Thickness and strain engineering of structural and electronic properties for 2D square-octagon AlN

ABSTRACT Two-dimensional (2D) semiconductors exhibit great potential to minimize the size and drastically reduce the energy consumption of optoelectronic devices due to promising features induced by quantum confinement. It has achieved many successes in infrared and visible light optoelectronic devices. The study on ultra-wide band gap 2D semiconductors except h-BN are still limited, however, the requirement is more and more urgent. Inspired by the progresses of III-nitride semiconductors in recent several decades, 2D AlN is highly expected to be a new member of ultra-wide band gap 2D semiconductors. In this work, we employed the first-principles calculations to investigate the structural and electronic properties of 2D AlN. We revealed that few-layer AlN acquires a square-octagon (so-AlN) configuration in the vertical direction when the number of atomic layers n is smaller than 16. With increasing the thickness from 2 ML to 8 ML, the band gap decreased due to the weakening of quantum confinement effect. We demonstrated the intrinsic indirect band gap can be tuned to be direct by applying different direction strains for so-AlN. Our results open new avenues for their application in nano-optoelectronics. Graphical Abstract


Introduction
Inspired by the successful of graphene [1,2], a great deal of research efforts are devoted toward the investigation of two-dimensional (2D) materials in last decade [3,4]. The 2D materials not only exhibit unique and fascinating physical features by comparing their bulk counterpart [5][6][7][8][9][10], but also support a new dimension to tune the properties of by engineering the interlayer coupling [11][12][13]. The linear dispersion at K point endows novel phenomena in monolayer graphene, including the ultra-high mobility, fantastic thermal and electronic conduction and the anomalous room-temperature quantum Hall effect. The graphene-based devices have also been explored [5][6][7]. Transition from indirect to direct bandgap is revealed in transition-metal chalcogenides (TMCs) by reducing the thickness to monolayer [8][9][10]. Moreover, a large number of new 2D materials have been theoretically designed and experimentally realized, like monoelemental materials (silicene, germanene, phosphorene, borophene), MXenes, organic materials and nitrides. However, most existing 2D materials are metal or semiconductor, ultra-wide band gap 2D material is rarely achieved except hexagonal boron nitride (h-BN).
Aluminum nitride (AlN) is a promising ultra-wide band-gap material due to the good chemical stability, excellent thermal conductivity, high chemical resistance, and high melting point [14]. The devices based on AlN have already obtained significant success [15][16][17][18]. Therefore, 2D AlN is highly expected to be an essential supplement for ultra-wide band-gap 2D materials. Naturally, hexagonal AlN (h-AlN) nanosheet, similar to h-BN, is a promising material for optoelectronic applications. Following the good thermodynamic stability of h-AlN was theoretically confirmed [19], Tsipas et al. experimentally realized h-AlN via molecular beam epitaxy (MBE) [20]. Meanwhile, the studies on the electronic, optic, and magnetic properties of h-AlN are spread [21][22][23]. However, the MBE scheme is hard for economic applications due to the extreme high cost. Recently, 2D AlN within a few atomic layers has been realized by metalorganic chemical vapor deposition (MOCVD), which has already been widely used in semiconductor industry [24]. This exciting achievement greatly promotes the industrial applications of 2D AlN, in spite of the relevant research is still deficient.
Unlike h-BN, the ground state of AlN is in wurtzite configuration but not hexagonal configuration, therefore, the interlayer coupling is strong covalent bonds rather than vdW interaction. As a result, the monolayer h-AlN is quite unstable due to the large number of dangling bonds on the surface. Additionally, the h-AlN possesses an indirect band-gap [25,26], which limited the applications on lighting devices. Recently, the h-GaN was demonstrated to be unstable and reconstructed into a haeckelite phase with squareoctagon (so-GaN) pattern and direct band-gap for few-layer thickness [27][28][29]. Naturally, the fundamental properties of 2D AlN is an interesting topic in ultra-wide band-gap semiconductors, however, the relevant research is still insufficient. Here, we employed the first-principles calculations based on density-functional theory (DFT) to investigate the structural and electronic properties for few-layer 2D AlN, which has obtained great success in 2D materials [30] and III-nitrides [31][32][33]. We found that the hexagonal structure (h-AlN) transferred into haeckelite (so-AlN) by adding the thickness higher than 4 ML, while the indirect band gap transferred to direct. The band gap decreased with increasing the thickness for so-AlN due to the quantum confinement effect. Moreover, we demonstrated that in-plane strain could effectively tune the electronic structures for few-layer so-AlN, which path a new way for their practical application in nano-electronics and nanooptoelectronics.

Methods
First-principles calculations were performed by employing the generalized gradient approximation (Perdew-Burke-Ernzerhof parametrization, PBE) and projector-augmented wave method, as implemented in the Vienna Ab-initio Simulation Package (VASP) [34]. The longrange noncovalent interactions was corrected by Grimme's dispersion (DFT-D3) [35,36]. A plane-wave basis set with the kinetic-energy of 500 eV was used. We employed 8 × 4 × 1 Monkhorst-Pack k-grids in self-consistent calculations and 20 k-points between high symmetry points of the Brillouin zone in the band structure calculations. In addition, the force and total energy convergence thresholds were set to 0.01 eV/Å and 10 −6 eV, respectively. The lattice parameter differences were smaller than 1% by comparing with experimental results of w-AlN. The simulation cells were built with vacuum slabs thicker than 20 Å to avoid artificial interaction of periodic images. The dangling bonds on the surfaces were passivated by hydrogen atoms and the thickness is defined by the number of layers (nML, represent n-monolayers thick), as shown in Figure 1(a).

Thickness-dependent geometry and electronic structures
The optimized structures of so-AlN and w-AlN are displayed in Figure 1(a). By comparing with the w-AlN, two differences can be observed. First, the w-AlN is still more stable than so-AlN by 78 meV per formula in bulk phase due to the so-AlN suffered considerable distortion. For w-AlN, the atoms keep ideal tetrahedral coordination with the bond angles are almost 109.5°. The case of so-AlN is a little different, one bond angle reduced to 90 ± 2° and others increased to 112.5 ± 1°. Second, the hexagon atomic arrangement transferred into square-octagon configuration along vertical direction.
In 2D AlN, the stability is terminated by two factors: (1) the bulk part and (2) the surface part. Undoubtedly, the bulk structure of w-AlN is more stable, however, the surface of so-AlN is energetically more favorable. The dynamical stability is confirmed by phonon calculation for 2 ML so-AlN as shown in Figure S1. According to Tasker's classification [37], the surface of w-AlN belongs to type-III, in which the cations or anions accumulated on opposite surfaces, respectively. The strong repulsion between the same charged on the surface resulted in intrinsically unstable due to the divergence of the surface energy. On the other hand, the surface of so-AlN is type-I surface with equal anions and cations on each plane, which should be more stable than type-III. This effect is subtle in bulk AlN, however, it played an important role in 2D AlN. The surface/bulk ratio of 2D AlN sharply increased with the reduction of material thickness. There should be a threshold that the high surface energy cannot be compensated by the bulk part, and the w-AlN will transform into so-AlN. We calculated the energy per layer and showed in Figure 1(b), the crossing appeared between 16 ML and 18 ML, indicating that the 2D so-AlN should be ground state for the structures thinner than 16 ML.
Next, we focused on the electronic structures of 2D so-AlN. First, the band structures for bulk so-AlN and w-AlN were calculated as the references, as shown in Figure 2(a,d). The direct band gap decreased from 4.18 eV for w-AlN to 3.85 eV for so-AlN. We plotted the spatial distribution of wavefunction for conduction band minimum (CBM) and valence band maximum (VBM) in insets of Figure 2(a,d). It is observed that the VBM was contributed by the N-p z orbitals for w-AlN, but by N-p x orbitals for so-AlN, while the CBMs were consistently contributed by N-s orbitals. Therefore, the raised energy level of VBM induced the band gap reduction of 2D so-AlN. With increasing the layer from 2 ML to 8 ML, the 2D so-AlN and w-AlN exhibited entirely different behavior. As shown in Figure 3, the band gap of 2 ML w-AlN was smaller than that of bulk phase and transformed to metal for the structures thicker than 4 ML, which was not consistent with the normal quantum confinement effect. The similar mechanism has been reported in 2D gallium nitride [38], zinc dioxide [39], and boron nitride [40]. The evolution of the band edge states is shown in Figure S3. The absence of the N-s state during increasing the thickness may lower the energy level of CBM which leads metallization for 2D w-AlN. For 2D so-AlN, the band gap became larger due to the quantum confinement effect, and gradually closed to the band gap in bulk phase. Therefore, we can control the band gap from 4.76 to 3.85 eV by tuning the thickness for 2D so-AlN. The gapless for 2D w-AlN, limits the applications in optoelectronic devices, is overcame in 2D so-AlN. Moreover, the direct band gap changed into indirect band gap for both 2D so-and w-AlN. For 2 ML w-AlN (Figure 2(e)), the CBM is still at G point, and the VBM located between G→Y path. However, for 2 ML so-AlN (Figure 2(b)), the CBM located between G→X path, and the VBM located between G→Y path. After further increase the thickness, the CBM will still located at G point for 2D so-AlN. We also checked the effect of hydrogen-passivated on the band structures of 2D so-AlN, although it is practically unstable. The band gap variation with thickness for nonpassivation 2D so-AlN is displayed in Figure S2. The dangling bonds on the surface induce a band gap reduction in thin slabs. The effect is decayed by increasing thickness, as a result, the band gap gradually increased.

Strain engineering of the electronic structures
The indirect band gap seriously hindered the applications of 2D so-AlN on lighting devices. It should be promising to realize direct band gap. The application of strain engineering in 2D materials is different from that in traditional materials, as nanomaterials are mechanically much stronger. We can apply far greater tensile stresses to tune their properties than is possible with traditional materials. Many reports have demonstrated that strain engineering is an effective tool to control the properties of 2D materials [41][42][43]. Here, we employed a 5 ML 2D so-AlN as an example and applied in-plane stress from −5% (compression) to 5% (tension) along the X, Y, and XY axes.
As shown in Figure 4(a-c), under uniaxial and biaxial strains, the effect on the length of shorter interatomic Al-N bonds was small, while the change for the longer interplane Al-N bonds was more significant. The influence of biaxial strain on distance was greater than that of uniaxial strain. First, we calculated the band structures under in-plane strain. The band gap variation with strain is displayed in Figure 4(d-f). Generally, the tensile stress resulted in band gap reduction for all directions strain. The effect of compression was a little different. The band gap monotonic increased with rising the uniaxial X and biaxial XY compression, however, the band gap first rose (0~-3%) and then dropped (<-3%) by strengthening uniaxial Y compression. We can observe that the indirect-direct band gap transition (yellow shadowed area in Figure 4(d-f)) can be realized by applying strain. Under uniaxial X strain, the transition occurred when the tensile stress was larger than 2%; under uniaxial Y strain, the transition occurred when the compression was larger than −1%; under biaxial XY, the transition occurred when the tensile stress was larger than 1% and the compression was larger than −2%. Therefore, the 2D so-AlN exhibited strong anisotropy response to strain.
To reveal the physical mechanism of strain engineering, we plotted the N-p orbitalprojected band structures in Figures 5 and 6. We found the CBM always located at G point, therefore the indirect to direct band gap transition was governed by the change of VBM (marked by colored circles). Here, we neglected the conduction bands and just discussed the effect of strain on valence bands near the Fermi-level. In strain-free structure, the VBM located at the point between G → X path and contributed by the p z orbital. By applying strain along X axis, the VBM shifted to the G point under 3% tensile stress and the indirect band gap changed to be direct, due to the Al-N interplane distance was shortened, as discussed in Figure 4(a). The evolution of the VBM was marked by blue circles in Figure 5. It was observed that the VBM shifted close to the G point along the G → X path. On the other hand, the p x states shifted up under compressive stress (−3%) due to the bond along X axis was shortened, however, the energy level was still lower than the p z states. Under tensile stress (3%), the p x states shifted down and away from the VBM. By applying strain along Y axis, the p y states shifted up and became VBM at G point under −3% compressive stress and shifted down under 3% tensile stress. Therefore, the tensile stress along the X axis and compressive stress along the Y axis can induce the indirect to direct band gap transition. By applying biaxial strain, the effect was the superposition of uniaxial X and Y strain, as shown in Figure 6. The direct band gap was terminated by p y states when the compressive stress was bigger than −2%, and by p z when the tensile stress was bigger than 1%.

Conclusion
In summary, we systematically investigated the structural and band properties of 2D AlN by using first-principles calculations based on DFT. We found that the so-AlN structure was energetic more favorable than traditional w-AlN due to the unstable surface. According to our calculation, the so-AlN was the ground state when the number of atomic layer n was smaller than 16. The 2D so-AlN was an indirect band gap semiconductor, however, its bulk structures were direct band gap. With increasing the thickness from 2 ML to 8 ML, the band gap decreased due to the weakening of quantum confinement effect. This entirely different from the case for 2D w-AlN. The intrinsic metallic behavior induced by the nearly free electron states and charge transfer between two surfaces has been overcome in 2D so-AlN. The indirect band gap can be tuned to be direct by applying in-plane strain. The 2D so-AlN exhibited strong anisotropy response to strain. We believe our results will significantly promote the applications of optoelectronic devices based on ultra-wide band gap semiconductors.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
This work was supported by the National Natural Science Foundation of China [61804152, 61834008].