The Atomic and Electronic Structure of Dislocations in Ga Based Nitride Semiconductors Imad Belabbas, Pierre Ruterana, Jun Chen, Gérard Nouet

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The atomic and electronic structure of dislocations in Ga based nitride semiconductors Imad Belabbas, Pierre Ruterana, Jun Chen, Gérard Nouet

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Imad Belabbas, Pierre Ruterana, Jun Chen, Gérard Nouet. The atomic and electronic structure of dislocations in Ga based nitride semiconductors. Philosophical Magazine, Taylor & Francis, 2006, 86 (15), pp.2245-2273. 10.1080/14786430600651996. hal-00513682

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HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Philosophical Magazine & Philosophical Magazine Letters

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The atomic and electronic structure of dislocations in Ga based nitride semiconductors

Journal: Philosophical Magazine & Philosophical Magazine Letters

Manuscript ID: TPHM-05-Sep-0420.R2

Journal Selection: Philosophical Magazine

Date Submitted by the 08-Dec-2005 Author:

Complete List of Authors: BELABBAS, Imad; ENSICAEN, SIFCOM Ruterana, Pierre; ENSICAEN, SIFCOM CHEN, Jun; IUT, LRPMN NOUET, Gérard; ENSICAEN, SIFCOM

Keywords: GaN, atomic structure, dislocations, electronic structure

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30 31 Abstract 32 33 34 35 The atomic and electronic properties of dislocations in III-N semiconductor layers, especially 36 r 37 GaN are presented. The atomic structure of the a edge threading dislocation is now well 38 39 established with three different cores (8 or full core, 5/7 or open core and 4 atom ring). The 40 41 42 use of atomistic simulations has confirmed these atomic structures and has given a good 43 44 understanding of the electronic structure of the screw dislocation. Partial dislocations which 45 46 are mostly confined in the area close to the substrate are now also being investigated. It is 47 48 49 becoming clear that the electrical activity of all these defects is dependent on the layer quality, 50 51 which is governed by the growth conditions. 52 53 54 55 56 57 58 59 60

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1 2 3 4 1. Introduction 5 6 During the last decade, III-V nitride semiconductors have taken an important part in 7 8 9 optoelectronic devices since the first commercial light emitting diode (LED) in 1993 10 11 fabricated from metal organic vapour phase epitaxy (MOVPE) GaN/InGaN heterostructures 12 13 containing a very large number of threading dislocations (10 10 cm -2) [1]. These LEDs were 14 15 16 reliable althoughFor the dislocation Peer density Review was higher compared Only to LEDs based on GaAs which 17 18 emitted in the red region with defect densities below 10 2-10 3 cm -2. The nature and properties 19 20 21 of the dislocations in GaN needed to be understood, and the first reports tended to show that 22 23 these dislocations should have at least a particular atomic structure which allows them to be 24 25 non-active in the electronic processes [2]. By conventional transmission electron microscopy 26 27 28 (TEM), it was shown that the only dislocations which formed in wurtzite GaN corresponded 29 r r r r r 30 to the dislocations of the hexagonal lattice with the Burgers vectors b = a , a + c and c [3- 31 32 33 4]. The non activity of threading dislocations was assumed in the first theoretical report on the 34 r 35 atomic structure of the a edge threading dislocation; it was proposed that the edge threading 36 37 dislocation should have either a core based on an 8 atom ring with the dangling bonds 38 39 40 reconstructed along the [0001] line or an empty core [5]. At the same time, a theoretical 41 42 investigation of the motion of the prismatic threading edge dislocations and of the basal screw 43 44 dislocations in GaN concluded that the mobility of the dislocations in GaN was very small at 45 46 -10 -16 47 room temperature, a factor of approximately 10 to 10 with respect to GaAs, which could 48 49 help to explain the remarkable reliability of GaN based LED [6]. 50 51 52 A confirmation of the atomic structure came from the first report of Z-contrast results 53 r 54 using high resolution scanning transmission microscopy [7], it was suggested that the a edge 55 56 threading dislocation in GaN should have the reconstructed 8 atom core structure. In the 57 58 59 meantime, extensive experimental work had been done on other extended defects which 60

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1 2 3 seemed to be typical for the GaN; these were prismatic stacking faults [8] and inversion 4 5 6 domains [9-10]. 7 8 At the same time, the electrical properties investigations were also analysed showing 9 10 that GaN nitride layers had quite low carrier mobility due to the presence of the large 11 12 13 densities of dislocations [11]. In fact, it was becoming clear that in order to fabricate devices 14 15 such as lasers in which there is propagation of carriers in the basal plane, the density of 16 For Peer Review Only 17 18 threading dislocations needed to be decreased. As a consequence, the first 10 000 hours life 19 20 time laser diode was fabricated in a GaN layer grown using epitaxial lateral overgrowth and 21 22 having an average threading dislocation density <10 8cm -2 [12]. So, it was necessary to carry 23 24 25 out extensive work on the dislocations in order to explain their true behaviour in GaN layers. 26 27 Simultaneously to the Z-contrast report, our high resolution transmission electron microscopy 28 29 (HRTEM) investigation showed that the edge threading dislocation had more than the 8 atom 30 31 32 core configuration [13]. Mainly, in agreement with the theoretical work of Wright [14] as the 33 34 open core configuration could not be distinguished with the proposed 5/7 atom structure in 35 36 HRTEM observations. 37 38 39 During the last few years, a large number of investigations have been carried out on the 40 41 structure and properties of all types of dislocations in GaN as well as the possible effect of 42 43 44 deviation from stoichiometric composition [15-16] and impurities [17]. Latterly, this effort 45 46 has also been focused on the partial dislocations and their connections to other extended 47 48 defects [18-19]. 49 50 51 In this paper, we discuss the numerous results that have been reported along with our 52 53 contribution on experimental HRTEM and theoretical investigation of these defects. 54 55 Typically, our work has allowed to determine the multiple configuration of the threading edge 56 57 58 dislocation and to clarify the crystallographic relationships between them [20-21]. The related 59 60 study of electronic properties is a topic of high interest and different methods have been used

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1 2 3 to calculate the energy and electronic structure of defects in semiconductors. Empirical 4 5 6 potentials still provide guidance in the most complex situations where large sets of atoms 7 8 need to be used, but they cannot give any information on the electronic properties due to their 9 10 analytical characteristics chosen to fit with elastic or phonon properties. The tight-binding 11 12 13 theory has addressed an important field of computational materials science; it is a reasonable 14 15 approach for the calculation of atomic and electronic structures in covalently bonded 16 For Peer Review Only 17 18 materials. In this vein, the density functional theory (DFT)-based tight-binding (DFTB) 19 20 method operating in a self-consistent charge mode has offered a robust and transferable 21 22 method to model a semiconductor crystal on the atomic scale [22]. Indeed, in the case of 23 24 25 dislocations in GaN, insight has been gained in the most recent approaches which are 26 27 multiscale, going from the empirical potentials to deal with large sets of atoms, to ab-initio 28 29 modelling of the core of area [23]. In GaN, many configurations of the dislocations have now 30 31 32 been investigated using these methods, and their atomic and electronic structures are reported 33 34 on and discussed here. In a first part, we describe the crystallography of the structure and 35 36 mainly of the dislocations. The following part deals with the experimental analysis of 37 38 39 prismatic and basal dislocations, and their electrical behaviour. In the end, we discuss the 40 41 atomistic simulation of the dislocation cores, and the calculations of their electronic 42 43 44 structures. 45 46 47 48 49 50 2. Crystallographic data 51 52 53 2.1. Structure 54 55 Gallium nitride, GaN, crystallises in the cubic system with the zincblende form 56 57 58 (sphalerite) or in the hexagonal system (wurtzite) [24]. For both forms, atoms have a 59 60 tetrahedral coordination and the ideal angle between bonds is 109°5. The sphalerite structure

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1 2 3 corresponds to the zincblende structure, 3C, (space group F 4 3m) with a = 0.452nm. This 4 5 6 structure is identical to the diamond crystal structure with two interpenetrating face-centred 7 8 cubic lattices occupied by nitrogen or gallium, respectively, and shifted along the diagonal by 9 10 11 ¼<111> (Fig.1a). For GaN, the wurtzite structure (space group P6 3mc with the lattice 12 13 parameters a = 0.319nm and c = 0.518nm, c/a = 1.6238) is thermodynamically stable under 14 15 conventional growth conditions on various substrates, e.g. sapphire, silicon carbide,…This 16 For Peer Review Only 17 18 structure, corresponding to the 2H polytype, is described by two hexagonal close-packed 19 20 lattices shifted by u along the <0001> direction (Fig.1b). In the ideal wurtzite structure ( c/a = 21 22 1.633), u is equal to 0.375, for GaN u = 0.377. One lattice is occupied by nitrogen atoms and 23 24 25 the other by gallium atoms, therefore only one family of tetrahedral sites of the hexagonal 26 27 structure is occupied. This requirement may lead to the occurrence of two structural variants 28 29 30 (polarities) during the growth of the layers, corresponding to the orientation of Ga-N bonds 31 32 along the <0001> direction. 33 34 35 (a) (b) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Fig.1: Structures of zinc blende and wurtzite crystals. a) zinc blende unit cell. 51 b) wurtzite unit cell ( Ga: large black spheres, N: small grey spheres) 52 53 54 55 56 The zinc blende structure has only one type of first neighbour distance, which means 57 58 that the four bond lengths in a tetrahedron are equal. This is also valid for a wurtzite structure 59 60 with the ideal values c/a =1.633 and u = 3/8. Otherwise, the bond parallel to the c axis is

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1 2 3 different, within less than 1% for the III-V nitrides. For the second nearest neighbours, the 4 5 6 zinc blende structure has only one type of bond lengths (12 bonds). The wurtzite structure 7 8 presents three types of second neighbours, and for the ideal values, the difference between the 9 10 shortest and the longest bonds is 13% [25]. 11 12 13 14 15 16 2.2. DislocationsFor Peer Review Only 17 18 19 20 In the frame of the linear elasticity theory of isotropic materials, the displacement field 21 22 of the dislocation can be calculated as well as the induced stresses, except in the vicinity of 23 24 the dislocation line or dislocation core where both stress and strain become infinite and this 25 26 27 analysis breaks down. The strain energy of an infinite straight dislocation in a perfect crystal 28 29 is calculated per unit length when the dislocation is contained in a cylinder of radius R. For a 30 31 screw or an edge dislocation, this stored elastic energy is proportional to the square of the 32 33 2 34 Burgers vector, b . The ratio of their energies is equal to the factor (1- ν), ν is the Poisson’s 35 36 ratio, and the energy of an edge dislocation is larger than that of a screw dislocation. The total 37 38 39 energy of the dislocation also includes the energy stored in the dislocation core. In the linear 40 41 elastic theory, the displacements vary slowly; this assumption breaks down in the core region 42 43 and atomistic calculations become necessary to calculate the corresponding energy. 44 45 46 Since the elastic energy of a dislocation is proportional to the square of the Burgers 47 48 vector, this value of b2 may be used to define the stability of a dislocation by applying the 49 50 r r 51 Frank criterion to the splitting of a dislocation with Burgers vector b1 into dislocations b2 and 52 r 53 2 2 2 54 b3 . The splitting takes place only if: (b1) > (b2) + (b3) . Applying this criterion, the possible 55 56 Burgers vectors are only the primitive translations of the lattice. As a consequence, the 57 58 59 Burgers vectors of the perfect dislocations in the zinc blende and wurtzite structures are 60 identical to those of diamond or hexagonal close-packed material, respectively [26] (Table 1).

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1 2 3 Zinc blende Wurtzite 4 r 2 r 2 5 Burgers vector ( b ) (b ) Burgers vector (b ) (b ) 2 2 6 1/2<110> a /2 1/3 < 1102 > a 7 <100> a2 <0001> c2 8 2 2 9 1/3 < 1132 > a + c 10 11 r 12 Table 1: Perfect dislocations in zinc blende and wurtzite structures: Burgers vector (b ) 2 13 and energy (b ). 14 15 16 For Peer Review Only 17 By considering the link between the crystallographic structure of crystals and the 18 19 structure of dislocations, dislocations with Burgers vectors not belonging to lattice 20 21 translations must be present. Such dislocations are defined as partial dislocations and the area 22 23 24 connecting two partial dislocations is faulted (Table 2). As a first approximation, the 25 26 application of the Frank criterion shows that the dissociation of a perfect dislocation into 27 28 partials may take place. 29 30 31 Zincblende Wurtzite r 2 r 2 32 Type Burgers vector (b ) (b ) Type Burgers vector (b ) (b ) 33 Shockley 1/6<112> a2/6 Shockley a2/3 34 1/3 < 10 10 > 2 2 35 Frank 1/3<111> a /3 Frank 1/2<0001> c /4 2 2 2 36 1/6<110> a /18 Frank-Shockley 1/6 < 20 23> a /3+ c /4 37 1/3<001> a2/9 38 1/3<110> 2a 2/9 39 2 40 1/6<301> 5a /18 41 r 42 Table 2: Partial dislocations in zinc blende and wurtzite structures: Burgers vector (b ) 43 2 44 and energy (b ). 45 46 For the nitrides, the perfect dislocations that have been characterised are the prismatic 47 48 r 49 dislocation or edge dislocation b = 1/3< 11 20 >, l = < 0001> with three different atomic cores 50 r 51 and the screw dislocation b = <0001>, l = < 0001> with two atomic cores (Fig.2). 52 53 54 55 56 57 58 59 60 b a c

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1 2 3 4 5 6 7 8 9 10 Full core Open core 11 d e 12 13 r 14 Fig.2: Prismatic dislocation or edge dislocation b = 1/3< 11 20 >, l = < 0001> 15 a: Full core or 8 atom ring, b: 4 atom ring, c: Open core or 5/7 atom ring 16 For Peerr Review Only 17 and screw dislocation b = <0001>, l = < 0001> 18 d: Full core, e: Open core 19 20 In the basal plane, they may be 60° (the angle between the line direction and the 21 22 r r 23 Burgers vector is 60°), b = [ 11 20 ], l = [ 2 1 1 0 ] or screw dislocations, b = [ 11 20 ], l = 24 25 26 [11 20 ]. 27 28 29 30 31 32 33 3. Experimental observations 34 35 36 37 3.1. Prismatic dislocations 38 39 40 41 The heteroepitaxially grown GaN layers on (0001) sapphire substrates whatever the 42 43 growth process, e.g. molecular beam epitaxy (MBE) or metal organic chemical vapour 44 45 46 deposition (MOCVD), are characterised by high densities of threading dislocations running 47 48 across the layer from the layer/substrate interface to the top surface with their line mainly 49 50 9 -2 51 parallel to the <0001> growth direction [27]. This density is in the order of 10 cm in 52 11 -2 53 conventional growth and can go up to 10 cm whatever the growth method; pure edge 54 r r 55 56 dislocation ( b =1/3< 1102 >, l = <0001>) and mixed dislocation ( b = 1/3< 11 23 >, l = <0001>) 57 r 58 concentrations may be comparable and the fraction of pure screw dislocations ( b =<0001>, l 59 60 = <0001>) is usually low: 0.1 to 1% (Fig. 3) [28].

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 Fig. 3: Typical threading dislocations in MBE GaN layers grown on sapphire: 19 20 dark field a) g = 1102 b) g = 0002 [29] 21 22 3.1.1. Edge or mixed threading dislocations 23 24 25 The first observations of these threading dislocations by HRTEM showed that in good 26 27 quality GaN layers grown by MBE at 800°C on (0001) sapphire, two atomic configurations 28 29 coexisted: the 8 atom core and a 5/7 atom core (Fig.4) [13] . 30 31 32 33 34 35 Fig. 4: HREM images along <0001> 36 of the 1/3 < 1102 >edge dislocation: 37 38 8 atom ring (a and b), 39 5/7 atom ring (c and d), 40 (defocus values, a and c:-24nm, 41 b and d:-54nm) [18] 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Later, in the investigation of low and high angle grain boundaries [18], it was shown that 56 57 58 a configuration with a 4 atom core is also present in the GaN layers (Fig.5). The identification 59 60 of the atom cores is based on the analysis of experimental and simulated contrasts of the

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1 2 3 images [30]. This was shown to be in agreement with the atomistic calculations of 4 5 6 stoichiometric configurations [20]. 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 Fig.5: Occurrence of 4 atom ring configurations (arrows) for the 1/3< 1102 > edge dislocation 19 observed in a non symmetric Σ= 7 grain boundary (Black dots delimit the unit periods of Σ= 7, 20 and the white lines the different atom rings: 6 for the perfect crystal, 5/7, 8 and 4 for the cores 21 22 of the 1/3< 1102 > edge dislocation) [18]. 23 24 25 Simultaneously, a report was issued using High Angle Annular Dark Field (HAADF) (Z- 26 27 28 contrast) imaging showing that the edge dislocation atomic structure was made of 8 atom core 29 30 [31]. It was argued that such a core should be the only one occurring in GaN in agreement 31 32 with the theoretical predictions that tried to explain the good electrical and optical properties 33 34 35 of GaN layers. For such low electrical activity, the three-fold coordinated atoms in the core 36 37 had to form dimers along the <0001> line direction. 38 39 In epitaxial GaN layers grown at 800°C on a GaN or AlN buffer layer deposited at 550°C, 40 41 42 low-angle and high angle grain boundaries were found and analysed (Fig. 6) [32]. By electron 43 44 diffraction, grain boundaries were identified with rotation angles in the range 1.5-22°. The 45 46 47 dislocations were still 1/3< 1102 > edge type as deduced from the use of the invisibility 48 r r r r 49 criterion g.b = 0 ( g : diffraction vector,b : Burgers vector). 50 51 52 Three high angle grain boundaries crossing all the GaN layers were perfectly analysed 53 54 from HRTEM images by combining topological theory [33] and image simulation [30]. They 55 56 57 were described by rotations around the <0001> direction and the values of the rotation angle, 58 59 as determined from the diffraction patterns, were 13.2±0.2°, 19±0.2°, and 22.0±0.2° [18]. It is 60 well known that the atomic structure of low angle grain boundaries is periodic and based on a

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1 2 3 regular array of dislocations. This concept was then extended to specific high angle grain 4 5 6 boundaries, establishing that the atomic structure of coincidence grain boundaries is also 7 8 periodic [34]. 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 Fig.6: Plan view along [0001] direction showing arrays of dislocations forming low and high 30 31 angle grain boundaries [32]. 32 33 34 35 These coincidence grain boundaries are defined for specific values of the axis and of the 36 37 38 angle of rotation giving rise to a 3D superlattice, the Coincidence Site Lattice (CSL), common 39 40 to the two adjacent crystals. In the hexagonal system, for rotations around <0001>, angles of 41 42 13.17°, 17.90° and 21.79° lead to CSLs which are characterized by their periodic unit cells 43 44 45 [35]. The common characteristic of the atomic structures of these coincidence grain 46 47 boundaries is the regular array of the cores of the edge dislocation 1/3<1102 >. In Fig.5, 48 49 50 between two black dots delimiting the CSL unit cell, 6 atom rings corresponding to the 51 52 perfect crystal are combined with other atom rings. According to the contrast observed in the 53 54 HRTEM image and by comparison with the simulated images, the cores were identified as 4, 55 56 57 5/7 or 8 atom rings. These investigations have allowed us to show that the above dislocation 58 59 cores are the only structural units, which in addition to the 6 atom unit of the hexagonal 60

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38 39 40 r 41 Fig.7: A nanopipe with a Burgers edge component of 2 a [36] 42 43 44 45 46 47 In conclusion, the atomic structures of the cores of the1/3< 1102 > prismatic edge 48 49 50 dislocations in GaN analysed by HRTEM combined with simulated images present a multiple 51 52 atomic configuration: three atomic structures were identified (8 atom ring or full core, 5/7 53 54 atom ring or open core and 4 atom ring). The 8 atom ring or full core was the only one 55 56 57 identified by HAADF. 58 59 60

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1 2 3 4 5 6 3.1.2. Screw prismatic dislocations 7 8 The first investigations of the surface of GaN layers, grown by MOCVD at 1040°C on 9 10 11 an AlN buffer layer deposited at 450-500°C, using scanning force microscopy have shown the 12 13 presence of tunnel-like defects aligned along the <0001> growth direction. The radii of theses 14 15 tunnels are in the 3.5-50nm range and they propagate along the growth direction. These 16 For Peer Review Only 17 18 defects are called nanopipes. These experimental investigations have also shown that the 19 20 screw dislocation associated with a nanopipe emerges on the top surface as a wide crater with 21 22 60-100 nm radii. By combining these observations with HRTEM analysis, it was concluded 23 24 r 25 that the nanopipes are the open cores of screw dislocations ( b =0001) [39]. This result was 26 27 later confirmed by showing that such defects may alternate from an open (nanopipe) to closed 28 29 30 core along their way to the surface of the epitaxial layer (classical character of a dislocation) 31 32 [40]. The atomic structure of full core screw dislocations was reported in a high resolution Z- 33 34 contrast analysis [31]. The growth mode can affect the dislocation core and as was shown in 35 36 37 hydride vapour phase epitaxy (HVPE) grown materials, screw dislocations are decorated by 38 39 voids or pinholes [41]. The fluctuations in the intensity of the atomic columns in HRTEM of 40 41 42 the HVPE specimens have been attributed to local excess of gallium atoms in the core [42]. 43 44 45 46 3.2. Basal dislocations 47 48 49 GaN layers deposited on top of the (0001) sapphire are characterised by the well known 50 51 epitaxial relationship: (0001) //(0001) and [ 1102 ] //[ 10 10 ] [43]. The network of 52 sap GaN sap GaN 53 54 anions is continued across the interface. The misfit is large (-16.07%) and it is accommodated 55 56 by misfit dislocations in the basal plane. The possible Burgers vectors of the perfect 57 58 59 dislocations are 1/3< 1102 >, and the line directions are < 1102 > leading to pure screw or 60° 60 dislocations according to the angle between the Burgers vector and the line direction.

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1 2 3 After Bragg filtering of HRTEM images, it was shown that this lattice misfit is relaxed 4 5 6 in the first monolayer of GaN with a network of regularly spaced 60° dislocations. A residual 7 8 stress of –2.1% was evaluated near the interface and related to the high density of threading 9 10 dislocations present in the epitaxial layer [44]. 11 12 13 Since threading and misfit dislocations are always present, investigations were carried 14 15 out at an interface between AlN and sapphire in order to analyse the connection of these two 16 For Peer Review Only 17 18 dislocation networks [45]. Molecular Beam Epitaxy (MBE) was used for the deposition of the 19 o 20 AlN buffer on Al 2O3, at 800 C, until a thickness of 40 nm was reached. In HRTEM plan view 21 22 23 images, a set of three-fold moiré patterns due to the overlap of the { 1001 }AlN and { 1102 }sap 24 25 planes is formed at the layer-substrate interface with a mean spacing of 2.16nm instead of 26 27 2.029nm for the theoretical value. This discrepancy means that 7% of the compressive stress 28 29 30 is not relaxed by the misfit dislocations. From the moiré pattern, the occurrence of threading 31 32 dislocations is readily deduced from the terminating moiré fringes (Fig.8). 33 34 35 36 37 38 39 40 41 42 Fig.8: Plan-view HRTEM image showing a 43 translation moiré pattern (a) one set of 44 reflections, (b) a second equivalent set [45] 45 46 47 48 49 50 51 52 53 54 55 56 The dislocation density measurements from various areas of the moiré pattern showed an 57 58 average density in the order of 1.5 x10 11 cm -2 with a lower rate near the top surface of 8x10 10 59 60 cm -2. In figure 9, the white arrows indicate the terminating fringes due to the threading

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32 33 34 35 Fig.9: (a) Threading dislocations imaged by the terminating moiré fringes (b) Schematic illustration of the misfit network 36 37 (c) Fourier filtered image showing only the AlN structure [45] 38 39 40 41 The corresponding missing half-planes are associated with two misfit dislocations of the 42 43 44 interfacial network as shown in Fig.9b. The Burgers vector of each threading dislocation is 45 46 equal to the algebraic sum of the Burgers vectors of the two associated misfit dislocations. 47 48 Similar observations with moiré analysis were carried out on HVPE grown layers on SiC 49 50 51 substrates [46]. Therefore, threading dislocations existing in GaN films can be related to the 52 53 misfit dislocations at the interface with the substrate. This view is complemented by other 54 55 investigations which show that many threading dislocations can originate inside the buffer 56 57 58 layer due to the recombination of stacking faults and subsequent climb of the dislocations in 59 60 the prismatic planes [47].

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1 2 3 4 3.3. Partial dislocations 5 6 7 In MOCVD layers grown on (0001) sapphire, evidence of dissociation in the basal plane 8 9 10 was shown using the weak beam technique and the following mechanism was proposed: 11 r r r r r r r r 12 c + a = ( c 2/ + b ) + ( c 2/ + b ), with b and b being Shockley partials, corresponding to the 13 1 2 1 2 14 15 formation of an intrinsic stacking fault I 1 (Ponce et al. , 1996). However, after introduction of 16 For Peer Review Only 17 dislocations by indentation, dissociation of the perfect screw dislocation or 60° dislocation 18 19 20 into partial dislocations was not observed in the limit of the weak beam resolution, 2nm, 21 22 however stacking faults were present in the nodes formed by the screw dislocations [48]. In 23 24 hexagonal structures, three basal faults are possible: two intrinsic I 1 and I 2 and one extrinsic E. 25 26 27 I1 is formed by removing the B plane above the A plane and shearing the remaining part by 28 29 1/3 < 10 10 >, I 2 is formed by considering only the shear, and E by inserting one C plane 30 31 32 between two adjacent basal planes. The energy of the basal stacking faults was calculated 33 2 34 using DFT: I 1 = 18, I 2 = 43 and E = 69 mJ/m [49, 50]. They are of the low-energy type. In 35 36 HRTEM, the density of stacking faults near the interface with the substrate is very high, most 37 38 39 of them are of the I 1 and I 2 types even if segments of the E fault were also observed and partial 40 41 dislocations were identified. 42 43 The I fault was interpreted as the climb-dissociation process: 44 1 45 46 of the 1/3< 1102 > following the reaction: 47 48 49 1/3< 1102 > 1/6< 2032 > + 1/6< 0223 > 50 51 or of the <0001> perfect dislocation: 52 53 54 <0001> 1/6< 2032 > + 1/6< 2203 >. 55 56 The I 2 fault results from the shear of the structure leading to a partial dislocation loop, the 57 58 59 two partial dislocations bounding the basal fault have opposite Burgers vectors 1/3< 10 10 > 60 [51]. Partial dislocations, 1/3< 1001 >, can also be formed at the intersection of a basal stacking

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1 2 3 fault with an inversion domain [19]. Besides the above dislocations, the dissociation of the 4 5 r r 6 mixed a + c dislocation, has recently been reported from Z contrast observations, where the 7 8 edge and screw cores were separated by a stacking fault lying in a { 1001 } plane. As this 9 10 11 dissociation is not energetically favourable, it was assumed to occur in the presence of point 12 13 defects or impurities [52]. 14 15 16 For Peer Review Only 17 18 3.4. Electrical properties of the threading dislocations in GaN 19 20 21 Seeing the high brightness of the first GaN based devices which contained a very large 22 23 number of threading dislocations, it has first been assumed that the electrical activity should 24 25 be taken as substantially low. In the last ten years, a number of reports have shown that this is 26 27 28 not the case after the use of two techniques: the scanning probes in the atomic force 29 30 microscope that mostly analyse the properties of the individual defects close to the sample 31 32 surface, and cathodoluminescence (CL) in TEM. 33 34 35 36 37 3.4.1. Scanning probe microscopy investigations 38 39 40 In their leakage current comparative work on GaN based devices from layers grown by 41 42 HVPE and MBE, Hsu et al . showed that the reverse bias leakage was not uniformly 43 44 distributed in the sample [53]. A small portion of the sample was found to be responsible for 45 46 47 the majority of the leakage. The correlation between reverse bias leakage locations and 48 49 topographic hillocks in samples suggested that reverse bias leakage primarily occurred at 50 51 screw/mixed dislocations. Further confirmation was given from the similar density between 52 53 54 the leakage spots and screw/mixed dislocation density determined by TEM. The fact that 55 56 samples had distinctly different morphologies but showed similar density of leakage spots led 57 58 to the conclusion that the origin of the reverse bias leakage was the same in the set of samples. 59 60 They showed that screw/mixed dislocations contribute significantly more to gate leakage than

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1 2 3 pure edge dislocations. This was in agreement with other reports where screw/mixed 4 5 6 dislocations had been found to be more effective recombination centers [54], and to have 7 8 reduced barrier heights compared to pure edge dislocations [55]. In such devices, the reverse 9 10 bias leakage can be orders of magnitude different for samples grown under slightly different 11 12 13 conditions. For example, the reverse bias current was orders of magnitude higher for Ga-rich 14 15 samples. Given that dislocations with a screw component are responsible for the reverse bias 16 For Peer Review Only 17 18 leakage and their density is the same for the HVPE template and the two MBE/HVPE films, 19 20 these results led to conclude that the dislocation electrical activity was sensitive to local 21 22 chemical and/or structural changes, which depend on growth methods and conditions. 23 24 25 3. 4. 2. Cathodoluminescence investigations 26 27 Correspondence between the individual dislocations and the active centres in MOVPE 28 29 GaN layers by combining TEM and cathodoluminescence has shown that the dislocations are 30 31 r 32 non-radiative recombination centers [56]. Remmele et al. [57] were able to distinguish the a 33 r r 34 threading dislocations and a + c dislocations in their bright field images, since the 35 36 r r r 37 c component of the a + c dislocations caused a black and white lobe contrast due to surface 38 r 39 relaxation effects [58]. The a dislocations showed only a dark contrast. The comparison of 40 41 the bright field images and the monochromatic CL mapping (band edge luminescence) gave 42 43 r r 44 the following results: (i) the major part of the a + c dislocations is not recombination active. 45 r 46 (ii) a threading dislocations reduced the band edge luminescence, thus representing centres of 47 r 48 a 49 non-radiative recombination, (iii) dislocations in the basal plane caused non-radiative 50 51 recombination. 52 53 54 55 4. Atomistic simulation of dislocations in GaN 56 57 The main goal of atomistic modelling of dislocations is to find realistic models of the 58 59 60 cores and provide information on the microscopic mechanisms occurring in this area. From

such studies one expects to derive, at least, two types of information. The first is to identify

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1 2 3 the stable core structure which could provide an access to electronic structures and the second 4 5 6 consists of deriving a set of parameters which could be used for large scale simulations. 7 8 4.1. Methods 9 10 11 Once an atomistic model is built and adequate boundary conditions chosen, the 12 13 equilibrium configuration of the dislocation is obtained by minimising the energy of the 14 15 16 system with respectFor to the Peer atomic coordinates. Review Therefore, one Only needs to determine the various 17 18 interactions between the atoms of the system. They are obtained using various methods: 19 20 empirical potentials, tight-binding and ab-initio. These methods describe the interactions with 21 22 23 different degrees of accuracy. The choice between them is often a difficult compromise 24 25 between necessary theoretical rigor and available computational expediency. 26 27 28 29 30 4.1.1. The ab initio methods 31 32 In the ab initio methods, the interatomic interactions are described rigorously in the 33 34 framework of quantum mechanics. Among the ab-initio methods, those based on DFT are 35 36 37 largely used in the field of computational materials science [59, 60]. In these latter methods, 38 39 the electronic density plays a key role; the quantities of interest in atomistic simulation: 40 41 42 energy and forces are derived from it. The electronic density is obtained by solving the self- 43 44 consistent Kohn-Sham equations [60]. To perform ab initio DFT calculations in a tractable 45 46 way, a number of approximations are necessary. The most important are made on the form of 47 48 49 the exchange and correlation functional (Local Density Approximation, Generalised Gradient 50 51 Approximation …etc.) and on the basis set used to represent the single-electron wave function 52 53 (plane waves, Gaussian type functions, Slater type functions). Moreover, to make these 54 55 56 calculations more tractable, the pseudopotential approximation is usually used [61]. Despite 57 58 these approximations, the ab initio based DFT calculations remain computationally expensive 59 60 and their applications are limited to systems of a few hundred atoms (typically 200 atoms).

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1 2 3 Ab-initio-DFT methods using pseudopotentials were implemented in several codes like: 4 5 6 VASP (Vienna Ab-initio Simulation Package) [62], FHI-md (Fritz-Haber Institute’s 7 8 Molecular Dynamics code) [63], AIMPRO (Ab Initio Modelling PROgram) [64] and SIESTA 9 10 (Spanish Initiative for Electronic Simulations with Thousands of Atoms) [65]. While the first 11 12 13 two use a representation based on the plane waves, AIMPRO and SIESTA use Gaussian-type 14 15 and numerical Slater-type atomic orbital, respectively. Except SIESTA, these codes have been 16 For Peer Review Only 17 18 used in different investigations of dislocations in GaN: VASP [15, 16, 66], FHI-md [23] and 19 20 AIMPRO [2, 22, 67, 68]. 21 22 23 24 25 4.1.2. The empirical potentials 26 27 Less sophisticated than ab initio and tight-binding methods, the empirical potentials 28 29 allow dealing with systems of many thousands of atoms, and this of interest for dislocation 30 31 32 modelling [69]. In empirical potential methods, one postulates a relatively simple analytical 33 34 form of the potential energy including a set of adjustable parameters. These are fitted to 35 36 experimental measurements or ab initio calculations in order to reproduce a set of properties 37 38 39 of the material under investigation (lattice parameter, elastic constants, bulk modulus, phonon 40 41 spectrum,). It is assumed that the approximated form of the empirical potential will reproduce 42 43 44 the main feature of the atom-atom interactions and that the number of adjustable parameters is 45 46 sufficient to ensure its transferability. 47 48 Some empirical potential have previously been used to calculate the energies of 49 50 51 dislocations and grain boundaries in semiconductors [70-73]. They brought about a good 52 53 insight on the intrinsic properties of elemental semiconductors. Keating and Baraff potentials 54 55 are limited by their parameterisations which exclude dangling bonds. However, the two other 56 57 58 potentials: Stillinger-Weber and Tersoff, take into account different atomic surroundings. The 59 60 Stillinger-Weber potential has been used for III-V compound semiconductors [20, 74-76]. Of

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1 2 3 course, the treatment of compound semiconductors raises the problem of the wrong bonds, 4 5 6 which may form in the cores of crystallographic defects. For GaN, we have made a new 7 8 parameterisation of the Stillinger-Weber potential in order to allow a complete calculation of 9 10 any atomic configuration with dangling bonds, wrong bonds and excess bonds [75]. This 11 12 13 parameterisation was successively used by Chen et al. [20], Béré et al. [76], Kioseoglou et al. 14 15 [77], Lymperakis et al. [23] and Belabbas et al . [78] to investigate the atomic structures of 16 For Peer Review Only 17 18 dislocations in GaN. 19 20 21 22 4.1.3. The tight-binding methods 23 24 25 26 Coming right in between the ab initio and empirical potential methods, tight-binding 27 28 methods combine a minimal amount of quantum mechanics of electrons with classical 29 30 potentials. This allows achieving more transferable description of the interatomic interactions 31 32 33 than empirical potentials, at a small fraction of the computational cost of ab-initio 34 35 calculations. Consequently, tight-binding methods are appropriate to model systems with 36 37 many hundred to a thousand atoms and can be applied to deal with problems beyond the reach 38 39 40 of ab-initio methods. In standard tight-binding methods, the total energy of the system is 41 42 approximated by a sum of two terms [79]. The first, called the band structure energy, contains 43 44 45 the quantum electronic effects; it is obtained by solving non self-consistent Kohn-Sham like- 46 47 equation [80]. Here, the single electron wave functions are represented by linear combinations 48 49 of atomic orbital. Hamiltonian and overlap matrix elements are evaluated in the framework of 50 51 52 the two-centre approach of Slater-Koster [81]. The second is a short-ranged diatomic 53 54 potential, which is fitted to ab-initio calculations or experimental measurements in order to 55 56 reproduce a selected set of materials properties. Better accuracy and transferability is obtained 57 58 59 using the self-consistent tight-binding methods [82]. In these methods, an additional term is 60 added to the energy functional and adjusted through a self-consistent procedure. This is useful

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1 2 3 to take into account the charge transfer occurring in compound semiconductors like GaN. The 4 5 6 Self-Consistent Charge Density Functional Tight-Binding (SCC-DFTB) [83-85] is a self- 7 8 consistent extension of the standard DFTB method [86]. The SCC-DFTB total energy was 9 10 derived by expanding the Kohn-Sham energy functional to the second order with respect to 11 12 13 the electronic density fluctuations around a given reference density [80, 83]. Besides the two 14 15 usual energetic terms, i.e. the band structure energy and the short-ranger diatomic potential, a 16 For Peer Review Only 17 18 third term is introduced where a self-consistent procedure is incorporated at the level of 19 20 Mulliken charges to account for charge transfer. This last term allowed to the SCC-DFTB 21 22 technique to achieve accuracy comparable to that of ab-initio methods. Among the tight- 23 24 25 binding methods, the SCC-DFTB method is one of most successful as applied to dislocations 26 27 in GaN [2, 78, 87- 91]. 28 29 30 31 32 4.2. Results of dislocation modelling in GaN 33 34 From 1997, there has been a tremendous effort in the field of atomistic modelling to 35 36 37 study dislocations in GaN. These studies attempt to provide some information about the core 38 39 configuration of these dislocations and their effect on the electronic performance of the grown 40 41 42 layers. Several kinds of dislocations have been investigated in wurtzite GaN; these were 43 44 perfect or partial with edge, screw or mixed character, belonging to the prismatic or the basal 45 46 plane. 47 48 49 4.2.1. Perfect prismatic edge dislocation 50 r 51 The prismatic edge dislocation ( b = a/3< 11 20 >, l=<0001>) was the first dislocation to 52 53 54 be investigated in wurtzite GaN [2]. This dislocation displays different core structures with 55 56 stoichiometric configurations (8, 5/7 and 4 atom rings) (Fig.10) or non-stoichiometric 57 58 configurations (8-V and 8-V atom rings). The core with 8 atom ring structure or full-core 59 Ga N 60 contains a column of three fold coordinated atoms whereas the 5/7 atom ring structure or

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1 2 3 open-core contains wrong bonds (Ga-Ga, N-N). The core with 4 atom ring structure contains 4 5 6 fully coordinated atoms establishing four in-plane bonds [20]. The non-stoichiometric 8-VGa 7 8 or 8-VN cores can be obtained from the core with 8 atom rings removing some of Ga or N 9 10 atoms from the central column, while the complete removal of this column leads to the 5/7 11 12 13 core [2, 14, 21, 66, 88, 92]. Béré et al. have shown that the different cores (8, 5/7, 4) are, in 14 15 fact, obtained in a straightforward manner only by changing the origin of the displacement 16 For Peer Review Only 17 18 elastic field during the generation of the model [21]. In the framework of ab-initio and tight- 19 20 binding ( SCC-DFTB ) calculations, Elsner et al. [2] reported that the core with 8 atom ring 21 22 structure is more energetically favorable than that with 5/7 atom ring structure. However, all 23 24 25 the subsequent calculations performed with different methods: empirical potentials -Modified 26 27 Stillinger-Weber- [20, 76], tight-binding -SCC-DFTB- [88] and ab initio [23] suggest the 28 29 opposite. In the case of the core with 4 atom ring structure, Chen et al. found it less 30 31 32 energetically favorable than that with 8 atom ring structure [20]. 33 34 35 (a) (b) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 (c) 53 54 55 56 57 58 59 60

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42 43 Fig.11: Structural units for coincidence grain boundaries from rotations around [0001] based 44 on the 5/7 atom ring core, the corresponding Σ is indicated [93] 45 46 47 This was a good indication that the hexagonal system did not exhibit fundamentally 48 49 50 different mechanisms for defect formation than the cubic, at least along high symmetry 51 52 directions. 53 54 A set of calculations based respectively on ab-initio [66], tight-binding –SCC-DFTB - 55 56 57 [88] and Monte-Carlo [92] methods revealed that the formation energy of the prismatic edge 58 59 dislocations with non-stoechiometric cores (8-VGa and 8-VN) strongly depends on both the 60

growth conditions and the doping nature of the material. The 8-VGa core was shown to be

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1 2 3 more energetically favourable in n-type material grown under N-rich conditions whereas the 4 5 6 8-VN core is favourable in p-type material grown under Ga-rich conditions [66]. However, 7 8 Lee et al. obtained favorable formation energies for cores with both 8 and 5/7 atom rings 9 10 structures in material grown under Ga-rich conditions [88]. 11 12 13 The electronic structure of the prismatic perfect edge dislocation with different core 14 15 configurations has also been investigated extensively [2, 23, 66, 67, 88]. According Elsner et 16 For Peer Review Only 17 18 al. the edge dislocation with 8 atom ring core structure is electrically inert and induces no gap 19 20 states [2]. Therefore, it has undergone a relaxation of the three fold coordinated Ga (N) core 21 22 atoms toward sp 2 (p 3) similar to the ( 10 10 ) surface, which leads the dimerization of the 23 24 25 bonds along the dislocation line. However, several calculations performed on the same core 26 27 configuration have revealed the presence of empty states at the half top of the band gap [22, 28 29 30 23, 67, 88]. A quite similar electronic structure has been reported for the dislocation with 5/7 31 32 atom ring core structure (Fig.12) [23, 88]. 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

53 core-8 (a) core-8 (b) core-8 V Ga (a) core-8 V N (a) core-5/7 (a) core-5/7 (b) core-4 (b) 54 55 56 Fig.12: Schematic diagram of energy levels induced in the band gap by different cores of 57 the prismatic edge dislocation: 8 atom ring core (core-8), 5/7 atom ring core (core-5/7) 58 and the 4 atom ring core (core-4), dark balls indicate filled levels, (a) [88], (b) [23] 59 60

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1 2 3 For the 4 atom ring edge dislocation, an unexpected behavior has been reported recently: 4 5 6 despite its fully coordinated core, it exhibits deep states in the band gap [23]. This was 7 8 attributed to the large strain field surrounding the dislocation core which leads to the 9 10 formation of bonding between Ga second neighbor atoms similar to metallic gallium. Tight- 11 12 13 Binding calculations carried out on the non-stoichiometric structures have revealed for the 8- 14 15 VGa core, the presence of both occupied states at 0.2 eV from the VBM (Valence Band 16 For Peer Review Only 17 18 Maximum) and empty states just below the CBM (Conduction Band Minimum) [88]. The 8- 19 20 VN core has been shown to induce different states throughout the band gap; it may be 21 22 expected to be an origin of yellow luminescence. 23 24 25 The electronic structures of the 3(740 ) Σ=37 ( θ = 9.3º), 3(520 ) Σ=19 ( θ = 13.4º) and 26 27 28 1(320 ) Σ=7 ( θ = 21.6º) tilt grain boundaries were calculated. They were investigated by 29 30 means of SCC-DFTB approach. Among the three possible atomic configurations of these 31 32 33 boundaries, namely, the interfaces based on the 5/7, the 4 and the, it was found that the 34 35 structure based on the 8 atom ring core introduces deep states in the very center and the upper 36 37 half of the band gap whereas the grain boundaries based on the 5/7 atom ring possess only 38 39 40 states close to the conduction band (Fig.13) [90]. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 β 4 Fig.13: Schematic diagram of energy levels in the band gap, (notation Iα , α refers to the grain 5 boundary and β to the dislocation core type, Cβ denotes the core of the edge dislocation [88, 6 90]. 7 8 9 10 The comparison with the electronic structure of the prismatic dislocation shows a 11 12 similar behaviour for the grain boundaries with the 8 atom rings and the introduction of deep 13 14 15 states inside the band gap. Given that for an electrically neutral boundary the deep states are 16 For Peer Review Only 17 unoccupied, the 8 atom ring structure may contribute to yellow luminescence in GaN layers. 18 19 In any case, empty gap states will localize carriers for the recombination. For the grain 20 21 22 boundaries built up with the 5/7 atom rings only states close to the conduction band are 23 24 predicted. 25 26 27 28 29 30 4.2.2. Perfect prismatic screw dislocation 31 32 r 33 The prismatic perfect screw dislocation ( b = c<0001>, l = <0001>,) is one of the most 34 35 studied dislocation in wurtzite GaN. Several calculations have been carried out on their 36 37 atomic and electronic core structures. Different core structures have been investigated: the 38 39 40 full-core [2, 67, 76, 89], the open-core [2, 15] and non-stoichiometric configurations [15, 16] 41 42 (Fig.14). In the first configuration, six stoichiometric atomic columns, in helical like 43 44 symmetry arrangement along the direction [0001], form a hexagonal atomic core. By 45 46 47 removing the latter, the open-core configuration is obtained. However, filling the core with 48 49 different amounts of Ga and N atoms leads to non- stoichiometric configurations, where the 50 51 52 Ga-filled and N-filled cores represent the extreme limits. In their report, Elsner et al. have 53 54 investigated prismatic screw dislocation with both full-core and open-core configurations [2]. 55 56 The calculation of the line energy, in a cylinder of radius about 8 Å, gave 4.88 eV/ Å for the 57 58 59 full-core and 4.55 eV/ Å for the open-core configuration. This was higher than their value of 60 2.19 eV/ Å found for the full-core edge prismatic dislocation. Similar high line energy values

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1 2 3 were also reported by different authors for the screw full-core dislocation. This probably 4 5 6 explains why the screw dislocations represent a small fraction with respect to the edge type in 7 8 GaN epitaxial layers [15, 76, 89]. 9 10 Recent ab initio calculations performed by Northrup [15, 16] revealed that screw 11 12 13 dislocation with non-stoichiometric core configurations could be more energetically 14 15 favourable than those with stoichiometric cores under some growth conditions. The Ga-filled 16 For Peer Review Only 17 18 core, obtained by removing all the N atoms from the hexagonal core, is predicted to be the 19 20 most stable configuration under the Ga-rich conditions [15]. However, in N- rich conditions, a 21 22 non-stoechiometric core structure with Ga (50%) and N (25%) atoms was found more 23 24 25 energetically favourable [16]. 26 27 28 29 (A) (B) 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (C) 46 47 48 49 Fig.14: Atomic core structures of the 50 51 prismatic screw dislocation: 52 A) View along the [0001] direction of 53 the full-core structure. B) View along 54 the [ 11 20 ] direction of the full-core 55 structure. C) View along the [0001] 56 57 direction of the open-core structure. 58 59 60

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1 2 3 4 5 6 In the full-core configuration, due to the presence of heavily distorted bonds, additional 7 8 charge transfers should occur and gap states are induced. Belabbas et al. have identified an 9 10 extra charge transfer of 0.12e, besides that naturally occurring in GaN bulk material, from Ga 11 12 13 to N atoms [89]. The electronic structure calculations performed on the full-core dislocation 14 15 have revealed the presence in the band gap of shallow as well as deep states [2, 67]. In the 16 For Peer Review Only 17 18 open-core dislocation, in order to lower the surface energy, the internal wall of the core 19 20 relaxes like the ( 10 10 ) surface and then the threefold coordinated atoms Ga (N) adopt sp2 21 22 (p 3) hybridization. For this dislocation, only shallow states were reported and attributed to the 23 24 25 distortion of the wall surface along the direction [0001] due to the Burgers vector [2]. For the 26 27 non-stoichiometric dislocations, the Ga-filled core configuration was predicted to have a 28 29 30 metallic like-behaviour as its induced states are highly dispersed in the entire band gap [15, 31 32 16, 67]. However, this behaviour is less pronounced in the most favourable core structure (Ga 33 34 50%, N 25%) in N-rich conditions [16]. 35 36 37 38 39 4.2.3. Perfect basal edge and screw dislocations 40 41 Up to date, there are only a few reports on the atomic core structures of the perfect basal 42 43 r r 44 edge ( b = c<0001>, l= < 11 20 >) and screw ( b =a/ 3< 11 20 >, l= < 11 20 >) dislocations [76, 45 46 78]. In the ELO (Epitaxial Lateral Overgrowth) process, the threading dislocations are bent 47 48 49 [94]. Thus, a dislocation changes its line direction from <0001> to < 11 20 > resulting in a new 50 51 character, edge or screw. These basal dislocations can occur during the heteroepitaxial growth 52 53 54 on the non-polar ( 11 20 ) a-plane [95]. 55 56 Recently, Belabbas et al. have investigated the atomic structure and the electronic 57 58 59 activity of the basal edge dislocation in wurtzite GaN by combining empirical potentials 60 (Modified Stillinger-Weber) and tight-binding methods (SCC-DFTB)[78]. For this dislocation

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1 2 3 four stable core configurations have been determined, and each corresponds to a particular 4 5 6 position of the origin of the applied displacements field before relaxation (Fig.15a) [21]. G1 7 8 and G2 configurations belong to the glide set, S1 and S2 to the shuffle set. The G2 and S1 9 10 configurations display a 4/8 atom ring structure without wrong bonds (Fig.15c, d), whereas 11 12 13 the G1 and S2 configurations which include wrong bonds, display a 5/8/5-atom rings structure 14 15 (Fig.15b, e). The G1 and S2 configurations were already reported in the framework of 16 For Peer Review Only 17 18 empirical potentials [76]. 19

20 (b) (a) (d) 21 22 23 [10-10] 24 b =c 25 26 [0001] [1-210] 27 28 29 (c) (e) 30 S1 S2 31 32 33 G1 G2 34 35 36 37 38 39 r 40 Fig.15: The four core configuration of the c edge basal dislocation: (a) Different 41 positions of the origin of the applied displacements field, (b) G1 core configuration, (c) 42 G2 core configuration, (d) S1 core configuration, (e) S2 core configuration. Black 43 circles represent Ga atoms whereas white ones represent N atoms. 44 45 46 The SCC-DFTB energetic calculations for a core radius of 8.58 Å gave for the four 47 48 configurations: G1, G2, S1, S2, the following core energies: 5.24, 4.90, 5.73 and 4.44 eV/Å, 49 50 51 respectively [78]. In both sets, the most favourable configuration is S2 with wrong bonds. In 52 53 the glide set, the core without wrong bonds, G2, is energetically favoured. The electronic 54 55 levels induced by each core configuration are presented in figure 16, where their positions in 56 57 58 the band gap were corrected using the linear scaling method. 59 60

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 (a) G1 configuration (b) G2 configuration (c) S1 configuration (d) S2 configuration 25 26 27 Fig. 16 : Electronic gap states associated with different configurations of the basal edge 28 dislocation. The zero has put on the top of the valence band maximum while the 29 conduction band minimum is at 3.4 eV. 30 31 32 As can be seen, each core configuration induces deep as well as tail states. Filled states 33 34 exist in the bottom half of the band gap, up to 1eV from the VBM. For all the configurations, 35 36 unfilled deep states are present on the top half of the band gap, and are located mainly 37 38 39 between 2 and 3 eV, from the VBM. In this area, the states induced by G1 are more spread 40 41 than those of the other configurations. Due to the presence of the deep states, one could 42 43 44 expect the basal edge dislocations to be at the origin of parasitic luminescence. However, it 45 46 cannot be excluded that the G1 configuration may be involved in non-radiative recombination 47 48 processes. 49 50 51 The atomic structure of the perfect basal screw dislocation has been only investigated by 52 53 Béré et al. , their study is based on a modified Stillinger-Weber potential [76]. Two stable core 54 55 configurations were identified; one belongs to the glide set while the other belongs to the 56 57 58 shuffle set. The screw dislocations were found to have a core diameter of 6.7 Å. The glide 59 60

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1 2 3 configuration has a line energy of 1.20 eV/Å, 2% higher than that of the shuffle 4 5 6 configuration. 7 8 9 10 4.2.4. Perfect basal 60° dislocation 11 12 13 In zinc-blende GaN, Blumenau et al. have studied the atomic and electronic structures 14 r 15 and the relative energies of the 60° basal dislocation ( b = a/2[ 1 10 ], l = < 01 1 >), with both 16 For Peer Review Only 17 18 glide and shuffle configurations (Fig.17) [22, 95]. 19 20 21 22 23 (A) (B) 24 25 26 27 28 29 30 31 32 33 34 35 (C) (D) 36 37 38 39 40 41 42 43 44 45 46 47 Fig. 17: The core configurations of the perfect 60° dislocation in wurtzite GaN. (A) The α 48 49 (N-terminated) shuffle configuration. (B) The β (Ga-terminated) shuffle configuration. (C) 50 The α (N-terminated) glide configuration. (D) The β (Ga-terminated) glide configuration. 51 Black balls represent gallium atoms and the white ones nitrogen atoms. 52 53 54 55 56 For the shuffle dislocations both the α (N-terminated) and β (Ga-terminated) 57 58 configurations were investigated. The α core shuffle dislocation was found to have an 8 atom 59 60 rings like structure, with three fold coordinated atoms exhibiting a sp 3 like hybridisation

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1 2 3 despite their relaxation along the [111] direction. The β core shuffle dislocation was shown to 4 5 6 exhibit a 5/9 atom ring like structure with wrong bonds (Ga-Ga). Moreover, this core presents 7 8 a double period reconstruction leading to a charge modulation of ± 0.2 e - along the dislocation 9 10 11 line direction. The glide dislocation with α(β) core was obtained by only removing the Ga (N) 12 13 three fold coordinated atoms column from the shuffle β(α) core dislocation. Its core exhibited 14 15 16 5/7 atom ringsFor like structure Peer and it was Review shown to be more energeticallyOnly favourable than its 17 18 corresponding shuffle dislocation with β(α) core (Fig.17). 19 20 21 The calculated electronic structures of the 60° dislocation have shown that the shuffle α 22 23 core configuration induces half filled gap states at 0.2 eV from the VBM, while the shuffle β 24 25 26 core configuration induces states at 0.3 eV from the VBM. The 60° glide β core introduces 27 28 shallow occupied states at 0.3 eV from the VBM as well as deep non-occupied states at 1.6 29 30 31 eV from the VBM, whereas the glide α-core induces only shallow occupied states at 0.5 eV 32 33 from the VBM. These results show that the 60° dislocation is electrically active and suggest 34 35 that those with the shuffle core configurations could act as a shallow acceptor in agreement 36 37 38 with the results of As et al. showing that dislocations in cubic GaN act as acceptors and are 39 40 electrically active [96]. 41 42 43 44 45 4.2.5. Partial basal dislocations 46 47 From their recent investigation, Savini et al. have reported the atomic and electronic 48 49 r 50 structures of the 90° Shockley partials, ( b = a/3[ 10 10 ], l = < 11 20 >), in wurtzite GaN 51 52 (Fig.18) [68]. They used ab-initio calculations, implemented in the AIMPRO code, to model 53 54 55 partial dislocations with α (N-terminated) and β (Ga-terminated) cores in both supercells and 56 57 cluster-supercell hybrids. By limiting their investigations to the glide configurations, they 58 59 60 showed that the two partials can adopt both symmetric and asymmetric core reconstructions depending on the environment of the dislocation. The asymmetric reconstruction was found to

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1 2 3 be the most favourable and the energy difference between the two reconstructions was 83.2 4 5 6 meV for the β-core and 196.4 meV for the α-core. The calculated electronic structure 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 Fig.18: The core configurations of the 90° Shockley partials. (A) The α (N-terminated) 23 24 core configuration. (B) The β (Ga-terminated) core configuration. The doted line 25 indicates the intrinsic stacking fault. Black balls represent gallium atoms and the white 26 ones nitrogen atoms. 27 28 29 30 exhibited mid gap states for both dislocations cores, and for the α core a deep acceptor level 31 32 at 1.11 eV and for the β core a deep donor level at 0.87 eV, from the VBM, was pointed out. 33 34 35 The first level is expected to give rise to a 2.3 eV radiative transition which could contribute 36 37 to the yellow luminescence [97], while the second one may be correlated to the 2.4 eV 38 39 absorption peak in agreement with energy loss spectroscopy measurements [98]. Based on 40 41 42 Voronoi cell analysis of the charges density, it was shown that these partial dislocations 43 44 present a charge polarization along [0001] with a negatively charged compressed region and a 45 46 positively charged tensile region. Moreover, when these dislocations were brought together 47 48 49 and in the presence of a high stress, a charge transfer was shown to occur from the β-core 50 51 dislocation to the α-core dislocation. It was concluded that such charges may be able to screen 52 53 54 the carriers from recombination in the dislocation cores and explain why GaN devices may 55 56 tolerate high dislocation densities. 57 58 et al. 59 In their empirical potentials investigation, Kioseoglou have performed a systematic 60 investigation of the atomic core structures and the corresponding energies of both edge

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1 2 3 r r 4 (b =1/6[ 20 23], l = [ 1210 ],) and mixed ( b =1/6[ 2203 ], l = [ 1210 ]) Frank-Shockley partials 5 6 that bound the I 1 intrinsic basal stacking fault in wurtzite GaN [99]. For the edge and mixed 7 8 partials, twelve stable configurations were found for each Ga and N core polarity, they consist 9 10 11 of 5/7, 8 and 12 atom rings like structures. For the edge partials, the 5/7 atom rings structure 12 13 was reported as the most energetically favourable with energies less than 0.76 eV/Å. Whereas 14 15 the 8 and 12 atom rings have energies ranging from 1.28 to 1.48 eV/Å. For the mixed partials, 16 For Peer Review Only 17 18 both the 5/7 and 12 atom rings structures were most stable. Their core energies are larger than 19 20 those of the edge dislocations and the energetically most favourable configurations have 21 22 23 energies ranging from 0.81 to 1.05 eV/Å. These partial dislocations should be electrically 24 25 active since they present similar structures to those of the 60° dislocations, already reported 26 27 by Blumenau et al. in cubic GaN [95]. 28 29 30 31 32 5. Discussion 33 34 35 The GaN layers are mostly grown on sapphire which exhibits a large mismatch, 36 37 38 and the area in the vicinity of the interface with the substrate contains a lot of defects. As 39 40 early as 1986, low temperature buffer layers (AlN, GaN) were largely used in the growth of 41 42 GaN resulting in high quality epitaxial layers [100]. In these layers deposited in the 500- 43 44 45 600°C temperature range, it was shown that many basal stacking faults form and during the 46 47 subsequent increase of the temperature for the active layer growth they may become the 48 49 origin of the threading dislocations[47]. The connection of the stacking faults and the misfit 50 51 52 dislocations has not yet been clearly demonstrated. However, the connection between the 53 54 origin of the threading dislocations and the highly strained interfacial area with substrate was 55 56 established [19]. This confirms more or less the rather simple picture of mosaic growth which 57 58 59 was published as early as 1997 [101]. Following their climb at grain boundaries or from the 60 SF reaction area in the buffer layer, the threading dislocations obtain their equilibrium

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1 2 3 structure as determined by the growth kinetics. i.e.: their line becomes mainly parallel to the 4 5 6 [0001] growth direction. The three topological dislocations of the hexagonal lattice have been 7 r 8 observed with a vast majority of a edge ones, as reported from the start. The mosaic growth 9 r 10 of the layers allows the a 60° interfacial dislocations to easily become pure edge along the c 11 12 13 axis forming low angle grain boundaries. The growth along the c axis limits the formation of 14 r r r 15 a + c < 10% dislocation and even more the c ~1% as observed experimentally. 16 For Peer Review Only 17 18 As for the atomic structure, the investigations were first misled by the fact that, even if 19 20 the first layers contained 10 10 cm -2 dislocations, the LEDs emission was the brightest known 21 22 in semiconductor optoelectronics. 23 24 25 The multiplicity of the atomic configurations was shown as early as 1998 with the 26 27 coexistence of the 5/7 and 8 atom ring cores in good quality GaN layers types[13] and the 28 29 occurrence of the additional 4 atoms core inside grain boundaries[18]. Of course, as it was 30 31 32 demonstrated later on, the three configurations are just a consequence of the wurtzite 33 34 structure, and the occurrence of each depends on the position of the dislocation line inside the 35 36 37 unit cell [21]. Then, by using our empirical potential [75] along with ab initio calculations, 38 39 Lymperakis at al. have carried out a multiscale analysis of this edge threading dislocation 40 41 [23]. They convincingly demonstrated that, the 4 atom ring core which has been first reported 42 43 44 in grain boundaries may be the most stable in strained layers [18]. 45 46 At the initial stages of the growth, many stacking faults are involved and partial 47 48 dislocations can be present. However, it is of interest to investigate their atomic structure. It is 49 50 51 may be noticed that as stressed by Narayan et al . [47], they will quickly develop in threading 52 r r r r 53 dislocations and behave like the dislocations a , a + c and c of the hexagonal lattice. 54 55 56 The electronic structure of the threading dislocations has been extensively debated and 57 58 now the situation is clearer. For the prismatic edge dislocation with full or open core, empty 59 60 states are present in the half top of the band gap. Some discrepancies still remain about their

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1 2 3 positions for the open core. As demonstrated in the recent multiscale approach, the 4 atom 4 5 6 ring configuration exhibits deep states in the band gap, although it has no broken bond. These 7 8 states originate from the strain induced by the atomic structure, and cannot be removed. 9 10 Therefore, this configuration is forecast to be the most detrimental for the devices. 11 12 13 The prismatic screw dislocations display various atomic structures, full core, open core 14 15 and non-stoichiometric configurations under different growth conditions. Levels are present 16 For Peer Review Only 17 18 and the Ga-rich core induces levels which are spread all over the band gap. When these 19 20 dislocations bend and have their lines in the basal plane to become edge, screw or 60° 21 22 dislocations, they exhibit glide and shuffle configurations and wrong bonds may be present. In 23 24 25 these configurations, shallow or deep band gap states are present. 26 27 In the long run with the combined large experimental and theoretical work, it has 28 29 become obvious that the good optical emission of the GaN layer had little to do with the 30 31 32 recombination activity at the dislocation cores. In fact, the dislocations are harmful to the 33 34 transports properties of all the materials, probably depending on their geometry as well as 35 36 their chemistry (impurities, dangling bonds,). This was established when the fabrication of 37 38 39 laser diodes started, their lifetimes could only be substantially increased when the density of 40 41 the dislocations was brought in the low 10 8 cm -2 range using epitaxial lateral overgrowth. 42 43 44 45 6. Conclusion 46 47 48 In this paper, we presented and discussed our results dealing with the dislocations in 49 50 GaN layers. The dislocations are strongly involved in degrading the performance of the 51 52 devices. The atomic core structures of the perfect edge threading dislocations are based on 53 54 55 only three types of atom rings, however, depending on the layer growth conditions, they can 56 57 be stoichiometric or not. The perfect dislocations, threading and basal dislocations, have now 58 59 been largely investigated unlike the partial dislocations. Their electrical activity is in good 60

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1 2 3 agreement with their atomic structure. A number of theoretical reports show that their 4 5 6 electronic structures exhibit deep and shallow levels. 7 8 9 Acknowledgements: The authors acknowledge the support of the EU under contracts “IPAM” 10 11 12 HPRN-CT-1999-00040, and “PARSEM” MRTN-CT-2004-005583. The computations were 13 14 performed at “CRIHAN” (http://www.crihan.fr). 15 16 For Peer Review Only 17 18 19 20 7. References 21 22 23 24 25 [1] S. Nakamura, T. Mukai and M. Senoh, Appl. Phys. Lett. 64 1687 (1994). 26 27 [2] J. Elsner, R. Jones, P. K. Sitch, V. D. Porezag, M. Elstner, Th. Frauenheim, M. I. Heggie, 28 S. Öberg and P. R. Briddon, Phys. Rev. Lett., 79 3672 (1997). 29 30 31 [3] F.R. Chien, X.J. Ning, S. Stemmer, P. Pirouz, M.D. Bremser and R.F. Davis, Appl. Phys. 32 Lett., 68 2678 (1996). 33 34 [4] X.H. Wu, L.M. Brown, D. Kapolnek, S. Keller, B. Keller, S.P. DenBaars, and J.S. Speck, 35 J.Appl. Phys., 80 3228 (1996). 36 37 38 [5] A.F. Wright and J.S. Nelson, Phys.Rev.B, 51 7866 (1995). 39 40 [6] L. Sigiura, J. Appl. Phys., 81 1633 (1997). 41 42 [7] Y. Xin, S. J. Pennycoock, N.D. Browning, P.D. Nelist, S. Sivananthan, B. Beaumont, 43 44 J. P. Faurie and P. Gibart, Mat. Res. Soc. Symp. Proc., 482 781 (1998). 45 46 [8] P. Vermaut, P. Ruterana, G. Nouet and H. Morkoç, Phil. Mag. A, 75 239 (1997). 47 48 [9] B. Daudin, J. L Rouviere. and M. Arlery, Appl.Phys.Lett., 69 2480 (1996). 49 50 51 [10] V. Potin, P. Vermaut, P. Ruterana and G. Nouet, J. Electron. Mater., 27 266 (1998). 52 53 [11] N.G. Weimann, L.F. Eastman, D. Doppalapudi, H.M. Ng and T.D. Moustakas, J. Appl. 54 Phys., 83 3656 (1998). 55 56 57 [12] S. Nakamura and G. Fasol, The Blue Laser Diodes (Springer, Heidelberg, 1997). 58 59 [13] P. Ruterana, V. Potin and G. Nouet, Mat. Res. Soc. Symp. Proc., 482 459 (1998). 60 [14] A.F. Wright, Mat. Res. Soc. Symp. Proc., 482 795 (1998).

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 For Peer Review Only 15 16 17 18 19 20 21 22 23 24 25 The atomic and electronic structure of dislocations in Ga based nitride 26 semiconductors 27 28 29 30 31 Journal: Philosophical Magazine & Philosophical Magazine Letters 32 33 Manuscript ID: TPHM-05-Sep-0420.R2 34 Journal Selection: Philosophical Magazine 35 36 Date Submitted by the n/a 37 Author: 38 Complete List of Authors: BELABBAS, Imad; ENSICAEN, SIFCOM 39 CHEN, Jun; IUT, LRPMN 40 RUTERANA, Pierre; ENSICAEN, SIFCOM 41 NOUET, Gérard; ENSICAEN, SIFCOM 42 43 Keywords: GaN, atomic structure, dislocations, electronic structure 44 Keywords (user supplied): 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 http://mc.manuscriptcentral.com/pm-pml Page 145 of of 43 87 Philosophical Magazine & Philosophical Magazine Letters

1 2 3 4 The atomic and electronic structure of dislocations in Ga 5 6 based nitride semiconductors 7 8 9 10 11 12 1,3 1 2 1 13 I. Belabbas , P.Ruterana , J. Chen , G. Nouet 14 15 16 1 For Peer Review Only 17 Laboratoire Structure des Interfaces et Fonctionnalité des Couches Minces, UMR CNRS 18 6176, Ecole Nationale Supérieure d‘Ingénieurs de Caen, 6 Bld du Maréchal Juin, 14050 19 Caen cedex, France. 20 21 2 Laboratoire de Recherche sur les Propriétés des Matériaux Nouveaux, IUT d’Alençon, 22 23 61250 Damigny, France 24 3 25 Groupe de Physique du Solide, Laboratoire de Physique Théorique, Université A.Mira, 26 Béjaia, 06000, Algérie. 27 28 29 30 31 Abstract 32 33 34 35 The atomic and electronic properties of dislocations in III-N semiconductor layers, especially 36 37 GaN are presented. The atomic structure of the ar edge threading dislocation is now well 38 39 established with three different cores (8 or full core, 5/7 or open core and 4 atom ring). The 40 41 42 use of atomistic simulations has confirmed these atomic structures and has given a good 43 44 understanding of the electronic structure of the screw dislocation. Partial dislocations which 45 46 are mostly confined in the area close to the substrate are now also being investigated. It is 47 48 49 becoming clear that the electrical activity of all these defects is dependent on the layer quality, 50 51 which is governed by the growth conditions. 52 53 54 55 56 57 58 59 60

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1 2 3 4 1. Introduction 5 6 During the last decade, III-V nitride semiconductors have taken an important part in 7 8 9 optoelectronic devices since the first commercial light emitting diode (LED) in 1993 10 11 fabricated from metal organic vapour phase epitaxy (MOVPE) GaN/InGaN heterostructures 12 13 containing a very large number of threading dislocations (1010cm-2) [1]. These LEDs were 14 15 16 reliable althoughFor the dislocation Peer density Review was higher compared Only to LEDs based on GaAs which 17 18 emitted in the red region with defect densities below 102-103 cm-2. The nature and properties 19 20 21 of the dislocations in GaN needed to be understood, and the first reports tended to show that 22 23 these dislocations should have at least a particular atomic structure which allows them to be 24 25 non-active in the electronic processes [2]. By conventional transmission electron microscopy 26 27 28 (TEM), it was shown that the only dislocations which formed in wurtzite GaN corresponded 29 r 30 to the dislocations of the hexagonal lattice with the Burgers vectors b = ar , ar + cr and cr [3- 31 32 33 4]. The non activity of threading dislocations was assumed in the first theoretical report on the 34 35 atomic structure of the ar edge threading dislocation; it was proposed that the edge threading 36 37 dislocation should have either a core based on an 8 atom ring with the dangling bonds 38 39 40 reconstructed along the [0001] line or an empty core [5]. At the same time, a theoretical 41 42 investigation of the motion of the prismatic threading edge dislocations and of the basal screw 43 44 dislocations in GaN concluded that the mobility of the dislocations in GaN was very small at 45 46 -10 -16 47 room temperature, a factor of approximately 10 to 10 with respect to GaAs, which could 48 49 help to explain the remarkable reliability of GaN based LED [6]. 50 51 52 A confirmation of the atomic structure came from the first report of Z-contrast results 53 54 using high resolution scanning transmission microscopy [7], it was suggested that the ar edge 55 56 threading dislocation in GaN should have the reconstructed 8 atom core structure. In the 57 58 59 meantime, extensive experimental work had been done on other extended defects which 60

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1 2 3 seemed to be typical for the GaN; these were prismatic stacking faults [8] and inversion 4 5 6 domains [9-10]. 7 8 At the same time, the electrical properties investigations were also analysed showing 9 10 that GaN nitride layers had quite low carrier mobility due to the presence of the large 11 12 13 densities of dislocations [11]. In fact, it was becoming clear that in order to fabricate devices 14 15 such as lasers in which there is propagation of carriers in the basal plane, the density of 16 For Peer Review Only 17 18 threading dislocations needed to be decreased. As a consequence, the first 10 000 hours life 19 20 time laser diode was fabricated in a GaN layer grown using epitaxial lateral overgrowth and 21 22 having an average threading dislocation density <108cm-2 [12]. So, it was necessary to carry 23 24 25 out extensive work on the dislocations in order to explain their true behaviour in GaN layers. 26 27 Simultaneously to the Z-contrast report, our high resolution transmission electron microscopy 28 29 (HRTEM) investigation showed that the edge threading dislocation had more than the 8 atom 30 31 32 core configuration [13]. Mainly, in agreement with the theoretical work of Wright [14] as the 33 34 open core configuration could not be distinguished with the proposed 5/7 atom structure in 35 36 HRTEM observations. 37 38 39 During the last few years, a large number of investigations have been carried out on the 40 41 structure and properties of all types of dislocations in GaN as well as the possible effect of 42 43 44 deviation from stoichiometric composition [15-16] and impurities [17]. Latterly, this effort 45 46 has also been focused on the partial dislocations and their connections to other extended 47 48 defects [18-19]. 49 50 51 In this paper, we discuss the numerous results that have been reported along with our 52 53 contribution on experimental HRTEM and theoretical investigation of these defects. 54 55 Typically, our work has allowed to determine the multiple configuration of the threading edge 56 57 58 dislocation and to clarify the crystallographic relationships between them [20-21]. The related 59 60 study of electronic properties is a topic of high interest and different methods have been used

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1 2 3 corresponds to the zincblende structure, 3C, (space group F 4 3m) with a = 0.452nm. This 4 5 6 structure is identical to the diamond crystal structure with two interpenetrating face-centred 7 8 cubic lattices occupied by nitrogen or gallium, respectively, and shifted along the diagonal by 9 10 11 ¼<111> (Fig.1a). For GaN, the wurtzite structure (space group P63mc with the lattice 12 13 parameters a = 0.319nm and c = 0.518nm, c/a = 1.6238) is thermodynamically stable under 14 15 conventional growth conditions on various substrates, e.g. sapphire, silicon carbide,…This 16 For Peer Review Only 17 18 structure, corresponding to the 2H polytype, is described by two hexagonal close-packed 19 20 lattices shifted by u along the <0001> direction (Fig.1b). In the ideal wurtzite structure (c/a = 21 22 1.633), u is equal to 0.375, for GaN u = 0.377. One lattice is occupied by nitrogen atoms and 23 24 25 the other by gallium atoms, therefore only one family of tetrahedral sites of the hexagonal 26 27 structure is occupied. This requirement may lead to the occurrence of two structural variants 28 29 (polarities) during the growth of the layers, corresponding to the orientation of Ga-N bonds 30 31 32 along the <0001> direction. 33 34 35 (a) (b) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Fig.1: Structures of zinc blende and wurtzite crystals. a) zinc blende unit cell. 51 b) wurtzite unit cell ( Ga: large black spheres, N: small grey spheres) 52 53 54 55 56 The zinc blende structure has only one type of first neighbour distance, which means 57 58 that the four bond lengths in a tetrahedron are equal. This is also valid for a wurtzite structure 59 60 with the ideal values c/a=1.633 and u = 3/8. Otherwise, the bond parallel to the c axis is

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1 2 3 different, within less than 1% for the III-V nitrides. For the second nearest neighbours, the 4 5 6 zinc blende structure has only one type of bond lengths (12 bonds). The wurtzite structure 7 8 presents three types of second neighbours, and for the ideal values, the difference between the 9 10 shortest and the longest bonds is 13% [25]. 11 12 13 14 15 16 2.2. DislocationsFor Peer Review Only 17 18 19 20 In the frame of the linear elasticity theory of isotropic materials, the displacement field 21 22 of the dislocation can be calculated as well as the induced stresses, except in the vicinity of 23 24 the dislocation line or dislocation core where both stress and strain become infinite and this 25 26 27 analysis breaks down. The strain energy of an infinite straight dislocation in a perfect crystal 28 29 is calculated per unit length when the dislocation is contained in a cylinder of radius R. For a 30 31 screw or an edge dislocation, this stored elastic energy is proportional to the square of the 32 33 2 34 Burgers vector, b . The ratio of their energies is equal to the factor (1- ν), ν is the Poisson’s 35 36 ratio, and the energy of an edge dislocation is larger than that of a screw dislocation. The total 37 38 39 energy of the dislocation also includes the energy stored in the dislocation core. In the linear 40 41 elastic theory, the displacements vary slowly; this assumption breaks down in the core region 42 43 and atomistic calculations become necessary to calculate the corresponding energy. 44 45 46 Since the elastic energy of a dislocation is proportional to the square of the Burgers 47 48 vector, this value of b2 may be used to define the stability of a dislocation by applying the 49 50 r r 51 Frank criterion to the splitting of a dislocation with Burgers vector b1 into dislocations b2 and 52 53 r 2 2 2 54 b3 . The splitting takes place only if: (b1) > (b2) + (b3) . Applying this criterion, the possible 55 56 Burgers vectors are only the primitive translations of the lattice. As a consequence, the 57 58 59 Burgers vectors of the perfect dislocations in the zinc blende and wurtzite structures are 60 identical to those of diamond or hexagonal close-packed material, respectively [26] (Table 1).

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1 2 3 Zinc blende Wurtzite 4 r 2 r 2 5 Burgers vector (b ) (b ) Burgers vector (b ) (b ) 2 2 6 1/2<110> a /2 1/3 <11>20 a 7 <100> a2 <0001> c2 8 2 2 9 1/3 <11>23 a + c 10 11 r 12 Table 1: Perfect dislocations in zinc blende and wurtzite structures: Burgers vector (b ) 2 13 and energy (b ). 14 15 16 For Peer Review Only 17 By considering the link between the crystallographic structure of crystals and the 18 19 structure of dislocations, dislocations with Burgers vectors not belonging to lattice 20 21 translations must be present. Such dislocations are defined as partial dislocations and the area 22 23 24 connecting two partial dislocations is faulted (Table 2). As a first approximation, the 25 26 application of the Frank criterion shows that the dissociation of a perfect dislocation into 27 28 partials may take place. 29 30 31 Zincblende Wurtzite r 2 r 2 32 Type Burgers vector (b ) (b ) Type Burgers vector (b ) (b ) 33 Shockley 1/6<112> a2/6 Shockley a2/3 34 1/3 <10 10 > 2 2 35 Frank 1/3<111> a /3 Frank 1/2<0001> c /4 2 2 2 36 1/6<110> a /18 Frank-Shockley 1/6 < 2023> a /3+ c /4 37 1/3<001> a2/9 38 1/3<110> 2a2/9 39 2 40 1/6<301> 5a /18 41 r 42 Table 2: Partial dislocations in zinc blende and wurtzite structures: Burgers vector ( b ) 43 2 44 and energy (b ). 45 46 For the nitrides, the perfect dislocations that have been characterised are the prismatic 47 48 r 49 dislocation or edge dislocation b = 1/3<1120 >, l = <0001> with three different atomic cores 50 r 51 and the screw dislocation b = <0001>, l = <0001> with two atomic cores (Fig.2). 52 53 54 55 56 57 58 59 60 a b c

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1 2 3 4 5 6 7 8 9 10 Full core Open core 11 d e 12 13 r 14 Fig.2: Prismatic dislocation or edge dislocation b = 1/3<1120 >, l = <0001> 15 a: Full core or 8 atom ring, b: 4 atom ring, c: Open core or 5/7 atom ring 16 For Peerr Review Only 17 and screw dislocation b = <0001>, l = <0001> 18 d: Full core, e: Open core 19 20 In the basal plane, they may be 60° (the angle between the line direction and the 21 22 r r 23 Burgers vector is 60°), b = [1120 ], l = [ 2 1 1 0 ] or screw dislocations, b = [1120 ], l = 24 25 26 [1120 ]. 27 28 29 30 31 32 33 3. Experimental observations 34 35 36 37 3.1. Prismatic dislocations 38 39 40 41 The heteroepitaxially grown GaN layers on (0001) sapphire substrates whatever the 42 43 growth process, e.g. molecular beam epitaxy (MBE) or metal organic chemical vapour 44 45 46 deposition (MOCVD), are characterised by high densities of threading dislocations running 47 48 across the layer from the layer/substrate interface to the top surface with their line mainly 49 50 9 -2 51 parallel to the <0001> growth direction [27]. This density is in the order of 10 cm in 52 11 -2 53 conventional growth and can go up to 10 cm whatever the growth method; pure edge 54 55 r r 56 dislocation (b =1/3<11>,20 l = <0001>) and mixed dislocation (b = 1/3<1123 >, l = <0001>) 57 r 58 concentrations may be comparable and the fraction of pure screw dislocations (b =<0001>, l 59 60 = <0001>) is usually low: 0.1 to 1% (Fig. 3) [28].

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 Fig. 3: Typical threading dislocations in MBE GaN layers grown on sapphire: 19 20 dark field a) g = 1120 b) g = 0002 [29] 21 22 3.1.1. Edge or mixed threading dislocations 23 24 25 The first observations of these threading dislocations by HRTEM showed that in good 26 27 quality GaN layers grown by MBE at 800°C on (0001) sapphire, two atomic configurations 28 29 coexisted: the 8 atom core and a 5/7 atom core (Fig.4) [13]. 30 31 32 33 34 35 Fig. 4: HREM images along <0001> 36 of the 1/3 <1120 >edge dislocation: 37 38 8 atom ring (a and b), 39 5/7 atom ring (c and d), 40 (defocus values, a and c:-24nm, 41 b and d:-54nm) [18] 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Later, in the investigation of low and high angle grain boundaries [18], it was shown that 56 57 58 a configuration with a 4 atom core is also present in the GaN layers (Fig.5). The identification 59 60 of the atom cores is based on the analysis of experimental and simulated contrasts of the

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1 2 3 images [30]. This was shown to be in agreement with the atomistic calculations of 4 5 6 stoichiometric configurations [20]. 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 Fig.5: Occurrence of 4 atom ring configurations (arrows) for the 1/3<1120 > edge dislocation 19 observed in a non symmetric Σ=7 grain boundary (Black dots delimit the unit periods of Σ=7, 20 and the white lines the different atom rings: 6 for the perfect crystal, 5/7, 8 and 4 for the cores 21 22 of the 1/3<1120 > edge dislocation) [18]. 23 24 25 Simultaneously, a report was issued using High Angle Annular Dark Field (HAADF) (Z- 26 27 28 contrast) imaging showing that the edge dislocation atomic structure was made of 8 atom core 29 30 [31]. It was argued that such a core should be the only one occurring in GaN in agreement 31 32 with the theoretical predictions that tried to explain the good electrical and optical properties 33 34 35 of GaN layers. For such low electrical activity, the three-fold coordinated atoms in the core 36 37 had to form dimers along the <0001> line direction. 38 39 In epitaxial GaN layers grown at 800°C on a GaN or AlN buffer layer deposited at 550°C, 40 41 42 low-angle and high angle grain boundaries were found and analysed (Fig. 6) [32]. By electron 43 44 diffraction, grain boundaries were identified with rotation angles in the range 1.5-22°. The 45 46 47 dislocations were still 1/3<1120 > edge type as deduced from the use of the invisibility 48 r r 49 criterion gr.b = 0 ( gr : diffraction vector,b : Burgers vector). 50 51 52 Three high angle grain boundaries crossing all the GaN layers were perfectly analysed 53 54 from HRTEM images by combining topological theory [33] and image simulation [30]. They 55 56 57 were described by rotations around the <0001> direction and the values of the rotation angle, 58 59 as determined from the diffraction patterns, were 13.2±0.2°, 19±0.2°, and 22.0±0.2° [18]. It is 60 well known that the atomic structure of low angle grain boundaries is periodic and based on a

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1 2 3 regular array of dislocations. This concept was then extended to specific high angle grain 4 5 6 boundaries, establishing that the atomic structure of coincidence grain boundaries is also 7 8 periodic [34]. 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 Fig.6: Plan view along [0001] direction showing arrays of dislocations forming low and high 30 31 angle grain boundaries [32]. 32 33 34 35 These coincidence grain boundaries are defined for specific values of the axis and of the 36 37 38 angle of rotation giving rise to a 3D superlattice, the Coincidence Site Lattice (CSL), common 39 40 to the two adjacent crystals. In the hexagonal system, for rotations around <0001>, angles of 41 42 13.17°, 17.90° and 21.79° lead to CSLs which are characterized by their periodic unit cells 43 44 45 [35]. The common characteristic of the atomic structures of these coincidence grain 46 47 boundaries is the regular array of the cores of the edge dislocation 1/3<1120 >. In Fig.5, 48 49 50 between two black dots delimiting the CSL unit cell, 6 atom rings corresponding to the 51 52 perfect crystal are combined with other atom rings. According to the contrast observed in the 53 54 HRTEM image and by comparison with the simulated images, the cores were identified as 4, 55 56 57 5/7 or 8 atom rings. These investigations have allowed us to show that the above dislocation 58 59 cores are the only structural units, which in addition to the 6 atom unit of the hexagonal 60

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1 2 3 lattice, can be present in all the possible grains boundaries that form by a rotation around the 4 5 6 [0001] direction in GaN [18, 35]. 7 8 Other extended defects have been shown to exhibit a dislocation character with larger 9 10 Burgers vectors than unitary lattice parameters. In figure 7, the circuit around the defect 11 12 r 13 exhibits a closure failure, corresponding to a basal component equal to 2 a [36]. These defects 14 15 were identified as nanopipes in comparison to the micropipes observed in SiC [37], but with 16 For Peer Review Only 17 18 rather small radii in contrast to the previsions of the Frank formula [38]. 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 r 42 Fig.7: A nanopipe with a Burgers edge component of 2 a [36] 43 44 45 46 47 In conclusion, the atomic structures of the cores of the1/3<1120 > prismatic edge 48 49 50 dislocations in GaN analysed by HRTEM combined with simulated images present a multiple 51 52 atomic configuration: three atomic structures were identified (8 atom ring or full core, 5/7 53 54 atom ring or open core and 4 atom ring). The 8 atom ring or full core was the only one 55 56 57 identified by HAADF. 58 59 60

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1 2 3 4 5 6 3.1.2. Screw prismatic dislocations 7 8 The first investigations of the surface of GaN layers, grown by MOCVD at 1040°C on 9 10 11 an AlN buffer layer deposited at 450-500°C, using scanning force microscopy have shown the 12 13 presence of tunnel-like defects aligned along the <0001> growth direction. The radii of theses 14 15 tunnels are in the 3.5-50nm range and they propagate along the growth direction. These 16 For Peer Review Only 17 18 defects are called nanopipes. These experimental investigations have also shown that the 19 20 screw dislocation associated with a nanopipe emerges on the top surface as a wide crater with 21 22 60-100 nm radii. By combining these observations with HRTEM analysis, it was concluded 23 24 r 25 that the nanopipes are the open cores of screw dislocations (b =0001) [39]. This result was 26 27 later confirmed by showing that such defects may alternate from an open (nanopipe) to closed 28 29 30 core along their way to the surface of the epitaxial layer (classical character of a dislocation) 31 32 [40]. The atomic structure of full core screw dislocations was reported in a high resolution Z- 33 34 contrast analysis [31]. The growth mode can affect the dislocation core and as was shown in 35 36 37 hydride vapour phase epitaxy (HVPE) grown materials, screw dislocations are decorated by 38 39 voids or pinholes [41]. The fluctuations in the intensity of the atomic columns in HRTEM of 40 41 42 the HVPE specimens have been attributed to local excess of gallium atoms in the core [42]. 43 44 45 46 47 3.2. Basal dislocations 48 49 GaN layers deposited on top of the (0001) sapphire are characterised by the well known 50 51 epitaxial relationship: (0001) //(0001) and [11]20 //[10 10 ] [43]. The network of 52 sap GaN sap GaN 53 54 anions is continued across the interface. The misfit is large (-16.07%) and it is accommodated 55 56 by misfit dislocations in the basal plane. The possible Burgers vectors of the perfect 57 58 59 dislocations are 1/3<1120 >, and the line directions are <1120 > leading to pure screw or 60° 60 dislocations according to the angle between the Burgers vector and the line direction.

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1 2 3 After Bragg filtering of HRTEM images, it was shown that this lattice misfit is relaxed 4 5 6 in the first monolayer of GaN with a network of regularly spaced 60° dislocations. A residual 7 8 stress of –2.1% was evaluated near the interface and related to the high density of threading 9 10 dislocations present in the epitaxial layer [44]. 11 12 13 Since threading and misfit dislocations are always present, investigations were carried 14 15 out at an interface between AlN and sapphire in order to analyse the connection of these two 16 For Peer Review Only 17 18 dislocation networks [45]. Molecular Beam Epitaxy (MBE) was used for the deposition of the 19 o 20 AlN buffer on Al2O3, at 800 C, until a thickness of 40 nm was reached. In HRTEM plan view 21 22 23 images, a set of three-fold moiré patterns due to the overlap of the {10}10 AlN and {11}20 sap 24 25 planes is formed at the layer-substrate interface with a mean spacing of 2.16nm instead of 26 27 2.029nm for the theoretical value. This discrepancy means that 7% of the compressive stress 28 29 30 is not relaxed by the misfit dislocations. From the moiré pattern, the occurrence of threading 31 32 dislocations is readily deduced from the terminating moiré fringes (Fig.8). 33 34 35 36 37 38 39 40 41 42 Fig.8: Plan-view HRTEM image showing a 43 translation moiré pattern (a) one set of 44 45 reflections, (b) a second equivalent set [45] 46 47 48 49 50 51 52 53 54 55 56 The dislocation density measurements from various areas of the moiré pattern showed an 57 58 average density in the order of 1.5 x1011 cm-2 with a lower rate near the top surface of 8x1010 59 60 cm-2. In figure 9, the white arrows indicate the terminating fringes due to the threading

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1 2 3 dislocation marked by the black fringes and corresponding to two extra prismatic half planes. 4 5 r 6 The circuit around the defect gives as Burgers vector a suggesting an edge or mixed type 7 8 dislocation. 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Fig.9: (a) Threading dislocations imaged by the terminating moiré fringes 36 (b) Schematic illustration of the misfit network 37 (c) Fourier filtered image showing only the AlN structure [45] 38 39 40 41 The corresponding missing half-planes are associated with two misfit dislocations of the 42 43 44 interfacial network as shown in Fig.9b. The Burgers vector of each threading dislocation is 45 46 equal to the algebraic sum of the Burgers vectors of the two associated misfit dislocations. 47 48 Similar observations with moiré analysis were carried out on HVPE grown layers on SiC 49 50 51 substrates [46]. Therefore, threading dislocations existing in GaN films can be related to the 52 53 misfit dislocations at the interface with the substrate. This view is complemented by other 54 55 investigations which show that many threading dislocations can originate inside the buffer 56 57 58 layer due to the recombination of stacking faults and subsequent climb of the dislocations in 59 60 the prismatic planes [47].

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1 2 3 4 3.3. Partial dislocations 5 6 7 In MOCVD layers grown on (0001) sapphire, evidence of dissociation in the basal plane 8 9 10 was shown using the weak beam technique and the following mechanism was proposed: 11 r r r r 12 cr + ar = ( cr / 2 + b ) + ( cr / 2 + b ), with b and b being Shockley partials, corresponding to the 13 1 2 1 2 14 15 formation of an intrinsic stacking fault I1 (Ponce et al., 1996). However, after introduction of 16 For Peer Review Only 17 dislocations by indentation, dissociation of the perfect screw dislocation or 60° dislocation 18 19 20 into partial dislocations was not observed in the limit of the weak beam resolution, 2nm, 21 22 however stacking faults were present in the nodes formed by the screw dislocations [48]. In 23 24 hexagonal structures, three basal faults are possible: two intrinsic I1 and I2 and one extrinsic E. 25 26 27 I1 is formed by removing the B plane above the A plane and shearing the remaining part by 28 29 1/3 < 10 10 >, I2 is formed by considering only the shear, and E by inserting one C plane 30 31 32 between two adjacent basal planes. The energy of the basal stacking faults was calculated 33 2 34 using DFT: I1 = 18, I2 = 43 and E = 69 mJ/m [49, 50]. They are of the low-energy type. In 35 36 HRTEM, the density of stacking faults near the interface with the substrate is very high, most 37 38 39 of them are of the I1 and I2 types even if segments of the E fault were also observed and partial 40 41 dislocations were identified. 42 43 The I fault was interpreted as the climb-dissociation process: 44 1 45 46 of the 1/3<1120 > following the reaction: 47 48 49 1/3<1120 > 1/6< 2023 > + 1/6< 02>23 50 51 or of the <0001> perfect dislocation: 52 53 54 <0001> 1/6< 2023 > + 1/6< 2>.203 55 56 The I2 fault results from the shear of the structure leading to a partial dislocation loop, the 57 58 59 two partial dislocations bounding the basal fault have opposite Burgers vectors 1/3<10 10 > 60 [51]. Partial dislocations, 1/3<1010 >, can also be formed at the intersection of a basal stacking

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1 2 3 fault with an inversion domain [19]. Besides the above dislocations, the dissociation of the 4 5 r r 6 mixed a + c dislocation, has recently been reported from Z contrast observations, where the 7 8 edge and screw cores were separated by a stacking fault lying in a {1010 } plane. As this 9 10 11 dissociation is not energetically favourable, it was assumed to occur in the presence of point 12 13 defects or impurities [52]. 14 15 16 For Peer Review Only 17 18 3.4. Electrical properties of the threading dislocations in GaN 19 20 21 Seeing the high brightness of the first GaN based devices which contained a very large 22 23 number of threading dislocations, it has first been assumed that the electrical activity should 24 25 be taken as substantially low. In the last ten years, a number of reports have shown that this is 26 27 28 not the case after the use of two techniques: the scanning probes in the atomic force 29 30 microscope that mostly analyse the properties of the individual defects close to the sample 31 32 surface, and cathodoluminescence (CL) in TEM. 33 34 35 36 37 3.4.1. Scanning probe microscopy investigations 38 39 40 In their leakage current comparative work on GaN based devices from layers grown by 41 42 HVPE and MBE, Hsu et al. showed that the reverse bias leakage was not uniformly 43 44 distributed in the sample [53]. A small portion of the sample was found to be responsible for 45 46 47 the majority of the leakage. The correlation between reverse bias leakage locations and 48 49 topographic hillocks in samples suggested that reverse bias leakage primarily occurred at 50 51 screw/mixed dislocations. Further confirmation was given from the similar density between 52 53 54 the leakage spots and screw/mixed dislocation density determined by TEM. The fact that 55 56 samples had distinctly different morphologies but showed similar density of leakage spots led 57 58 to the conclusion that the origin of the reverse bias leakage was the same in the set of samples. 59 60 They showed that screw/mixed dislocations contribute significantly more to gate leakage than

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1 2 3 pure edge dislocations. This was in agreement with other reports where screw/mixed 4 5 6 dislocations had been found to be more effective recombination centers [54], and to have 7 8 reduced barrier heights compared to pure edge dislocations [55]. In such devices, the reverse 9 10 bias leakage can be orders of magnitude different for samples grown under slightly different 11 12 13 conditions. For example, the reverse bias current was orders of magnitude higher for Ga-rich 14 15 samples. Given that dislocations with a screw component are responsible for the reverse bias 16 For Peer Review Only 17 18 leakage and their density is the same for the HVPE template and the two MBE/HVPE films, 19 20 these results led to conclude that the dislocation electrical activity was sensitive to local 21 22 chemical and/or structural changes, which depend on growth methods and conditions. 23 24 25 3. 4. 2. Cathodoluminescence investigations 26 27 Correspondence between the individual dislocations and the active centres in MOVPE 28 29 GaN layers by combining TEM and cathodoluminescence has shown that the dislocations are 30 31 r 32 non-radiative recombination centers [56]. Remmele et al. [57] were able to distinguish the a 33 34 threading dislocations and ar + cr dislocations in their bright field images, since the 35 36 r r r 37 c component of the a + c dislocations caused a black and white lobe contrast due to surface 38 39 relaxation effects [58]. The ar dislocations showed only a dark contrast. The comparison of 40 41 the bright field images and the monochromatic CL mapping (band edge luminescence) gave 42 43 r r 44 the following results: (i) the major part of the a + c dislocations is not recombination active. 45 46 (ii) ar threading dislocations reduced the band edge luminescence, thus representing centres of 47 48 r 49 non-radiative recombination, (iii) a dislocations in the basal plane caused non-radiative 50 51 recombination. 52 53 54 55 4. Atomistic simulation of dislocations in GaN 56 57 The main goal of atomistic modelling of dislocations is to find realistic models of the 58 59 60 cores and provide information on the microscopic mechanisms occurring in this area. From

such studies one expects to derive, at least, two types of information. The first is to identify

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1 2 3 course, the treatment of compound semiconductors raises the problem of the wrong bonds, 4 5 6 which may form in the cores of crystallographic defects. For GaN, we have made a new 7 8 parameterisation of the Stillinger-Weber potential in order to allow a complete calculation of 9 10 any atomic configuration with dangling bonds, wrong bonds and excess bonds [75]. This 11 12 13 parameterisation was successively used by Chen et al. [20], Béré et al. [76], Kioseoglou et al. 14 15 [77], Lymperakis et al. [23] and Belabbas et al. [78] to investigate the atomic structures of 16 For Peer Review Only 17 18 dislocations in GaN. 19 20 21 22 4.1.3. The tight-binding methods 23 24 25 26 Coming right in between the ab initio and empirical potential methods, tight-binding 27 28 methods combine a minimal amount of quantum mechanics of electrons with classical 29 30 potentials. This allows achieving more transferable description of the interatomic interactions 31 32 33 than empirical potentials, at a small fraction of the computational cost of ab-initio 34 35 calculations. Consequently, tight-binding methods are appropriate to model systems with 36 37 many hundred to a thousand atoms and can be applied to deal with problems beyond the reach 38 39 40 of ab-initio methods. In standard tight-binding methods, the total energy of the system is 41 42 approximated by a sum of two terms [79]. The first, called the band structure energy, contains 43 44 45 the quantum electronic effects; it is obtained by solving non self-consistent Kohn-Sham like- 46 47 equation [80]. Here, the single electron wave functions are represented by linear combinations 48 49 of atomic orbital. Hamiltonian and overlap matrix elements are evaluated in the framework of 50 51 52 the two-centre approach of Slater-Koster [81]. The second is a short-ranged diatomic 53 54 potential, which is fitted to ab-initio calculations or experimental measurements in order to 55 56 reproduce a selected set of materials properties. Better accuracy and transferability is obtained 57 58 59 using the self-consistent tight-binding methods [82]. In these methods, an additional term is 60 added to the energy functional and adjusted through a self-consistent procedure. This is useful

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1 2 3 to take into account the charge transfer occurring in compound semiconductors like GaN. The 4 5 6 Self-Consistent Charge Density Functional Tight-Binding (SCC-DFTB) [83-85] is a self- 7 8 consistent extension of the standard DFTB method [86]. The SCC-DFTB total energy was 9 10 derived by expanding the Kohn-Sham energy functional to the second order with respect to 11 12 13 the electronic density fluctuations around a given reference density [80, 83]. Besides the two 14 15 usual energetic terms, i.e. the band structure energy and the short-ranger diatomic potential, a 16 For Peer Review Only 17 18 third term is introduced where a self-consistent procedure is incorporated at the level of 19 20 Mulliken charges to account for charge transfer. This last term allowed to the SCC-DFTB 21 22 technique to achieve accuracy comparable to that of ab-initio methods. Among the tight- 23 24 25 binding methods, the SCC-DFTB method is one of most successful as applied to dislocations 26 27 in GaN [2, 78, 87- 91]. 28 29 30 31 32 4.2. Results of dislocation modelling in GaN 33 34 From 1997, there has been a tremendous effort in the field of atomistic modelling to 35 36 37 study dislocations in GaN. These studies attempt to provide some information about the core 38 39 configuration of these dislocations and their effect on the electronic performance of the grown 40 41 42 layers. Several kinds of dislocations have been investigated in wurtzite GaN; these were 43 44 perfect or partial with edge, screw or mixed character, belonging to the prismatic or the basal 45 46 plane. 47 48 49 4.2.1. Perfect prismatic edge dislocation 50 r 51 The prismatic edge dislocation (b = a/3<1120 >, l=<0001>) was the first dislocation to 52 53 54 be investigated in wurtzite GaN [2]. This dislocation displays different core structures with 55 56 stoichiometric configurations (8, 5/7 and 4 atom rings) (Fig.10) or non-stoichiometric 57 58 configurations (8-V and 8-V atom rings). The core with 8 atom ring structure or full-core 59 Ga N 60 contains a column of three fold coordinated atoms whereas the 5/7 atom ring structure or

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1 2 3 open-core contains wrong bonds (Ga-Ga, N-N). The core with 4 atom ring structure contains 4 5 6 fully coordinated atoms establishing four in-plane bonds [20]. The non-stoichiometric 8-VGa 7 8 or 8-VN cores can be obtained from the core with 8 atom rings removing some of Ga or N 9 10 atoms from the central column, while the complete removal of this column leads to the 5/7 11 12 13 core [2, 14, 21, 66, 88, 92]. Béré et al. have shown that the different cores (8, 5/7, 4) are, in 14 15 fact, obtained in a straightforward manner only by changing the origin of the displacement 16 For Peer Review Only 17 18 elastic field during the generation of the model [21]. In the framework of ab-initio and tight- 19 20 binding (SCC-DFTB) calculations, Elsner et al. [2] reported that the core with 8 atom ring 21 22 structure is more energetically favorable than that with 5/7 atom ring structure. However, all 23 24 25 the subsequent calculations performed with different methods: empirical potentials -Modified 26 27 Stillinger-Weber- [20, 76], tight-binding -SCC-DFTB- [88] and ab initio [23] suggest the 28 29 opposite. In the case of the core with 4 atom ring structure, Chen et al. found it less 30 31 32 energetically favorable than that with 8 atom ring structure [20]. 33 34 35 (a) (b) 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 (c) 53 54 55 56 57 58 59 60

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1 2 3 4 Fig. 10: View along the [0001] direction of the atomic core configurations of the prismatic 5 edge dislocation. a) 8 atom ring core, b) 4 atom ring core, c) 5/7 atoms ring core. 6 7 8 More recently, the core with 4 atom ring structure was reinvestigated by means of 9 10 multiscale calculations: ab-initio, empirical potential and continuum elastic theory [23]. The 11 12 13 authors showed that under a tensile strain, the 4 atom ring core becomes the most 14 15 energetically favorable among the three cores of the stoichiometric edge threading 16 For Peer Review Only 17 18 dislocations. 19 20 Since the structure of tilt grain boundaries is described with a periodic array of the edge 21 22 dislocation, they were investigated using our empirical potential. They were generated 23 24 25 through rotations around the [0001] direction and it was then possible to show that the 26 27 concept of structural units was valid for the hexagonal system [35]. In this instance, the 28 29 building units for all grain boundaries were the 6 atom ring for the perfect lattice and the 5/7 30 31 32 atom core for the grain boundary dislocations (Fig. 11) [93]. 33 34 35 36 37 38 39 + - 40 Σ=7: 57 Σ=13: 57/57 Σ=13: 57 57 41 42 43 Fig.11: Structural units for coincidence grain boundaries from rotations around [0001] based 44 on the 5/7 atom ring core, the corresponding Σ is indicated [93] 45 46 47 This was a good indication that the hexagonal system did not exhibit fundamentally 48 49 50 different mechanisms for defect formation than the cubic, at least along high symmetry 51 52 directions. 53 54 A set of calculations based respectively on ab-initio [66], tight-binding –SCC-DFTB- 55 56 57 [88] and Monte-Carlo [92] methods revealed that the formation energy of the prismatic edge 58 59 dislocations with non-stoechiometric cores (8-VGa and 8-VN) strongly depends on both the 60

growth conditions and the doping nature of the material. The 8-VGa core was shown to be

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1 2 3 more energetically favourable in n-type material grown under N-rich conditions whereas the 4 5 6 8-VN core is favourable in p-type material grown under Ga-rich conditions [66]. However, 7 8 Lee et al. obtained favorable formation energies for cores with both 8 and 5/7 atom rings 9 10 structures in material grown under Ga-rich conditions [88]. 11 12 13 The electronic structure of the prismatic perfect edge dislocation with different core 14 15 configurations has also been investigated extensively [2, 23, 66, 67, 88]. According Elsner et 16 For Peer Review Only 17 18 al. the edge dislocation with 8 atom ring core structure is electrically inert and induces no gap 19 20 states [2]. Therefore, it has undergone a relaxation of the three fold coordinated Ga (N) core 21 22 atoms toward sp2 (p3) similar to the (10 10 ) surface, which leads the dimerization of the 23 24 25 bonds along the dislocation line. However, several calculations performed on the same core 26 27 configuration have revealed the presence of empty states at the half top of the band gap [22, 28 29 30 23, 67, 88]. A quite similar electronic structure has been reported for the dislocation with 5/7 31 32 atom ring core structure (Fig.12) [23, 88]. 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 core-8 (a) core-8 (b) core-8 VGa (a) core-8 VN (a) core-5/7 (a) core-5/7 (b) core-4 (b) 54 55 56 Fig.12: Schematic diagram of energy levels induced in the band gap by different cores of 57 the prismatic edge dislocation: 8 atom ring core (core-8), 5/7 atom ring core (core-5/7) 58 and the 4 atom ring core (core-4), dark balls indicate filled levels, (a) [88], (b) [23] 59 60

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1 2 3 For the 4 atom ring edge dislocation, an unexpected behavior has been reported recently: 4 5 6 despite its fully coordinated core, it exhibits deep states in the band gap [23]. This was 7 8 attributed to the large strain field surrounding the dislocation core which leads to the 9 10 formation of bonding between Ga second neighbor atoms similar to metallic gallium. Tight- 11 12 13 Binding calculations carried out on the non-stoichiometric structures have revealed for the 8- 14 15 VGa core, the presence of both occupied states at 0.2 eV from the VBM (Valence Band 16 For Peer Review Only 17 18 Maximum) and empty states just below the CBM (Conduction Band Minimum) [88]. The 8- 19 20 VN core has been shown to induce different states throughout the band gap; it may be 21 22 expected to be an origin of yellow luminescence. 23 24 25 The electronic structures of the (3740) Σ=37 (θ = 9.3º), (3520) Σ=19 (θ = 13.4º) and 26 27 28 (1320) Σ=7 (θ = 21.6º) tilt grain boundaries were calculated. They were investigated by 29 30 means of SCC-DFTB approach. Among the three possible atomic configurations of these 31 32 33 boundaries, namely, the interfaces based on the 5/7, the 4 and the, it was found that the 34 35 structure based on the 8 atom ring core introduces deep states in the very center and the upper 36 37 half of the band gap whereas the grain boundaries based on the 5/7 atom ring possess only 38 39 40 states close to the conduction band (Fig.13) [90]. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 β 4 Fig.13: Schematic diagram of energy levels in the band gap, (notation Iα , α refers to the grain 5 boundary and β to the dislocation core type, Cβ denotes the core of the edge dislocation [88, 6 90]. 7 8 9 10 The comparison with the electronic structure of the prismatic dislocation shows a 11 12 similar behaviour for the grain boundaries with the 8 atom rings and the introduction of deep 13 14 15 states inside the band gap. Given that for an electrically neutral boundary the deep states are 16 For Peer Review Only 17 unoccupied, the 8 atom ring structure may contribute to yellow luminescence in GaN layers. 18 19 In any case, empty gap states will localize carriers for the recombination. For the grain 20 21 22 boundaries built up with the 5/7 atom rings only states close to the conduction band are 23 24 predicted. 25 26 27 28 29 30 4.2.2. Perfect prismatic screw dislocation 31 32 r 33 The prismatic perfect screw dislocation (b = c<0001>, l = <0001>,) is one of the most 34 35 studied dislocation in wurtzite GaN. Several calculations have been carried out on their 36 37 atomic and electronic core structures. Different core structures have been investigated: the 38 39 40 full-core [2, 67, 76, 89], the open-core [2, 15] and non-stoichiometric configurations [15, 16] 41 42 (Fig.14). In the first configuration, six stoichiometric atomic columns, in helical like 43 44 symmetry arrangement along the direction [0001], form a hexagonal atomic core. By 45 46 47 removing the latter, the open-core configuration is obtained. However, filling the core with 48 49 different amounts of Ga and N atoms leads to non- stoichiometric configurations, where the 50 51 52 Ga-filled and N-filled cores represent the extreme limits. In their report, Elsner et al. have 53 54 investigated prismatic screw dislocation with both full-core and open-core configurations [2]. 55 56 The calculation of the line energy, in a cylinder of radius about 8 Å, gave 4.88 eV/ Å for the 57 58 59 full-core and 4.55 eV/ Å for the open-core configuration. This was higher than their value of 60 2.19 eV/ Å found for the full-core edge prismatic dislocation. Similar high line energy values

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1 2 3 were also reported by different authors for the screw full-core dislocation. This probably 4 5 6 explains why the screw dislocations represent a small fraction with respect to the edge type in 7 8 GaN epitaxial layers [15, 76, 89]. 9 10 Recent ab initio calculations performed by Northrup [15, 16] revealed that screw 11 12 13 dislocation with non-stoichiometric core configurations could be more energetically 14 15 favourable than those with stoichiometric cores under some growth conditions. The Ga-filled 16 For Peer Review Only 17 18 core, obtained by removing all the N atoms from the hexagonal core, is predicted to be the 19 20 most stable configuration under the Ga-rich conditions [15]. However, in N- rich conditions, a 21 22 non-stoechiometric core structure with Ga (50%) and N (25%) atoms was found more 23 24 25 energetically favourable [16]. 26 27 28 29 (A) (B) 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (C) 46 47 48 49 Fig.14: Atomic core structures of the 50 51 prismatic screw dislocation: 52 A) View along the [0001] direction of 53 the full-core structure. B) View along 54 the [1120 ] direction of the full-core 55 structure. C) View along the [0001] 56 57 direction of the open-core structure. 58 59 60

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1 2 3 4 5 6 In the full-core configuration, due to the presence of heavily distorted bonds, additional 7 8 charge transfers should occur and gap states are induced. Belabbas et al. have identified an 9 10 extra charge transfer of 0.12e, besides that naturally occurring in GaN bulk material, from Ga 11 12 13 to N atoms [89]. The electronic structure calculations performed on the full-core dislocation 14 15 have revealed the presence in the band gap of shallow as well as deep states [2, 67]. In the 16 For Peer Review Only 17 18 open-core dislocation, in order to lower the surface energy, the internal wall of the core 19 20 relaxes like the (10 10 ) surface and then the threefold coordinated atoms Ga (N) adopt sp2 21 22 (p3) hybridization. For this dislocation, only shallow states were reported and attributed to the 23 24 25 distortion of the wall surface along the direction [0001] due to the Burgers vector [2]. For the 26 27 non-stoichiometric dislocations, the Ga-filled core configuration was predicted to have a 28 29 30 metallic like-behaviour as its induced states are highly dispersed in the entire band gap [15, 31 32 16, 67]. However, this behaviour is less pronounced in the most favourable core structure (Ga 33 34 50%, N 25%) in N-rich conditions [16]. 35 36 37 38 39 4.2.3. Perfect basal edge and screw dislocations 40 41 Up to date, there are only a few reports on the atomic core structures of the perfect basal 42 43 r r 44 edge ( b = c<0001>, l= <1120 >) and screw (b =a/3<1120 >, l= <1120 >) dislocations [76, 45 46 78]. In the ELO (Epitaxial Lateral Overgrowth) process, the threading dislocations are bent 47 48 49 [94]. Thus, a dislocation changes its line direction from <0001> to <1120 > resulting in a new 50 51 character, edge or screw. These basal dislocations can occur during the heteroepitaxial growth 52 53 54 on the non-polar (1120 ) a-plane [95]. 55 56 Recently, Belabbas et al. have investigated the atomic structure and the electronic 57 58 59 activity of the basal edge dislocation in wurtzite GaN by combining empirical potentials 60 (Modified Stillinger-Weber) and tight-binding methods (SCC-DFTB)[78]. For this dislocation

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 (a) G1 configuration (b) G2 configuration (c) S1 configuration (d) S2 configuration 25 26 27 Fig. 16: Electronic gap states associated with different configurations of the basal edge 28 dislocation. The zero has put on the top of the valence band maximum while the 29 conduction band minimum is at 3.4 eV. 30 31 32 As can be seen, each core configuration induces deep as well as tail states. Filled states 33 34 exist in the bottom half of the band gap, up to 1eV from the VBM. For all the configurations, 35 36 unfilled deep states are present on the top half of the band gap, and are located mainly 37 38 39 between 2 and 3 eV, from the VBM. In this area, the states induced by G1 are more spread 40 41 than those of the other configurations. Due to the presence of the deep states, one could 42 43 44 expect the basal edge dislocations to be at the origin of parasitic luminescence. However, it 45 46 cannot be excluded that the G1 configuration may be involved in non-radiative recombination 47 48 processes. 49 50 51 The atomic structure of the perfect basal screw dislocation has been only investigated by 52 53 Béré et al., their study is based on a modified Stillinger-Weber potential [76]. Two stable core 54 55 configurations were identified; one belongs to the glide set while the other belongs to the 56 57 58 shuffle set. The screw dislocations were found to have a core diameter of 6.7 Å. The glide 59 60

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1 2 3 configuration has a line energy of 1.20 eV/Å, 2% higher than that of the shuffle 4 5 6 configuration. 7 8 9 10 4.2.4. Perfect basal 60° dislocation 11 12 13 In zinc-blende GaN, Blumenau et al. have studied the atomic and electronic structures 14 r 15 and the relative energies of the 60° basal dislocation (b = a/2[1 10 ], l = < 011 >), with both 16 For Peer Review Only 17 18 glide and shuffle configurations (Fig.17) [22, 95]. 19 20 21 22 23 (A) (B) 24 25 26 27 28 29 30 31 32 33 34 35 (C) (D) 36 37 38 39 40 41 42 43 44 45 46 47 Fig. 17: The core configurations of the perfect 60° dislocation in wurtzite GaN. (A) The α 48 49 (N-terminated) shuffle configuration. (B) The β (Ga-terminated) shuffle configuration. (C) 50 The α (N-terminated) glide configuration. (D) The β (Ga-terminated) glide configuration. 51 Black balls represent gallium atoms and the white ones nitrogen atoms. 52 53 54 55 56 For the shuffle dislocations both the α (N-terminated) and β (Ga-terminated) 57 58 configurations were investigated. The α core shuffle dislocation was found to have an 8 atom 59 60 rings like structure, with three fold coordinated atoms exhibiting a sp3 like hybridisation

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1 2 3 despite their relaxation along the [111] direction. The β core shuffle dislocation was shown to 4 5 6 exhibit a 5/9 atom ring like structure with wrong bonds (Ga-Ga). Moreover, this core presents 7 8 a double period reconstruction leading to a charge modulation of ± 0.2 e- along the dislocation 9 10 11 line direction. The glide dislocation with α(β) core was obtained by only removing the Ga (N) 12 13 three fold coordinated atoms column from the shuffle β(α) core dislocation. Its core exhibited 14 15 16 5/7 atom ringsFor like structure Peer and it was Review shown to be more energeticallyOnly favourable than its 17 18 corresponding shuffle dislocation with β(α) core (Fig.17). 19 20 21 The calculated electronic structures of the 60° dislocation have shown that the shuffle α 22 23 core configuration induces half filled gap states at 0.2 eV from the VBM, while the shuffle β 24 25 26 core configuration induces states at 0.3 eV from the VBM. The 60° glide β core introduces 27 28 shallow occupied states at 0.3 eV from the VBM as well as deep non-occupied states at 1.6 29 30 31 eV from the VBM, whereas the glide α-core induces only shallow occupied states at 0.5 eV 32 33 from the VBM. These results show that the 60° dislocation is electrically active and suggest 34 35 that those with the shuffle core configurations could act as a shallow acceptor in agreement 36 37 38 with the results of As et al. showing that dislocations in cubic GaN act as acceptors and are 39 40 electrically active [96]. 41 42 43 44 45 4.2.5. Partial basal dislocations 46 47 From their recent investigation, Savini et al. have reported the atomic and electronic 48 49 r 50 structures of the 90° Shockley partials, (b = a/3[10 10 ], l = <1120 >), in wurtzite GaN 51 52 (Fig.18) [68]. They used ab-initio calculations, implemented in the AIMPRO code, to model 53 54 55 partial dislocations with α (N-terminated) and β (Ga-terminated) cores in both supercells and 56 57 cluster-supercell hybrids. By limiting their investigations to the glide configurations, they 58 59 60 showed that the two partials can adopt both symmetric and asymmetric core reconstructions depending on the environment of the dislocation. The asymmetric reconstruction was found to

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1 2 3 be the most favourable and the energy difference between the two reconstructions was 83.2 4 5 6 meV for the β-core and 196.4 meV for the α-core. The calculated electronic structure 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 Fig.18: The core configurations of the 90° Shockley partials. (A) The α (N-terminated) 23 24 core configuration. (B) The β (Ga-terminated) core configuration. The doted line 25 indicates the intrinsic stacking fault. Black balls represent gallium atoms and the white 26 ones nitrogen atoms. 27 28 29 30 exhibited mid gap states for both dislocations cores, and for the α core a deep acceptor level 31 32 at 1.11 eV and for the β core a deep donor level at 0.87 eV, from the VBM, was pointed out. 33 34 35 The first level is expected to give rise to a 2.3 eV radiative transition which could contribute 36 37 to the yellow luminescence [97], while the second one may be correlated to the 2.4 eV 38 39 absorption peak in agreement with energy loss spectroscopy measurements [98]. Based on 40 41 42 Voronoi cell analysis of the charges density, it was shown that these partial dislocations 43 44 present a charge polarization along [0001] with a negatively charged compressed region and a 45 46 positively charged tensile region. Moreover, when these dislocations were brought together 47 48 49 and in the presence of a high stress, a charge transfer was shown to occur from the β-core 50 51 dislocation to the α-core dislocation. It was concluded that such charges may be able to screen 52 53 54 the carriers from recombination in the dislocation cores and explain why GaN devices may 55 56 tolerate high dislocation densities. 57 58 59 In their empirical potentials investigation, Kioseoglou et al. have performed a systematic 60 investigation of the atomic core structures and the corresponding energies of both edge

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1 2 3 r r 4 (b =1/6[ 2023], l = [1210 ],) and mixed (b =1/6[ 2203], l = [1210 ]) Frank-Shockley partials 5 6 that bound the I1 intrinsic basal stacking fault in wurtzite GaN [99]. For the edge and mixed 7 8 partials, twelve stable configurations were found for each Ga and N core polarity, they consist 9 10 11 of 5/7, 8 and 12 atom rings like structures. For the edge partials, the 5/7 atom rings structure 12 13 was reported as the most energetically favourable with energies less than 0.76 eV/Å. Whereas 14 15 the 8 and 12 atom rings have energies ranging from 1.28 to 1.48 eV/Å. For the mixed partials, 16 For Peer Review Only 17 18 both the 5/7 and 12 atom rings structures were most stable. Their core energies are larger than 19 20 those of the edge dislocations and the energetically most favourable configurations have 21 22 23 energies ranging from 0.81 to 1.05 eV/Å. These partial dislocations should be electrically 24 25 active since they present similar structures to those of the 60° dislocations, already reported 26 27 by Blumenau et al. in cubic GaN [95]. 28 29 30 31 32 5. Discussion 33 34 35 The GaN layers are mostly grown on sapphire which exhibits a large mismatch, 36 37 and the area in the vicinity of the interface with the substrate contains a lot of defects. As 38 39 40 early as 1986, low temperature buffer layers (AlN, GaN) were largely used in the growth of 41 42 GaN resulting in high quality epitaxial layers [100]. In these layers deposited in the 500- 43 44 45 600°C temperature range, it was shown that many basal stacking faults form and during the 46 47 subsequent increase of the temperature for the active layer growth they may become the 48 49 origin of the threading dislocations[47]. The connection of the stacking faults and the misfit 50 51 52 dislocations has not yet been clearly demonstrated. However, the connection between the 53 54 origin of the threading dislocations and the highly strained interfacial area with substrate was 55 56 established [19]. This confirms more or less the rather simple picture of mosaic growth which 57 58 59 was published as early as 1997 [101]. Following their climb at grain boundaries or from the 60 SF reaction area in the buffer layer, the threading dislocations obtain their equilibrium

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1 2 3 structure as determined by the growth kinetics. i.e.: their line becomes mainly parallel to the 4 5 6 [0001] growth direction. The three topological dislocations of the hexagonal lattice have been 7 8 observed with a vast majority of ar edge ones, as reported from the start. The mosaic growth 9 10 of the layers allows the ar 60° interfacial dislocations to easily become pure edge along the c 11 12 13 axis forming low angle grain boundaries. The growth along the c axis limits the formation of 14 15 ar + cr < 10% dislocation and even more the cr ~1% as observed experimentally. 16 For Peer Review Only 17 18 As for the atomic structure, the investigations were first misled by the fact that, even if 19 20 the first layers contained 1010 cm-2 dislocations, the LEDs emission was the brightest known 21 22 in semiconductor optoelectronics. 23 24 25 The multiplicity of the atomic configurations was shown as early as 1998 with the 26 27 coexistence of the 5/7 and 8 atom ring cores in good quality GaN layers types[13] and the 28 29 occurrence of the additional 4 atoms core inside grain boundaries[18]. Of course, as it was 30 31 32 demonstrated later on, the three configurations are just a consequence of the wurtzite 33 34 structure, and the occurrence of each depends on the position of the dislocation line inside the 35 36 37 unit cell [21]. Then, by using our empirical potential [75] along with ab initio calculations, 38 39 Lymperakis at al. have carried out a multiscale analysis of this edge threading dislocation 40 41 [23]. They convincingly demonstrated that, the 4 atom ring core which has been first reported 42 43 44 in grain boundaries may be the most stable in strained layers [18]. 45 46 At the initial stages of the growth, many stacking faults are involved and partial 47 48 dislocations can be present. However, it is of interest to investigate their atomic structure. It is 49 50 51 may be noticed that as stressed by Narayan et al. [47], they will quickly develop in threading 52 53 dislocations and behave like the dislocations ar , ar + cr and cr of the hexagonal lattice. 54 55 The electronic structure of the threading dislocations has been extensively debated and 56 57 58 now the situation is clearer. For the prismatic edge dislocation with full or open core, empty 59 60 states are present in the half top of the band gap. Some discrepancies still remain about their

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1 2 3 positions for the open core. As demonstrated in the recent multiscale approach, the 4 atom 4 5 6 ring configuration exhibits deep states in the band gap, although it has no broken bond. These 7 8 states originate from the strain induced by the atomic structure, and cannot be removed. 9 10 Therefore, this configuration is forecast to be the most detrimental for the devices. 11 12 13 The prismatic screw dislocations display various atomic structures, full core, open core 14 15 and non-stoichiometric configurations under different growth conditions. Levels are present 16 For Peer Review Only 17 18 and the Ga-rich core induces levels which are spread all over the band gap. When these 19 20 dislocations bend and have their lines in the basal plane to become edge, screw or 60° 21 22 dislocations, they exhibit glide and shuffle configurations and wrong bonds may be present. In 23 24 25 these configurations, shallow or deep band gap states are present. 26 27 In the long run with the combined large experimental and theoretical work, it has 28 29 become obvious that the good optical emission of the GaN layer had little to do with the 30 31 32 recombination activity at the dislocation cores. In fact, the dislocations are harmful to the 33 34 transports properties of all the materials, probably depending on their geometry as well as 35 36 their chemistry (impurities, dangling bonds,). This was established when the fabrication of 37 38 39 laser diodes started, their lifetimes could only be substantially increased when the density of 40 41 the dislocations was brought in the low 108 cm-2 range using epitaxial lateral overgrowth. 42 43 44 45 6. Conclusion 46 47 48 In this paper, we presented and discussed our results dealing with the dislocations in 49 50 GaN layers. The dislocations are strongly involved in degrading the performance of the 51 52 devices. The atomic core structures of the perfect edge threading dislocations are based on 53 54 55 only three types of atom rings, however, depending on the layer growth conditions, they can 56 57 be stoichiometric or not. The perfect dislocations, threading and basal dislocations, have now 58 59 been largely investigated unlike the partial dislocations. Their electrical activity is in good 60

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