The mechanism of plastic deformation in intact and irradiated GaN during indentation: A molecular dynamics study

Computational Materials Science 149 (2018) 230–242

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The mechanism of plastic deformation in intact and irradiated GaN during indentation: A molecular dynamics study

T

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Yu Qiana, Fulin Shanga, , Qiang Wanb, Yabin Yanb a b

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, PR China Institute of System Engineering, China Academy of Engineering Physics, Mianyang 621900, Sichuan, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Molecular dynamics GaN Plastic deformation Indentation

A series of molecular dynamics simulations are carried out to study the mechanical properties of GaN. Firstly, indentation simulations are performed on the c-plane and m-plane GaN. Combined with the evolution of defects in the GaN substrate, the anisotropic mechanical responses are discussed in detail. It is found that plastic deformation in an intact c-plane GaN starts with generation and extension of planar defects. These planar defects eventually gather together and transform into a disordered region with a growing size. While for the m-plane GaN, the deformation during an indentation is dominated by the nucleation and propagation of dislocations. Secondly, the irradiation effect on the mechanical properties of GaN is investigated. Irradiated models, which subjected to different irradiation dose ranging from 5 eV/atom to 50 eV/atom, are adopted in the indentation simulations. A hardening phenomenon is found for the low-dose irradiated m-plane GaN, and the hardnesses of cplane and m-plane GaN decrease significantly when the irradiation dose exceeds 30 eV/atom. In addition, the indentations conducted on the irradiated models induce dramatically different deformation behaviors. In particular, with the increase of irradiation dose, the deformation mechanism transforms from the plastic activities on slip systems to local rearrangements of atoms in disordered regions.

1. Introduction As a direct wide band gap semiconductor, gallium nitride (GaN) has attracted considerable interests for a wide range of applications in optical, high-power and high-frequency devices [1–4]. In most opticalelectronic devices, the GaN material is typically in the form of a c-plane (0 0 0 1) film, and the c-plane wurtzite heteroepitaxial crystal growth on substrates such as sapphire is a mature technology [5,6]. However, epitaxial growth of GaN in c-direction [0 0 0 1] leads to spontaneous and piezoelectric polarization which might negatively affect the performance of devices. In order to eliminate polarization in the electric field, fabricating the GaN material on a nonpolar crystal plane has been employed, and the stable m-plane (1 0 −1 0) GaN has been commercially available at present [7–9]. A comprehensive understanding of the mechanical property of GaN is crucial and necessary in designing and producing the semiconductor devices, since material is subjected to unavoidable contact loads through the fabrication and encapsulation of GaN devices. And the damage caused by mechanical loads can significantly degrade the performance of the GaN devices. In addition, there is a trend that the dimensions of optical- and electrical-devices are becoming smaller.

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Corresponding author. E-mail address: shangfl@mail.xjtu.edu.cn (F. Shang).

https://doi.org/10.1016/j.commatsci.2018.03.041 Received 9 January 2018; Received in revised form 18 March 2018; Accepted 19 March 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.

When the size of a device deceases to the micro/nano-scale, the mechanical behavior would even cause great influence on the stability of device. Persistent efforts have been made to investigate the mechanical characteristics of GaN using depth-sensing indentation tests [10–23]. Most of the indentation researches focus on the c-plane GaN, while little discussion has been conducted on the mechanical property of m-plane GaN. Besides, some of the experimental conclusions about the deformation behavior of GaN are ambiguous and inconsistent. Through the investigation on the indented surface of the specimen, Weyher [18] proposes that the slip systems on the m planes {1 0 −1 0} and c planes {0 0 0 1} are invoked during the indentation. While according to other experimental reports by Bradby [19], Jian [21], and Huang [22], the plastic deformation of c-plane GaN is primarily due to the slips on both c planes {0 0 0 1} and s planes {1 0 −1 1}. Fujikane [23] observes the nucleation of slips on the c planes {0 0 0 1}, m planes {1 0 −1 0}, and r planes {−1 0 1 2} in an indentation conducted on the m-plane GaN, and the experimental results manifest that the slip system firstly activated is {−1 0 1 2}〈−1 0 1 1〉. Hence, though it has been confirmed that the plastic deformation of GaN film in an indentation is dominated by nucleation and multiplication of dislocations on slip planes, further research is still necessary to reveal the accurate deformation

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cell parameters of a, b, c, and u which gave the minimal total energy E for a wurtzite GaN. A cubic GaN substrate with a dimension of about 20 nm × 20 nm × 20 nm was constructed. And nanoindentation simulations were performed on the c-plane and m-plane surfaces of the wurtzite GaN crystal, respectively. In each simulation, periodic boundary conditions were applied in the two directions perpendicular to the indent direction. Three bottom atomic layers were fixed to prevent the substrate from shifting. The simulation system was sufficiently relaxed, and the temperature was kept at 0 K by the Nose-Hoover method. An NPT ensemble was adopted in the indentation simulations using a time integration step of 1 fs. It was well accepted that the choice of the indenter was important for an indentation and depended upon the information one wanted to obtain from the test, since different mechanical responses and deformation behaviors would be induced according to the shapes of different indenters [36]. Spherical indenters, which offered a gradual transition from elastic to elastic-plastic contact, had been usually adopted in researches on the ceramics, and robust results were achieved [37–44]. Nevertheless, if an indenter with a sharp tip or steep edges was adopted, stress in the material would firstly concentrate at the region which contacted the tip or the edges of the indenter during penetrating, which result in the plasticity around the concentrated stress. For a wurtzite GaN, the slip planes were classified as the basal plane ({0 0 0 1}), the prism planes ({1 0 −1 0}, {1 1 −2 0}), and the pyramidal planes ({1 1 −2 2}, {1 1 −2 1}, {1 −1 0 1}, {1 −1 0 2}). In view of the slip planes, a cubic indenter, which was constructed in the diamond lattice with a flat square cross section of 40 Å × 40 Å, was intentionally set up in our simulations. More concretely, as shown in Fig. 2(a), for the indentation on the c-plane GaN, the indenter was oriented so that the bottom edges were parallel to the [1 0 −1 0] and [−1 2 −1 0] directions. While for the m-plane indentation model, the orthogonal edges of the indenter bottom followed the [0 0 0 −1] and [−1 2 −1 0] directions. Thus, in the c-plane indentation, the concentrated stress around the [−1 2 −1 0] indenter edges would activate plastic slips on the {1 0 −1 2}, {1 0 −1 1}, or {1 0 −1 0} planes. While the stress at the [1 0 −1 0] edges would induce plastic slips on the {−1 2 −1 2}, {−1 2 −1 1}, or {−1 2 −1 0} planes. Similarly, in the m-plane indentation, slips on the {−1 2 −1 0}, {1 0 −1 0}, {0 0 0 1}, {1 0 −1 1}, or {1 0 −1 2} planes would be activated by the stress concentrated around the orthogonal edges of the indenter. Consequently, plastic slips would be activated more directly. In addition, all the possible scenarios of plasticity were considered in the indentations conducted on the c-plane and m-plane GaN. A quasi-static loading method was adopted, i.e. the indenter was displaced 0.1 Å along the indent direction after every holding stage of 500 time steps. As a result the indenter penetrated into the GaN substrate at a velocity of 20 m/s by 15 Å. The load was calculated as the indent-direction component of the force exerted on the indenter. And the penetration depth was calculated as the distance between the indenter bottom and the substrate surface. Irradiated GaN models were generated by reproducing the simulation of successive 5 keV recoils in an intact crystal. A two-phase iteration scheme proposed by Nord was adopted to model the continuous irradiation, such method had been successfully applied to simulate the amorphization process in Si, Ge, GaAs, and GaN [31,32]. In the first phase, an energetic recoil was started from the center of the cell. The primary knock-on atom (PKA) was generated by giving a random Ga atom or N atom 5 keV of kinetic energy. The cell was cooled down towards 0 K at the borders using Berendsen temperature control method, and the volume of the crystal was not allowed to change. A variable time step was employed in case of overlapping atoms and to speed up the simulation. In the second phase, the cell was sufficiently relaxed. To be specific, the system was further cooled down to 0 K, meanwhile, the pressure was relaxed with Berendsen method to 0 kbar in all directions. After the relaxation phase, atoms in the cell were displaced by a random distance in the x, y and z directions, and the

mechanism of GaN. Another issue of interest is the irradiation effect on the mechanical behavior of GaN. Ion beam implantation, which implants dopant atoms into material and consequently alters the material properties, is an useful tool for design and fabrication of GaN-based devices. However, the inevitable implantation induced damage in lattice has not been efficiently controlled yet. Extensive experimental studies on the damage buildup in GaN under the ion bombardment have been made [24–27], and it is suggested that irradiation induced amorphization would be influenced by many conditions such as the mass of dopant atom, ion energy, implantation temperature, and beam flux. Moreover, there is considerable interest in determining the influence of ion implantation on the mechanical property, since it is the prerequisite for the successful application of implanted GaN [26,28–30]. The ion bombardment dramatically modifies the mechanical properties of GaN. For example, the amorphized GaN is much softer than the intact GaN, and there is no dislocation nucleated in the indentation of amorphized GaN, which is not alike with that of crystalline GaN. The deformation mechanism at atomic scale remains to be further studied. In the present work, the deformation mechanism of wurtzite GaN is studied using molecular dynamics (MD) simulation. Firstly, indentation simulations are performed on the c-plane and the m-plane (0 0 0 1) surfaces of an intact wurtzite GaN. The deformation behavior is discussed in detail by studying the relation between the load-depth curves and the defect evolution in the material. Secondly, irradiated GaN models are prepared by following a two-phase iteration scheme proposed by Nord [31,32]. Then a series of c-plane and m-plane indentation simulations are carried out to examine the irradiation effect on the deformation mechanism. 2. Methodology 2.1. Interatomic potential The indentation system was consist of a diamond indenter and a wurtzite GaN substrate. Hence the interactions between Ga, N, and C atoms were considered. We adopted a Tersoff-Berenner bond-order potential for Ga-Ga, N-N, and Ga-N, since this potential could accurately reproduce the structural and mechanical properties of GaN [33,34]. In order to achieve a reasonable response of contact loading and to reduce the computational cost, the Lennard-Jones potential was chosen to describe the interactions of C-Ga and C-N,

σ 12 σ 6 E = 4ε ⎡ ⎛ ⎞ −⎛ ⎞ ⎤, r < r0 ⎢ ⎝ ⎦ ⎣ r ⎠ ⎝r ⎠ ⎥

(1)

where r is the distance between two atoms; σ and ε are potential parameters for equilibrium distance and cohesive energy, respectively. These potential parameters were calculated according to the long-range Vander Waals interaction [35], and their values are listed in Table 1. Besides, in the irradiation simulation, the Ziegler-Biersack-Littmark (ZBL) universal repulsive potential was smoothly jointed to the Tersoff potential to describe the interaction between the high energy atoms at short interaction distance [31,32]. 2.2. Simulation model Fig. 1 shows the unit cell structure of wurtzite GaN. From a preliminary calculation by the MD method, we had determined the unit Table 1 Lennard-Jones potential parameters for C-Ga and C-N. Parameters

C-Ga

C-N

σ, equilibrium distance (Å) ε, cohesive energy (meV)

3.6919 8.4646

3.3677 3.7235

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Fig. 1. Wurtzite GaN unit cell. Red and blue circles represent Ga and N atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2.3. Von Mises stress analysis

periodic boundary conditions were used to bring the atoms outside the cell back on the other side. Then the iteration continued. Each energetic recoil was allowed to evolve for no less than 15 ps. More detail of the simulation method and the discussion on the evolution of the defects in GaN could be found in Ref. [31]. As a result, 10 irradiated GaN models were obtained corresponding to the irradiation dose of 5 eV/atom, 10 eV/atom, 15 eV/atom, 20 eV/atom, 25 eV/atom, 30 eV/atom, 35 eV/atom, 40 eV/atom, 45 eV/atom, and 50 eV/atom, respectively. And post-irradiation indentation simulations were conducted according to the aforementioned method.

In order to investigate the plastic deformation of GaN during indentation, the von Mises stress analysis was carried out. According to the yield criterion proposed by von Mises, which could also be referred to as maximum distortion energy theory, a material would start to yield when the second deviatoric stress invariant J2 reached a critical value [45,46]. This criterion could be also formulated by the von Mises stress, in particular, the yielding would start when the von Mises stress (or equivalent tensile stress 3J2 ) reached the yield strength of the material. The second invariant of the deviatoric stress is defined as

Fig. 2. (a) Indenter setting. For the indentation on the c-plane GaN, the indenter was oriented so that the edges were parallel to the [0 0 0 1], [1 0 −1 0], and [−1 2 −1 0] directions. For the m-plane indentation model, the orthogonal edges of the indenter followed the [1 0 −1 0], [0 0 0 −1], and [−1 2 −1 0] directions. (b) The possible slip planes activated during the cplane indentation. (c) The possible slip planes activated during the m-plane indentation.

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J2 =

1 Tr[(σ −pI )·(σ −pI )T] 2

beginning of indentation, which implied that the indenter was under an attractive force from the GaN substrate. With the indenter approaching the surface of GaN, the load started to increase, and the force on the tip became repulsive from attractive at the depth of about −2.2 Å and −1.2 Å (marked as a and x in the figure) for the c-plane and m-plane indentation, respectively. The curve of c-plane indentation showed a higher growth rate in load within the elastic stage a-b than that of m-plane indentation during the stage x-y, which implied that the c-plane GaN intrinsically possessed a higher elastic modulus. This was in accordance with the experimental result [5]. The state b and state y marked in Fig. 3(a), (d), and (e) were of special concern, because the mechanical response before and after these critical states were radically different. A distinctive feature of the subsequent loading curves was a series of randomly distributed load drops, which could be referred to as “pop-in” events. The discrete drops in load over a wide range of penetration depth indicated plastic deformation in the GaN substrate, which were always believed to be associated with the nucleation and propagation of dislocations and the consequently partial release of the elastic deformation inside the material. Therefore the first pop-in events (states b and y) were the signals of the transition between the elastic deformation and the elastoplastic deformation. Moreover, upon further indentation, the curve for the c-plane indentation displayed a convergence trend after several violent pop-in events, and the load exerted on the indenter kept smaller than the critical load of about 2 μN at the penetration depth of 7 Å. While for the m-plane indentation, it could be recognized that the load gradually increased with many small pop-in events in the following process. These phenomena would be discussed in the following sections combined with the analysis of defects evolution. Finally, during the elastic unloading stage in both c-plane and m-plane indentations, the load monotonically declined with a decrease in penetration depth and returned to nil.

(2)

1 p = − Tr(σ ) 3

(3)

where Tr denotes the trace of a matrix, I is the unit matrix, and p is the local hydrostatic pressure. 2.4. Coordination analysis The defect patterns in the GaN substrate were identified by the coordination analysis. The coordination number in a wurtzite lattice was four, that is, each Ga (or N) atom bonded with four neighbor N (or Ga) atoms. The Ga-N bond angles were nearly 109.5°, and the bond lengths were approximately 1.95 Å. A cutoff distance of 2.10 Å was chosen for coordination analysis and the software OVITO was adopted to visualize defects [47]. 2.5. Strain analysis Atomic strain analysis was carried out to quantify the plastic deformation in the irradiated GaN material during indentation [48]. In particular, the local deformation gradient tensor F for each particle was calculated firstly based on two configurations (the deformed atomic configuration and the original model). Then the Green-Lagrangian strain tensor ηi = 1/2(Fi FiT−I ) was derived. Finally, the von Mises shear invariant, which was recognized as a good measure of local inelastic deformation, could be obtained and expressed as follows,

ηimises =

2 2 ηyz + ηzx2 + ηxy +

2 2 2 2 (ηyy −ηzz2 ) + (ηxx −ηzz2 ) + (ηxx −ηyy )

6

(4)

3. Results and discussion 3.1. Load-displacement curve

3.2. Surface contacting

In general, the mechanical response during the loading stage in an indentation involved an initial elastic response followed by an elastoplastic response [49–51]. Additionally, the load-displacement curve usually had a linear dependence at the initial stage of indentation if a cubic indenter was employed [52,53]. But the curves obtained from our simulations did not show a strict linear growth of load with the penetration depth during the initial contacting. A similar trend could be found from the load-depth curves in the researches on silicon carbide [54,55]. Fig. 3 shows the load-depth curves of c-plane and m-plane GaN subjected to indentation load, demonstrating apparently different mechanical behavior. Both curves showed a negative value of load at the

As shown in Fig. 3, the load increased from negative to zero at different depths for c-plane and m-plane indentations. Hence the directional difference in mechanical property for a wurtzite GaN, which came from the specific atomic arrangements along different directions, was firstly reflected in the response during the surface contacting. In order to study the atomic movement in c-plane and m-plane surfaces during contacting, unloading simulations were also separately performed when the penetration depth were 0 Å and 1 Å. For the cplane indentation, the unloading curves in Fig. 4(a) clearly deviated from the loading path. As plotted in Fig. 4(c), after the unloading from 0 Å, atoms around the indent region did not return to their original locations and showed a shear strain of 0.06. For the m-plane

Fig. 3. (a) Load-depth curves of the indentation on c-plane and m-plane GaN. (b), (c), (d), and (e) are enlarged views of (a).

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Fig. 4. (a) Load-depth curve of c-plane indentation. (b) Load-depth curve of m-plane indentation. (c) Shear strain distribution of c-plane surface after the 0 Å – unloading. (d) Shear strain distribution of m-plane surface after the 0 Å – unloading. Indent regions were marked as yellow regions in (c) and (d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The plastic activity under the contact region became complicated with the proceeding of the indentation. Therefore, a close analysis was conducted on the appeared defects when the penetration depth was 8 Å (Fig. 6). Firstly, the forementioned defects nucleated at the penetration depth of 7.4 Å expended to be planar defects under each of the [−1 2 −1 0] indenter edges. The cross section along the black line, i.e., a side view of the planar defect under one [−1 2 −1 0] indenter edge, was shown in Fig. 6(b), and the atomic layers were printed with different colors in order to clarify the atomic movement in the material. Plastic slip on an r plane (−1 0 1 2) could be seen, and the slip direction (marked with a red arrow) was recognized as to be [−1 0 1 −1]. According to the topological structures of the crystallographic defects, it could be confirmed that the planar defects nucleated in our simulation were different from the common planar defects, such as grain boundary, antiphase boundary, stacking fault, or twin boundary. The crystal structure was still perfectly ordered on either side of the planar defect, while atoms on the planar defect did not maintain the original wurtzite structure and lost their long-range order along the slip direction. It was hard to determine dislocation structures on the planar defects, however, the leading dislocations could be defined based on the concept of that a dislocation was the boundary between the slipping part and the non-slipping part in a crystal. The locations of the edge segments in the leading dislocations were marked with solid lines in Fig. 6(a). Secondly, as introduced in Section 2.2, the cubic indenter was intentionally set up for the easy nucleation of plastic slips on the crystalline planes, and plastic slips on the {−1 2 −1 2}, {−1 2 −1 1}, or {−1 2 −1 0} planes were supposed to be induced by the concentrated stress at the [1 0 −1 0] edges of the indenter bottom. However, none of them had occurred in our simulation. Instead, under the [1 0 −1 0] indenter edges, multiple planar defects also nucleated on the {1 0 −1 2} planes and adjacent slip systems intersected with each other closely, as shown in Fig. 6(a). As a consequence, planar defects, which nucleated on a set of {1 0 −1 2} planes, made up the defect structure under the contact region. Fig. 6(c) and (d) are the bottom view and side view of the von Mises shear stress distribution around the defects when the penetration depth was 8 Å. Both snapshots illustrate that the shear stress higher than 120 GPa mainly concentrated at the leading dislocations. And this stress distribution induced by indentation would keep promoting the movement of the leading dislocation towards

indentation, as shown in Fig. 4(b), the load-depth curve corresponding to the unloading from 0 Å followed the loading path, while the other unloading curve (unloading from 1 Å) illustrated a slight deviation from the loading path. Compared with the intact model, only several atoms in the top atomic layer demonstrated distinct displacement after unloading from 0 Å, as shown in Fig. 4(d). Accordingly, it was necessary to elucidate that though both curves in Fig. 3(a) showed a characteristic of elastic response during the initial stage of indentation, there was a certain degree of plastic deformation occurred on the material surface, which could be verified in the unloading simulations. And the subtle atomic movement in the surface layers could be found at the very beginning of c-plane indentation.

3.3. Evolution of defect in c-plane indentation As introduced in Section 3.1, both indentations conducted on the cplane and m-plane GaN underwent an initial elastic deformation and a subsequent elastoplastic deformation during the loading stage. We then put focus on the plastic deformation in the material, since the elastic deformation would recover once unloading, and any permanent damage would greatly degrade the performance of semiconductor devices. In order to identify the defect locations, analyze the specific defect patterns and clarify the evolution of the defect structures, the coordination analysis was performed. For the c-plane indentation using a rigid cubic indenter, the stress would firstly concentrate at the corners of the indenter and reach the yield stress, leading to the formation of defects on substrate surface as shown in Fig. 5(a) and (b). Though subtle as it might be, the mechanical response of such defects nucleation could be detected as the “shoulder” in the load-depth curve (Fig. 3(d)) when the penetration depth was 6.2 Å. Fig. 5(c) and (d) are snapshots of the atomic configuration in the material when the penetration depth was 7.4 Å, at which the first pop-in event terminated. By investigating the defect evolution, it could be recognized that the first pop-in event was mainly related to the defects nucleation under the indenter edges which were parallel to the [−1 2 −1 0] direction. Besides, apart from the defects at the corners of the contact region, there was no large-scale defect formed under the [1 0 −1 0] edges of the indenter bottom. 234

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Fig. 5. (a) Defect nucleation at the indenter corners when the penetration depth was 6.2 Å. (b) Bottom view of the defects when the penetration depth was 6.2 Å. (c) Defect structure under the contact region when the penetration depth was 7.4 Å. (d) Bottom view of the defect structure when the penetration depth was 7.4 Å. The 4-coordinate atoms are removed for easy observation of the defects and their evolution during the indentation.

Fig. 6. (a) Bottom view of defect structure in the c-plane GaN when the penetration depth was 8 Å. The indent region is outlined with dash lines and the edge components of leading dislocations are marked with solid lines. (b) Side view of slip plane. Atomic layers are colored in order to illustrate the atomic movement. The red arrow indicates the slip direction. (c) Bottom view of von Mises shear stress distribution under the indent region. (d) Side view of von Mises shear stress distribution. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

found in an experimental study by Fujikane in 2012 [23]. Additionally, the r planes {1 0 −1 2} were experimentally confirmed to be the first slip planes in the indentation research on GaN by Yokogawa in 2016 [56]. To conclude, our simulation results on the initial plastic deformation of c-plane GaN was in accordance with the latest experimental evidence. As mentioned above, atoms on these r planes {1 0 −1 2} lost their long-range order along the slip directions. Consequently, a crystal with such disordered planar defects would lost its original mechanical strength. The load-depth curve of c-plane indentation in Fig. 3 began to converge at the penetration depth of 10 Å. It could be recognized that the indentation induced planar defects extended during the loading stage, and then they intersected with each other when the penetration

inside. Based on the above results, the mechanism for the plastic deformation could be explained. As shown in Fig. 7(a), in the c-plane indentation, the incipient plasticity was dominated by the activity of rplanes {1 0 −1 2} slip systems. Because of the orientation of the indenter, combined with the hexagonal symmetry of wurtzite lattice, there was only one slip system activated under each [−1 2 −1 0] edges of the indenter bottom, while there would be two or more slip systems invoked under each [1 0 −1 0] edges. Dislocations with edge or screw components were supposed to nucleate around the planar defect, separating the regions which under slipping from the perfect region. However, atoms on the slip planes became disordered promptly rather than made up dislocation structures. Such r-plane slip of GaN was also 235

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Fig. 7. (a) Illustration of slip systems in the c-plane GaN indentation. (b) Side view of an r plane. (c) and (d) Display the defect structure in the material when the penetration depth were 10 Å and 15 Å, respectively. Fig. 8. (a) Front view of the defect nucleation in the material during the m-plane indentation when the penetration depth was 10.5 Å. (b) Bottom view of the defects under the contact region. (c) Front view of the defect structure when the penetration depth was 12.0 Å. (d) Bottom view of the defect structure at the penetration depth of 12.0 Å. The corners of the indenter are marked as M, N, P, and Q in the figure. The 4-coordinate atoms are removed for easy observation of the defects and their evolution during the indentation.

depth was just 10 Å, forming an distorted pyramidal defect structure in the GaN substrate, as shown in Fig. 7(c). As the indentation proceeded, atoms around the pyramidal defect also became disordered, leading to the defect structure grew in size, while barely further extension of any slip system in substrate could be found (Fig. 7(d)). These phenomena indicated that during the indentation from penetration depth of 10–15 Å, the load from the indenter did not cause additional large-scale elastic deformation. Instead, atomic rearrangement around the distorted pyramidal defect was predominant. Different results were shown in a recent simulation research by Xiang et al. [57], in which the mechanism for the plastic deformation in GaN was well studied. Specifically, nucleation and propagation of dislocation loops were induced by the c-plane indentation using a spherical indenter. And the principle slip systems were determined as 1/ 3〈1 1 −2 0〉(0 0 0 1) and 1/3〈1 1 −2 0〉{1 −1 0 0}. Theses simulation results could also be supported by the experimental study by Weyher

[18]. But, the nucleation of disordered planar defect was absent. We ascribed the differences in the simulation results to the different potentials used. Concretely, the Stillinger-Weber (SW) potential for GaN by Bere [58] was adopted by Xiang et al., while we used the Tersoff potential proposed by Nord [33,34]. Though both the Tersoff and SW potentials were widely employed for atomic interactions in GaN, there was a certain difference between them leading to different simulation results. Moreover, the limitation of potentials should be of concern since the potentials cannot perfectly represent the interaction between atoms in reality. For instance, plastic slips on the s planes {1 0 −1 1} were observed in many experimental studies [19–22]. However, such phenomenon was not shown in our simulation, nor in the simulation by Xiang. Further researches with modified potentials were necessary, but that was outside the scope of this article. Another example was the simulation studies of Si. It had been experimentally confirmed that both

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Fig. 9. (a) Defect structure under the contact region when the penetration depth was 13.4 Å. (b), (c) and (d) display the perspective views of the defect structure during the indentation stage from depth of 12.6 Å to 13.4 Å. (e), (f) and (g) provide the side views of the screw component of the dislocation loop from the indentation depth of 12.6 Å to 13.4 Å.

(Fig. 3(e)). From Fig. 8(a) and (b), it could be recognized that the initial defects nucleated on the surface possessed a line shape and followed the [0 0 0 1] direction. Then, during the first pop-in event, i.e., the stage from penetration depth of 10.5–12 Å, an “U-shaped” half loop nucleated and emitted from the material surface under the indenter edge NP, as shown in Fig. 8(c) and (d). In order to characterize the defect evolution more clearly, a part of the dislocation loop under the indenter corner P, i.e., the defect structure under the dotted line marked region in Fig. 8(d), was extracted from the GaN model, and snapshots of the defect structure during the stage from the penetration depth of 12.6–13.4 Å are illustrated in Fig. 9. The U-shaped dislocation loop comprised an edge component and two screw components, the atomic structures of them were also provided in Fig. 9(a). By making Burgers circle around the dislocation and mapping it to a reference lattice, we identified the Burgers vector as being of 1/ 3[−2 1 1 0]. Before the indentation depth of 12.6 Å, the edge component of the shear loop slipped on an (0 1 −1 0) plane towards the [−2 1 1 0] direction, while the two screw components gradually extended from the material surface along the [−2 1 1 0] direction,

the phase transformation and the dislocations interaction could be induced in Si during an indentation [59]. However, though simulations with the SW potential could successfully result the generation of dislocations and stacking faults in Si, the phase transformation was hard to be activated. Because the SW potential overestimated the energy barrier for the high-pressure phase transformation of Si. While the simulations using the Tersoff potential showed Si crystal experienced a phase transition from the cubic diamond to the β-tin structure, but dislocation slip in the material was not obtained [60,61]. 3.4. Evolution of defect in m-plane indentation The GaN material experienced a different deformation in the mplane indentation. Fig. 8 illustrates the initial defects nucleation during the indentation, the indenter corners are marked as M, N, P, and Q. Because of the shape of the indenter and the consequent stress concentration at the indenter edges, the nucleation of defects occurred on the material surface when the penetration depth was 10.5 Å, and this was correspond to the first “shoulder” on the load-depth curve 237

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Fig. 10. (a) Bottom view of defect structure in the m-plane GaN when the penetration depth was 13.4 Å. The indent region was outlined with dashed lines. (b) Bottom view of von Mises shear stress distribution. (c) and (d) are the side view of the defect structure and von Mises distribution at the penetration depth of 13.4 Å, respectively.

Fig. 11. (a) Illustration of slip systems in m-plane GaN indentation. The defect evolution from the penetration depth of 12.5 Å to 15.0 Å are shown in (b), (c), and (d).

deformation during the m-plane indentation was summarized, as shown in Fig. 11(a). In general, plasticity in the m-plane GaN was dominated by the nucleation and propagation of the U-shaped dislocations. The edge segments of the loops would slip on the m planes {1 0 −1 0} towards inside, while the rear part of the screw segments would sweep on the c planes {0 0 0 1}. And the plastic slips nucleated on the m planes {1 0 −1 0} and c planes {0 0 0 1} did not cause a planar defect. Though dislocations were induced, the most part of the internal crystalline structure was intact during indentation, which signified that the GaN crystal still kept substantial mechanical strength. The load from the indenter would cause a large-scale elastic deformation in the material. Hence the load-depth curve of m-plane indentation (Fig. 3) showed a gradual rise in load from the depth of 12 Å to 15 Å. The fluctuations or pop-in events on the curve were correspond to the smallscale release of elastic deformations around the moving dislocations.

respectively. As shown in Fig. 9(b) to (g), with the advancing of the edge component on the (0 1 −1 0) plane, slips of the screw components on the {0 0 0 1} planes were induced. Specifically, only the rear part of the screw component underwent the slip on the (0 0 0 1) plane, while the front part kept extending along the [−2 1 1 0] direction. The angle between the front part and the rear part of the screw component became 120° when the penetration depth was 13.4 Å. Similar emission of dislocation loop could also be found under the other [0 0 0 1] indenter edge (marked as MQ in Fig. 8(b) and (d)) after the penetration depth of 13 Å, hence there were two dislocations shown in the m-plane indentation. In addition, it was worth noting that there was no disordered planar defect appeared during the m-plane indentation. The distribution of von Mises shear stress was also calculated, as shown in Fig. 10. We found that the stress higher than 120 GPa was responsible for the plastic slip of the dislocations, and shear stress higher than 140 GPa mainly concentrated at the screw components of the dislocation loops. Based on the simulation results, the mechanism of plastic 238

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Fig. 12. (a) Potential energy change compared to perfect crystal as a function of irradiation dose for GaN. (b) Percentage of wurtzite structure left in crystal during irradiation. (c) Change of density compared to the original crystal.

penetration depth compared to the other indentations, and the loaddepth curves showed unusual peaks with the indenter approaching the GaN surface. For an irradiated material, it was not appropriate to separate its mechanical response into an elastic stage and an elastoplastic stage, since large-scale plastic deformation might be induced at the beginning of indentation. As plotted in Fig. 13(a), the loading curves of c-plane indentations corresponding to the models A, B, C, and D still showed a monotonic increase in load at the initial stage and a convergence trend in the final stage, which was similar to that of intact crystal GaN, although there was only about 60–20% wurtzite lattice left in the irradiated models A, B, C, and D. While for the models E, F, G, H, I, and J, their load-depth curves did not show obvious transformation of the two stages as mentioned above. In stead, only a gradual increase in load could be observed. Based on the trend of the curves in the final stage ranging from depth of 10 Å to 15 Å, the irradiated models could be divided into two groups. The first group included the models which were subjected to irradiation less than 20 eV/atom dose, i.e. the models A, B, C, and D. The load-depth curves corresponded to the first group were close to the that of intact GaN in the final loading stage. The rest models (E, F, G, H, I, and J), which were subjected to irradiation more than the dose of 25 eV/atom, were classified as the second group. The load-depth curves corresponded to the second group were apparently lower than that of the intact GaN. It could also be recognized that the final load exerted on the indenter at the penetration depth of 15 Å declined with an increase in irradiation dose when the dose was higher than 30 eV/atom. And the loading curves of models I and J were almost overlapped, which was correspond to the total amorphization of material. The loading curves of m-plane indentations are shown in Fig. 13(b). The group mode remained valid, since the final parts of the loading

3.5. Mechanical response after 5 keV irradiation Irradiated GaN models were obtained from the irradiation simulation. Defects accumulated in the crystal during the successive energetic recoils, and full amorphization was finally achieved, where the potential energy of the system saturated at the dose of about 50 kV/atom, as shown in Fig. 12(a). Variations of some imperative aspects related to the mechanical property of the material were also collected in Fig. 12. Due to the irradiation, the wurtzite lattice might not maintain its original structure. As shown in Fig. 12(b), the percentage of wurtzite lattice in the system decreased dramatically. Volume expanded by about 15% when the irradiation dose was 50 eV/atom, and the consequent decrease in density could be recognized in Fig. 12(c). From the irradiation simulation, 10 irradiated GaN models were obtained corresponding to the irradiation dose of 5 eV/atom, 10 eV/ atom, 15 eV/atom, 20 eV/atom, 25 eV/atom, 30 eV/atom, 35 eV/atom, 40 eV/atom, 45 eV/atom, and 50 eV/atom. These models were referred to as models A, B, C, D, E, F, G, H, I, and J for simplicity in the following discussion. Then a series of c-plane and m-plane indentation simulations were conducted on these irradiated models. The load-depth curves are illustrated in Fig. 13(a) and (b). For the c-plane indentation conducted on model B and the m-plane indentations conducted on models A, B, and C, the load-depth curves showed unusual peaks at the indent depth of about −1 Å. These phenomena seemed to occur only in the indentations on the low-dose irradiated material. Through the observation of the irradiated lattice, combined with the structural analysis in Ref. [31], it could be known that the point defects did not distributed evenly over the low-dose irradiated GaN. There were several defect-concentrate regions just under the indenter. Therefore, the interaction force along the indent direction between the substrate and the indenter reached zero at an early 239

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Fig. 13. (a) Loading curves of c-plane indentations corresponding to different irradiated models. (b) Loading curves of m-plane indentations corresponding to different irradiated models.

These fluctuations implied atomic relocation, including nucleation of dislocations or local rearrangements of atoms in disordered clusters. Hardness was calculated according to Meyer definition [49,62,63],

H=

Pmax A

(5)

where Pmax stands for the maximum indentation load, and A is the area of the indent region. Fig. 14 shows the hardness of GaN as a function of irradiation dose. For an intact crystal, the c-plane GaN was slightly harder than m-plane GaN, which was in agreement with the experimental results. However, their hardnesses obtained in the present study, 125.3 GPa for c-plane GaN and 123.4 GPa for m-plane GaN, were about 6 times as much as those from experimental results by Fujikane [5,64]. This could be attributed to the indentation size effect, i.e. an increase in hardness as indentation size decreased. According to the reports [65–68], the magnitude of the size effect could be more than 3 times the hardness value on the macro scale, and the simulation study of diamond by Harrison even yielded results 10 times harder than experiments [69]. The curves in Fig. 14 demonstrated a great dependence of hardness on the irradiation dose. From the irradiation dose of 0 eV/atom to 20 eV/atom, the hardness of m-plane GaN showed few signs of subsiding, while the hardness of c-plane GaN decreased gradually from

Fig. 14. Hardnesses of c-plane and m-plane GaN as a function of irradiation dose.

curves corresponding to the first group (models A, B, C, and D) were distinctly higher than those curves corresponding to the second group (models E, F, G, H, I, and J). It could be identified that the load-depth curve corresponding to the model A was significant higher than other curves, demonstrating a hardening phenomenon. For the second group models, final load exerted on the indenter at the depth of 15 Å in the mplane indentations also declined with an increase in irradiation dose. Little fluctuations could be recognized on all the loading curves. 240

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which generated in the crystal under the low-dose irradiation, would have little impact on the generation and extension of planar defects in the c-plane GaN. But the pinning effect of point defects on the indentation induced dislocations would significantly change the deformation behavior of m-plane GaN. As for the irradiation induced hardening of c-plane GaN observed in experiments [28,29,60], such phenomenon might be related to the pre-existing dislocations, which nucleated during the preparation of material. Thus further simulation study upon the effect of pre-existing dislocations would be necessary in order to verify this assumption. By investigating the strain distribution in the crystalline and irradiated materials under the conditions of c-plane and m-plane indentations, as shown in Fig. 15, it was found that with the irradiation dose increasing, the deformation mechanism transformed from the plastic activities on slip systems inside the material to local atomic rearrangement in disordered regions near the material surface. Such transformation had also been observed in a simulation research on SiC [71].

Table 2 Hardnesses of intact GaN and irradiated models. Model

c-plane (GPa)

m-plane (GPa)

Intact A B C D E F G H I J

125.3254 123.3555 112.9116 117.5228 109.4889 88.1894 93.6594 88.0675 80.3260 72.9718 72.6664

123.4255 145.7524 125.7913 121.3270 123.3966 93.6611 102.2361 91.0925 80.5270 74.4769 67.6141

125.3 GPa to 109.5 GPa. In addition, Fig. 14 shows a notable increase in m-plane hardness to about 145.8 GPa at the irradiation dose of 5 eV/ atom, which was even higher than that of intact m-plane GaN, corresponding to the aforementioned hardening phenomenon. Though the hardness of an intact c-plane GaN was higher than that of intact m-plane GaN, the irradiated m-plane GaN was harder than the c-plane GaN under the irradiation less than the dose of 35 eV/atom. There was a sudden drop in both hardnesses at the dose of 25 eV/atom. After a reincrease when the dose was 30 eV/atom, the hardnesses decreased monotonically with the increasing of irradiation dose from 30 eV/atom to 50 eV/atom, and the c-plane GaN became harder than m-plane GaN again at the dose of 50 eV/atom. Eventually, the hardnesses decreased by about 63.6% and 45.2% for the c-plane GaN and m-plane GaN, respectively. The specific hardnesses of the intact and irradiated models are summarized in Table 2. According to the above discussions, two aspects were to be emphasized. Firstly, irradiation induced hardening could be found for the low-dose irradiated m-plane GaN. Secondly, the amorphous GaN prepared by high-dose irradiation was much softer than the crystalline GaN. The latter phenomenon was consistent well with the experimental results [28–30,70]. And this behavior was attributed to the fact that an amorphous GaN possessed a less dense structure which was composed of Ga-rich matrix with randomly embedded N2 bubbles. Densification, which was a main plastic deformation mechanism in the non-crystalline material, would be preferred once the amorphous GaN was under a compression load, leading the GaN to be softer. The former phenomenon, i.e. the irradiation induced hardening of GaN, had been found experimentally in the researches on c-plane GaN by Kucheyev [70] and Kavouras [28,29]. However, few studies had been done on the irradiated m-plane GaN until now. As mentioned in Sections 3.3 and 3.4, indentation induced plastic deformation in an intact c-plane GaN started with generation and extension of disordered planar defects. While for an m-plane GaN, the deformation was dominated by the nucleation and propagation of dislocations. Point defects,

4. Conclusion To summarize, molecular dynamics simulations are carried out to investigate the deformation mechanism of GaN, which would complement the experimental studies. It could be recognized from the loaddepth curves that the c-plane and m-plane GaN exhibit different mechanical responses under the condition of indentation, since the wurtzite GaN is anisotropic in nature. The atomic processes involved in the deformation illustrate that a series of r-plane slip systems are activated beneath the periphery of the contact region in the c-plane indentation, and finally result in a distorted pyramidal defect structure. For the mplane indentation, nucleation and propagation of dislocation loops are observed in the GaN substrate, and the activities of dislocations do not left any planar defect. A close discussion is made on the relationship between the pop-in events in the load-depth curves and the evolution of defects in the material. Besides, the irradiation effects on the mechanical properties of GaN have been investigated. A hardening effect of point defects on the m-plane GaN is observed. The hardnesses of c-plane and m-plane GaN decrease significantly when the irradiation dose is higher than 30 eV/atom. Additionally, with the irradiation dose increasing, the deformation mechanism transforms from the plastic activities on slip systems to local densification in disordered clusters. These results could be helpful in promoting the development of nanoscale semiconductor devices with required properties.

Acknowledgements This work was supported by NSAF Joint Fund through Grant No. U1330116 and National Natural Science Fund of China through Grants No. 11272243 and No. 11672220.

Fig. 15. Strain distribution in the material at the penetration of 15 Å according to different irradiation doses ranging from 0 to 50 eV/atom.

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