burgers vector Dislocation type References

a/2[110], a/2[011�], a/2[01�1] Edge dislocation [6], [23], [20], [8]

a/2[011], a/2[101] Mixed dislocation (45°) [6], [3], [32]

a/2[101], a/2[01�1 ], a/2[011�] Mixed dislocation (60°) [6], [20], [8]

3 About the necessity of studying crystallographic defects

Wide band gap (WBG) materials such as SiC and diamond have attracted considerable attention as advanced materials for high frequency, high power, high temperature and

harsh environment applications [17] However, for various reasons related to materials technology, the widespread application of WBG semiconductor materials has been limited

Defects have been reported as degrading the performance of power devices For example, they increase the leakage current and reduce the breakdown voltage of SiC devices The influence of dislocations in n-type 4H-SiC epitaxial wafers on the thermal oxides has been discussed [52] It is demonstrated that a decrease in the dislocation density of SiC wafers, in particular, the basal plane ones, is indispensable for further improving the thermal oxides of the SiC wafer [52-54] Actually the most detrimental defects are basal plane dislocations which transform into partials and stacking faults [60, 61] Y Wang et

al studied the effects of defects on the electrical properties of 4H-SiC Schottky devices, such as barrier height and the breakdown voltage The results indicated that the presence

of micropipes also affects the breakdown voltage [59]

It is well known that there are many potential applications of diamonds because of their unique physical, mechanical and optical properties However and despite the rapid advancement in the research and application of diamond, there are still many problems Crystal defects are one of the most important problems [42] It was demonstrated that some types of dislocations critically influence the reliability of power devices [32-34] In recent research, diamond-based Schottky barrier diodes have been shown to be interesting for electronic device applications However, there are some limitations on power electronic device applications due to the defects present in the CVD diamond layer [50] High quality crystals are therefore essential for a stable performance of diamond power devices

As mentioned above, the defects can affect the properties of the materials In order to improve material quality as well as to increase the range of technological applications of wide band gap materials, it is necessary to decrease the number of crystallographic defects In order to be able to control or totally eliminate these defects, understanding

their nature and origin as well as the role they play in device failure is therefore very important

X-ray topography offers a non-destructive method for studying the dislocation It is a powerful technique to characterize the various defects in semiconductor materials The high potential of x-ray topography allows one to provide useful information on the defects They can categorize the type of those defects with the use of various synchrotron white beam x-ray topographic images Thus, from the viewpoint of structure analysis science, synchrotron white beam x-ray topography is an actually useful method to investigate the dislocations However, in principle, the monochromatic x-ray topographic measurement should be applied to wafers with adequate quality This means that the measurement system for white beam x-ray topography is not suitable for the crystals that have relatively high dislocation densities The requirement of a synchrotron light source also limits its use for routine characterization in a laboratory or industrial setting

Because wide band gap materials are still very expensive, non-destructive characterization techniques are of primary interest From the industrial point of view, the current development of semiconductor materials requires a method for complementing

the monochromatic or white beam x-ray topography It is essential to develop an economic, rapid, and non-destructive characterization technique for identifying crystallographic defects

5 Layout of the thesis

From the considerations detailed above, it is highly desired to develop fast and low cost characterization techniques for defect identification Our research topic deals with the assessment, modelling and development of such an analysis technique Our work thus focuses on the identification and the characterization of crystallographic defects in wide band gap semiconductor materials The thesis consists of three main chapters following this introduction and is organised as follows:

Chapter 2

Chapter two provides the theoretical background about birefringence, a description of the

rotating polariser method and birefringence modelling

Chapter 3

In Chapter three, the results of the investigation of the dislocations in Silicon Carbide

are discussed We provide both experimental data and simulated results of various dislocation patterns appearing in SiC material This chapter successively presents the influence of the residual stress upon the birefringence pattern, the observation of dislocations with a small component of the Burgers vector in the basal plane, the comparison between birefringence measurement and KOH etching, the correlation between the birefringence and substrate thickness and the dependence of the birefringence pattern on the dislocation length along the z-axis

Chapter 4

Chapter four presents the results of the investigation of the dislocations in diamond We

provide experimental birefringence images due to dislocations and inclusions in diamond

We present the results of identification of the dislocations in diamond by the combined use of experiment and simulation Dependence of the birefringence pattern on the dislocation length along the z-axis is described Dislocation propagation from the HPHT substrate into the CVD layer is also discussed

References

[1] http://siced.com/download/CY5063ab4aX1190ed29602XY353c/Abstract_Peters.pdf

[2] Q Wahab et al., Mater Sci Forum 333-342 (2000), 1175

[3] C M Johnson, Int J Electron 90 (2003), 667

[4] N Tsubouchi, Y Mokuno, H Yamaguchi, N Tatsumi, A Chayahara, S Shikata,

Diamond Relat Mater 18 (2009) 216-219

[5] H Umezawa, K Ikeda, R Kumaresan, N Tatsumi, and S Shikata, Increase in

reverse operation limit by barrier height control of diamond Schottky barrier diode, IEEE

Electron Device Lett 30 (2009) 960-962

[6] W M Vetter, The characterization of defects in silicon carbide crystals by X-ray

topography in the back reflection geometry, Defects and Diffusion Forum 230-232 (2004)

1-16

[7] M Dudley, X Huang and W M Vetter, Contribution of x-ray topography and high

resolution diffraction to the study of defects in SiC, J Phys D: Appl Phys 36 (2003)

A30-A36

[8] W Si, M Dudley, R Glass, V Tsvetkov and C H Carter, Jr, Experimental studies of

hollow core screw dislocations in 6H-SiC and 4H-SiC single crystals, Mat Sci Forum

[10] T Ouisse, D Chaussende, L Auvray, E Pernot and R Madar, Mat Sci Forum 615-617

(2009) 271-274

[11] H Takeuchi, Circular polariscopic analysis of strains in semi-insulating SiC wafer: Its high potential to complement the information obtained from monochromatic X-ray

topography, Review Scientific Instruments 82 (2011) 033907

[12] T Ouisse, D Chaussende and L Auvray, Micropipe induced birefringence in 6H

silicon carbide, J Appl Cryst 43, 122-133, 2010

[13] Stephen E Saddow and A Agarwal, Advances in Silicon Carbide Processing and

Applications, Bonston London, 2004

[14] J Schardt, J Bernhardt, U Strarke, K Heinz, Atomic structure of hexagonal 6H-

and 3C-SiC surfaces, Surface Review and Letters 5(1) (1998) 181-186

[15] M H Hong, A V Samant, and P Pirouz, Stacking fault energy of 6H-SiC and

4H-SiC single crystals, Philosophical Magazine A 80 (2000) 919-935

[16] U Lindefelt, H Iwata, A Oberg and P R Briddon, Stacking faults in 3C-, 4H-, and

6H-SiC polytypes investigated by an ab initio supercell method, Phys Rev B 67 (2003)

155204

[17] V V Buniatyan and V M Aroutinounian, Wide gap semiconductor microwave

devices, J Phys D: Appl Phys 40 (2007) 6355-6385

[18] X Ma and T Sudarshan, Nondestructive defect characterization of SiC substrates

and epilayers, J Electronic Mat 33 (5) (2004) 450

[19] X Ma, A method to determine superscrew dislocation structure in silicon carbide,

Mater Sci Eng B 129 (2006) 216-221

[20] L Ning, X Hu, X Xu, X Chen, Y Wang, S Jiang and J Li, Birefringence images

of micropipes viewed end-on in 6H-SiC single crystals, J Appl Cryst 41 (2008)

939-943

[21] X Ma, M Dudley, W Vetter and T Sudarshan, Extended SiC defects: Polarized light microscopy delineation and synchrotron white beam X-ray topography ratification,

Jpn J Appl Phys 42 (2003) L1077-L1079

[22] W M Vetter and M Dudley, Transmission electron microscopy studies of

dislocations in physical vapour transport grown silicon carbide, Phil Mag A, 81 (2001)

2885-2902

[23] Y Yao, Y, Ishikawa, Y Sugawara, K Sato, K Danno, H Suzuli, T Bessho, S Yamaguchi, K Nishikawa, Correlation between etch pits formed by molten KOH+Na2O2 etching and dislocation types in heavily doped n+ - 4H-SiC studied by X-ray topography,

J Cryst Growth 364 (2013) 7-10

[24] W M Vetter and M Dudley, Micropipes and the closure of axial screw dislocation

cores in silicon carbide crystal, J App Phys 96 (2004) 348

[25] P Wutimakun, C Buteprongjit, J Morimoto, Nondestructive three-dimensional observation of defects in semi-insulating 6H-SiC single-crystal wafers using a scanning

laser microscope (SLM) and infrared light-scattering tomography (IR-LST), J Cryst

Growth 311 (2009) 3781-3786

[26] M Tajima, E Higashi, T Hayashi, H Kinoshita, and H Shiomi, Nondestructive characterization of dislocations and micropipes in high-resistivity 6H-Si wafers by deep-

level photoluminescence mapping, Appl Phys Lett 86 (2005) 061914

[27] M Kato, M Ichimura, E Arai and P Ramasamy, Etch pit observation for 6H-SiC

by electrochemical etching using an aqueous KOH solution, J Electrochemical Society

150 (2003) C208-C211

[28] J Wan, S Park, G Chung and M Loboda, A comparative study of micropipe

decoration and counting in conductive and semi-insulating silicon carbide wafers, J

Electron Mat 34 (2005) 1342-1348

[29] Y Sugawara, Y Yao, Y Ishikawa, K Danno, H Suzuki, T Bessho, Y Kawai and

Y Ikuhara, Characterization of dislocation structures in hexagonal SiC by transmission

electron microscopy, Mater Sci Forum 725 (2012) 11-14

[30] S A Sakwe, R Muller, P.J Wellmann, Optimization of KOH etching parameters

for quantitative defect recognition in n- and p-type dopted in SiC, J Cryst Growth 289

(2006) 520-526

[31] B Kallinger, S Polster, P Berwian, J Friedrich, G Muller and A N Danilewsky, Threading dislocations in n- and p-type 4H-SiC material analyzed by etching and

synchrotron x-ray topography, J Cryst Growth 314 (2011) 21-29

[32] P Wu, Etching study of dislocations in heavily nitrogen doped SiC crystals, J Cryst

Growth 312 (2010) 1193-1198

[33] M Dudley, S Wang, W Huang, C H Carter Jr, V F Tsvetkov and C Fazi, White

beam synchrontron topographic studies of defects in 6H-SiC single crystals, J Phys D:

Appl Phys 28 (1995) A63-A68

[34] C Ge, N Ming, K Tsukamoto, K Maiwa and I Sunagawa, Birefringence images of

screw dislocations viewed end-on in cubic crystals, J Appl Phys 69 (1991) 7556-7563

[35] A K Dutta, P K Ajmera, Simulation and observation of the images of dislocations

in (100) silicon using infrared piezobirefringence, J Appl Phys 69 (1991) 7411-7418

[36] A M Zaitsev, Optical properties of Diamond, Berlin: Springer, 2001

[37] R S Balmer, J R Brandon, S L Clewes, H K Dhillon, J M Dodson, I Friel, P

N Inglis, T D Madgwick, M L Markham, T P Mollart, N Perkins, G A Scasbrook,

D J Twitchen, A J Whitehead, J J Wilman, and S M Woollard, Chemical vapour

deposition synthetic diamond: materials, technology and applications, J Phys: Condens

Matter 21 (2009) 364221

[38] V V Buniatyan and V M Aroutinounian, Wide band gap semiconductor

microwave devices, J Phys D: Appl Phys 40 (2007) 6355-6385

[39] R Kalish, Diamond as a unique high-tech electronic material: difficulties and

prospects, J Phys D: Appl Phys 40 (2007) 6467-6478

[40] J E Butler, Y A Mankelevich, A Cheesman, J Ma and M N R Ashfold,

Understanding the chemical vapour deposition of diamond: recent progress, J Phys:

Condens Matter 21 (2009) 364201

[41] B Rezek, D Shin, H Uetsuka, C E Nebel, Microscopic diagnostics of DNA

molecules on mono-crystalline diamond, Phys Stat Sol (A) 204 (2007) 2888-2897

[42] K Ikeda, H Umezawa, K Ramanujam, and S Shikata, Thermally Stable Schottky

barrier diode by Ru/ Diamond, Appl Phys Express 2 (2009) 011202

[43] T Teraji, M Hamada, H Wada, M Yamamoto and T Ito, High quality

homoepitaxial diamond (100) films grown under high-rate growth condition, Diamond

[45] I Friel, S L Clewes, H K Dhillon, N Perkins, D J Twitchen, G A Scarsbrook, Control of surface and bulk crystalline quality in single crystal diamond grown by

chemical vapour deposition, Diamond Relat Mater 18 (2009) 808-815

[46] H Umezawa, Y Kato, H Watanabe, A M Omer, H Yamaguchi, S Shikata, Characterization of crystallographic defects in homoepitaxial diamond films by

synchrotron X-ray topography and cathodoluminescence, Diamond Relat Mater 20

(2011) 523-526

[47] M P Gaukroger, P M Martineau, M J Crowder, I Friel, S D Williams, and D J Twitchen, X-ray topography studies of dislocations in single crystal CVD diamond,

Diamond Relat Mater 17 (2008) 262-269

[48] R C Burns, A I Chumakov, S H Connell, D Dube, H P Godfried, J O Hansen,

J Hartwing, J Hoszowska, F Masiello, L Mkhonza, M Rebak, A Rommevaux, R Setshedi, and P Van Vaerenbergh, HPHT growth and x-ray characterization of high

quality type IIa diamond, J Phys Condens Matter 21 (2009) 364224

[49] Y Kato, H Umezawa, H Yamaguchi, S Shikata, Structural analysis of dislocations

in type-IIa single crystal diamond, Diamond Relat Mater 29 (2012) 37-41

[50] N Tsubouchi, Y Mokuno, H Yamaguchi, N Tatsumi, A Chayahara, S Shikata, Characterization of crystallinity of a large self-standing homoepitaxial diamond film,

Diamond Relat Mater 18 (2009) 216-219

[51] H Umezawa, N Tokuda, M Ogura, Sung-Gi Ri, S Shikata, Characterization of leakage current on diamond Schottky barrier diodes using thermionic-field emission

modelling, Diamond Relat Mater 15 (2006) 1949-1953

[52] J Senzakia, K Kojimab, T Katoc, A Shimozatod and K Fukuda, Effects of

Dislocations on Reliability of Thermal Oxides Grown on n-type 4H-SiC Wafer, Mater

Sci Forum 483-485 (2005) 661-664

[53] H Tsuchida, M Ito, I Kamata, and M Nagano, Formation of extended defects in

4H-SiC epitaxial growth and development of a fast growth technique, Phys Status Solidi

B 246 (2009) 1553-1568

[54] M Skowronski, S Ha, Degradation of hexagonal silicon carbide based bipolar

devices, J Appl Phys 99 (2006) 011101

[55] S Ha, P Mieszkowski, M Skowronski, L B Rowland, Dislocation conversion in

4H silicon carbide epitaxy, J Cryst Growth 244 (2002) 257-266

[56] M Dudley, H Wang, F Wu, S Byrappa, B Raghothamachar, G Choi, E K Sanchez, D Hansen, R Drachev, S G Mueller, and M J Loboda, Formation mechanism of stacking faults in PVT 4H-SiC created by defection of threading

dislocations with Burgers vector c+a, Mater Sci Forum 679-680 (2011) 269-272

[57] N Ohtani, M Katsuno, H Tsuge, T Fujimoto, M Nakabayashi, H Yashiro, M Sawamura, T Aigo, T Hoshino, Propagation behaviour of threading dislocations during

physical vapour transport growth of silicon carbide (SiC) single crystals, J Cryst Growth

[61] S Amelinckx, G Strumane and W W Webb, J Appl Phys 31 (1960) 1359

[62] J P Hirth and J Lothe, Theory of dislocations (1982), New York

[63] W T Read, Jr Dislocations in crystals (1953), London

Chapter 2

Birefringence and Rotating

polariser method

1 Introduction 32

2 Birefringence or Double refraction 32

2.1 The dielectric tensor and the refractive index 32 2.2 Birefringence 36

3 Elasticity 39

3.1 Stress and strain 39

3.1.1 Stress 39 3.1.2 Strain 41 3.2 Hooke’s law 42 3.3 Relation between compliance and stiffness 43 3.4 The matrix and tensor notations 43 3.5 Transformation rule of the stress tensor 44

4 Stress- induced birefringence 47

5 Birefringence microscopy 49

5.1 Introduction 49 5.2 Conventional set-up for birefringence measurements 51

5.2.1 The nature of light 51 5.2.2 Linear and circular polarized light 52 5.2.3 Quarter-wave plate 53 5.2.4 Plane polariscope 54 5.2.5 Circular polariscope 55 5.3 Experimental setup of the rotating polarised method 56

6 Birefringence modelling 59

6.1 Birefringence images of a dislocation in 6H-SiC crystals 59

6.1.1 Introduction 59 6.1.2 Birefringence modelling 60 6.1.3 The calculation of the residual stress field and birefringence image 62 6.2 Birefringence images of a dislocation in diamond 65

6.2.1 Introduction 65

6.2.2 The calculation of the birefringence image of a dislocation in Diamond 65 References 70