Room-Temperature Plasticity of a Nanosized GaN Crystal

GaN wurtzite crystal is commonly regarded as eminently brittle. However, our research demonstrates that nanodeconfined GaN compressed along the M direction begins to exhibit room-temperature plasticity, yielding a dislocation-free structure despite the occurrence of considerable, irreversible deformation. Our interest in M-oriented, strained GaN nanoobjects was sparked by the results of first-principles bandgap calculations, whereas subsequent nanomechanical tests and ultrahigh-voltage (1250 kV) transmission electron microscopy observations confirmed the authenticity of the phenomenon. Moreover, identical experiments along the C direction produced only a quasi-brittle response. Precisely how this happens is demonstrated by molecular dynamics simulations of the deformation of the C- and M-oriented GaN frustum, which mirror our nanopillar crystals.

S emiconductors have been the life blood of technology ever since the first contact-point transistor was invented in 1947. 1 It would seem therefore that every aspect of semiconducting materials has been thoroughly investigated, 2 yet their mechanical properties have received significantly less attention than the optoelectronic ones. The majority of inorganic semiconductors are stiff, barely deformable solids with powerful interatomic bonding reflected by high melting temperatures T m . 3 However, more recent research has challenged that idea with the synthesis of a first ever plastic Ag 2 S inorganic semiconductor 4 or the discovery of plasticity of ZnS crystals under complete darkness, 5 whereas the hightemperature mechanical behavior of ceramic and semiconductor nano-objects has been attracting increasing attention of the scientific world. 6 Our own findings show that even a brittle semiconductor such as GaN can, under appropriate conditions (a nanodeconfined state 7,8 and straining in a particular direction), display distinct plasticity even at room temperature (RT). At the same time, Kamimura, Kirchner, and Suzuki 9 have estimated that GaN's transition from brittle to ductile would require a temperature of 800°C, suggesting that any talk of GaN's plastic behavior would be possible only in the context of high temperatures. It is little wonder then that GaN's plastic deformation at room temperature is utterly expected. This is also a reason why GaN plasticity has previously been methodically examined exclusively in high temperatures. 10,11 GaN crystal has a well-established place in modern technology. 12,13 In bulk mode and room temperature, GaN has long been known to display considerable strength, hardness, and brittleness. 14−17 The same applies to GaN nano-objects that Huang et al. 18 characterized as displaying only limited local plasticity in contrast to the "global" one exhibited by metallic micro-objects (cf. studies by Nix,19 Minor, 20 or Schuh 21 and their research teams). Despite wideranging testing conditions, 18,22−26 no such "global GaN plastic behavior" has been detected, yet our Letter proposes that it is real. We turn therefore to GaN crystal, whose structure unlike that of other semiconductors, e.g., GaAs 27,28 or Si 29  has been shown to remain stable until the pressure reaches 47−60 GPa. 30−33 We began by performing density functional theory (DFT) calculations of the bandgap E g in a stressed GaN structure (Supporting Information A-1), using the Quantum Espresso software package. 34, 35 The exchange-correlation energy was determined according to the Perdew−Burke−Ernzerhof functional. 36 The ultrasoft Ga and N pseudopotentials were selected from the PSLibrary database. 37 The energy cutoff of 60 Ry was established as the threshold for the wave function expansion, whereas the first Brillouin zone was sampled by applying the 11 × 11 × 11 Monkhorst−Pack k-point mesh 38 (Supporting Information A-1 and Figure S1).
The obtained quasi-linear rise of E g with increasing hydrostatic pressure p ( Figure 1) agreed with earlier experimental observations, 39−42 lending credibility to our calculations (see Supporting Information B). However, the declining E g −ε relationship found for GaN when compressed along the M[101̅ 0] direction (marked in red) was quite unexpected, diverging both from the hydrostatic (marked in black) and the C[0001]-axis stressing (marked in green). It implies a stark contrast in GaN's mechanical response depending on whether it is stressed along the M-or C-axis ( Figure 1), where earlier reports 13,30,43 have considered its elastic anisotropy as insignificant.
Topical experiments by Porowski et al. 44 show the GaN bandgap commensurate with its melting temperature, and an increasing T m −p dependence. Because the T m value reflects crystal cohesion (Supporting Information B), it is reasonable to expect crystal "weakening" during straining along the M direction ( Figure 1). This significant loss of strength in GaN persuaded us to undertake an experimental assessment of its nanoscale deformation along the M direction, which, to the best of our knowledge, had never been attempted before.
Consequently, GaN wafers (5 × 5 × 0.4 mm) with the C(0001) and M[101̅ 0] oriented surfaces were cut from a larger crystal grown by hydride vapor phase epitaxy in a way to avoid defect generation. An initial cathode luminescence examination of the materials confirmed their high quality: the threading dislocation density in C-and M-oriented wafers equaled 1 ×10 10 and 4 × 10 9 m −2 , respectively. A set of virtually identical GaN nanopillars was carved in each of the prepared wafers using a two-stage focused ion beam (FIB) milling (Supporting Information A-2 and Figure S2), taking every precaution the FIB did not introduce dislocations in the fabricated items.
The RT nanocompression tests followed the approach developed by Schuh and his team 21 as well as the updated standards for GaN nano-objects reviewed by Fatahilah et al. 45 The experiments were carried out using a nanoindenter with precise test-geometry (Figure 2a), by compressing each pillar to a different force-limit in an effort to elicit a single strainburst response (Supporting Information A-3 and Figure S6). This strategy proved successful, revealing an entire, irreversible deformation of certain C-GaN and M-GaN nanopillars accomplished under constant nominal stress σ max ( Figure  2b). The recorded stress−strain curves display a disparity between the M-GaN and C-GaN nano-objects, with displacement bursts occurring at different stress levels, namely, σ max = 7.7 (red curve) and 12.7 GPa (green curve), respectively. The latter conforms to the RT hardness of GaN thick-films of H ≈ 12 GPa, 13,14 leading to the conclusion that the C-GaN case represents the commonly recognized mechanical properties of  GaN crystal, [13][14][15][16][17]25,26 whereas the M-GaN one corroborates the "unexpectedly weak behavior" foreseen by ab initio calculations ( Figure 1). Our claim is strengthened further by an inspection of nanopillars deformed according to a single strain-excursion pattern using scanning electron microscopy (SEM), which exposed the difference between a brittle-ceramic manner of the C-GaN deformation ( Figure 2c) and plastic performance by the M-GaN (Figure 2d). Credible proof of this idiosyncrasy came from ultrahigh-voltage (1250 kV) transmission electron microscopy (UHV-TEM), which enabled first-hand observation of GaN structure in our 500 nm thick nano-objects (Supporting Information C-1 and C-3 and Figure  S7). The deformed C-GaN nanopillar contains a huge number of accumulated dislocations ( Figure 2e) and a vertical crack, which confirms its quasi-brittle response. This is similar to the effect found for GaN nanowires by Huang et al. 18 and the conventional view of GaN properties. 13−17 Like the majority of earlier works on compressed GaN micropillars, they report a vertical crack, which is due to their exclusive concentration on C-oriented objects. 22−24 By contrast, our results concern a defect-free M-GaN structure obtained after severe (ε M-GaN = 8%) irreversible deformation ( Figure 2b). As it happened, thorough microscopic observations of the whole volume of the M-oriented pillars variously inclined to the incident electron beam (see Figure S8) failed to detect a single dislocation. There is no doubt that, if any such defects in the nano-object structure existed, they would have left a trace in bright-field UHV-TEM images (Figure 2f), similarly to the defects arrested within the C-GaN (Figure 2e). The absence of dislocations in the M-GaN pillar on the one hand, and their existence in the confined rootsubstrate (Figure 2f and Figure S8) on the other, is ample proof that dislocation activity did indeed occur, causing the hard GaN crystal to deform through slip. It bears emphasizing that the phenomenon we are dealing with differs from "dislocation starvation" or "mechanical annealing" reported for metallic nano-objects, 19,20,46 concerning as it does a strong solid with considerable resistance to dislocations motion. 16 We have tried to account for the experimental data using MD simulations. Our computations were performed with the LAMMPS code 47 for two frustum (Φ top × H × Φ bottom ) objects: C-GaN (14.7 × 29.8 × 17.9 nm) and M-GaN (14.9 × 29.9 × 17.7 nm) placed on a GaN wafer, which reflect the geometry of the examined samples. The interactions among the atoms within the wurtzite structure were described using    Supporting Information A-4). The MD-simulated deformation history of C-GaN frustum displayed in the contact pressure-strain (p c −ε) curves ( Figure  3) conforms qualitatively with the experimental data obtained for compressed GaN microprisms by Wheeler et al., 24 or those by Huang et al. 18 for GaN nanowires squeezed along their C[0001] axis. This agrees with a common perception of GaN objects as stiff and brittle materials in a range of testing temperatures. 13,17 However, the simulated p c (ε) characteristics unveiled a noticeable difference in the mechanical conduct of the C-and M-oriented frustums quite unlike the moderate directionality registered in our earlier nanoindentation experiments on bulk GaN crystal. 25,26 The abrupt stress-drop recorded in both p c (ε) relationships ( Figure 3) corresponds to the strain bursts (Figure 2b and Figure S6), as MD simulations commonly apply depth- Nano Letters pubs.acs.org/NanoLett Letter controlled compression, whereas nanomechanical testing is load-controlled. 7,50 It turns out that the C-GaN requires a significantly higher contact pressure than the M-GaN to initiate irreversible deformation (Figure 3), which accords with our experiments (Figure 2b). However, neither the simulated nor measured mechanical characteristics of C-and M-oriented nano-objects (Figure 2b and 3) appear to resolve the dilemma we are in, namely, of a sizable plastic M-GaN deformation with a resulting intact crystalline structure on the one hand, and a quasi-brittle response of the C-GaN with arrested dislocations (Figure 2) on the other. The answer was provided by a visualization of the evolution of a strained atomic GaN structure recently made available with OVITO (Open Visualization Tool) and the dislocation extraction algorithm (DXA). 51 In particular, our employment of the atomic shear strain modifier enabled us to envision the shear strains that atoms are subjected to and determine active slip planes, existing dislocations, and their Burgers vectors 52 (see Supporting Information D-1). We found that the onset of an irreversible C-GaN deformation ( Figure 3) concerns defect activity at the lower end of the modeled pillar (refer to Figure  4a). It involves limited local, quasi-elastic movement of dislocation lines on the C planes (DXA-details in Supporting Information D and Figure S3) that leads to accumulation of defects inside the crystal. The irreversible deformation starts with dislocation generation at the base of the frustum ( Figure  S3) despite the inevitable presence of higher stress close to its upper end (smaller cross-section area). We contend that the loading of a significantly strong and stiff C-GaN nanopillar results in a moderate stress concentration along the perimeter of the bottom contact and local change in the GaN lattice orientation.
As deformation proceeds, the R slip operates in the upper part of the nano-object and forms a typical "mushroom profile" of extruded material close to the contact (Figures 4b, c), similarly to the observations by Huang et al. 18 In reality, stress relaxation is realized by outward movement of the material immediately below the squeezing tool (with only a limited contribution from the C and R slip) and by vertical cracking of the C-GaN pillar which both we (Figure 2c (Figure 2e), because they are unable to escape the pillar volume or slip either during deformation or unloading (Supporting Information Figure S4).
The visualization highlights the plastic response of the M-GaN (Figures 4d−f and 3) in marked contrast to the vast defect accumulation in the compressed C-GaN (Figure 4a−c). This kind of C-GaN's "quasi-brittle" behavior is consistent with the common perception of the mechanical properties of our nitride. [13][14][15][16][17]30,43 Particularly revealing, however, is the unobstructed, well-defined, multiple dislocation slip on the M planes right across the M-GaN crystal (Figure 4d, e), with some of it entering the substrate area (Figure 4f), which our TEM experiments had detected (Figure 2f). Indeed, the Peierls−Nabarro stress for the GaN prismatic M⟨112̅ 0⟩{11̅ 00} slip, claimed by Kamimura et al. 53 as well as Yonenaga and Motoki 54 to be lower than the Peierls barrier for other slip systems, indicates the possibility of the M slip.
One final piece of the puzzle was missing: why should the above mechanism result in a dislocation-free M-GaN structure (Figure 2f) despite the sizable plastic deformation (Figure 2b)?
Our MD simulations of the loading path ( Figure 4) showed that, similarly to the C-GaN, the M-oriented frustum initially also contains dislocations, although to a much lesser degree (compare Figure (Figure 2f). Taken together, both our experiments and simulations stipulate that a specifically oriented GaN nanopillar will not perform like a brittle material.
Contemporary developments in GaN fabrication 55 are opening the way to appliances capable of outperforming Sibased products. They include nanocolumn LEDs, 13 the next generation of power-electronic devices, or wirelessly powered systems in autonomous cars. 56,57 Consequently, we are witnessing increased demand for all-embracing knowledge of the mechanical properties of GaN nanovolumes. 58 The plastic response of M-oriented GaN nano-objects goes some way toward meeting that demand.

Funding
This research was sponsored mainly by the Panasonic Corp., Japan, as part of their cooperation with Japanese universities. Nagaoka University of Technology and Osaka University were cosponsors of short-term "visiting scholar" positions. The Aalto University offered a part of the computational resources.

Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
We gratefully acknowledge Prof. Shuji Nakamura (University of California, Santa Barbara) for his invaluable criticism, stimulating comments. and important suggestions. Equally appreciated are the observations and remarks by Prof. William D. Nix (Stanford University). R.N. acknowledges invaluable discussions with Prof. Toshihiro Shimada (Hokkaido University) and his role in ascertaining the quality of the nanopillars used in our experiments. R.N. also expresses appreciation to Prof Koichi Niihara and Prof. Hisayuki Suematsu (Nagaoka University of Technology) as well as to Mr. Michael Berg (Bruker Nano Surfaces, Los Angeles) for their long-standing support and many an eye-opener. MF is thankful to Mr. Hideki Hata and Tomohiko Ueda (Panasonic Corp.) for rewarding discussions concerning TEM observations. Finally, R.N. and D.C. acknowledge the support from Osaka University and Nagaoka University of Technology during their time as guest-scholars. This research was sponsored by Panasonic Corp., Japan, as part of cooperation with Japanese universities.