# Tunable Electronic Properties of Graphene/g-AlN Heterostructure: The Effect of Vacancy and Strain Engineering

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## Abstract

**:**

_{N}) is energy favorable with the smallest sublayer distance and binding energy. Gr/g-AlN-V

_{N}is nonmagnetic, like that in the pristine Gr/g-AlN structure, but it is different from the situation of g-AlN-V

_{N}, where a magnetic moment of 1 μ

_{B}is observed. The metallic graphene acts as an electron acceptor in the Gr/g-AlN-V

_{N}and donor in Gr/g-AlN and Gr/g-AlN-V

_{Al}contacts. Schottky barrier height ${\Phi}_{\mathrm{B},\mathrm{n}}$ by traditional (hybrid) functional of Gr/g-AlN, Gr/g-AlN-V

_{Al}, and Gr/g-AlN-V

_{N}are calculated as 2.35 (3.69), 2.77 (3.23), and 1.10 (0.98) eV, respectively, showing that vacancies can effectively modulate the Schottky barrier height. Additionally, the biaxial strain engineering is conducted to modulate the heterojunction contact properties. The pristine Gr/g-AlN, which is a p-type Schottky contact under strain-free condition, would transform to an n-type contact when 10% compressive strain is applied. Ohmic contact is formed under a larger tensile strain. Furthermore, 7.5% tensile strain would tune the Gr/g-AlN-V

_{N}from n-type to p-type contact. These plentiful tunable natures would provide valuable guidance in fabricating nanoelectronics devices based on Gr/g-AlN heterojunctions.

## 1. Introduction

^{2}-hybridized monolayer carbon structure, was successfully prepared in 2004 [1,2]. It exhibits a strong ambipolar electric field effect, such that electron and hole concentrations reach up to 10

^{13}/cm

^{2}with room-temperature mobilities of ~10,000 cm

^{2}/V·s [1]. Additionally, graphene is well known for its other fascinating electronic and quantum transport properties, such as massless Dirac fermions, high carrier mobility, and an intriguing quantum Hall effect, which make it promising for nanoelectronics and devices [2].

_{2}[17], as well as graphene/g-GaN [18,19]. Besides, Ahmad et al. used a modified Hummer’s method to obtain a photoconducting material based on the boron nitride-graphene oxide composite layer. They found that the confine element composition of boron, nitrogen, carbon, and oxygen showed excellent photoconduction [20]. These graphene-based van der Waals (vdW) heterostructures not only exhibit novel optoelectronic properties far beyond their individual components, but also preserve their intrinsic electronic properties due to the lack of dangling bonds and the weak electron coupling between sublayers [19]. Experimentally, ultrathin Aluminum Nitrides (AlN) nanosheet with a larger lattice constant as compared to its bulk-like wurtzite phase was successfully epitaxially grown [21]. 2D AlN few-layer sandwiched between the graphene and Si substrates was also confirmed this year [22]. These experimental results not only prove that 2D AlN has a promising application in optoelectronic field, but also indicate that it is of practical significance in the theoretical calculation of heterojunction based on 2D AlN. It is well known that the heterostructure properties can be tuned by defects, such as vacancies, which is inevitably introduced during the fabrication of materials. However, it is difficult to intentionally introduce accurate quantity of vacancies into 2D materials in experiments. Thus, the theoretical calculation stands out, which is important for accurately capturing the impact of defects on the material properties and, in turn, contributes to explaining the phenomena experimentally observed. Additionally, strain engineering is another significant method for tuning the heterostructure electronic properties, as reported recently [23,24,25]. In recent years, van der Waals heterojunctions have been extensively reported, both experimentally and theoretically, and proved to be a broad application prospect [26,27]. Very recently, Sciuto et al. have investigated the Fermi-level engineering for graphene by contacting it with bulk AlN rather than 2D AlN, and found that the Fermi-level can be tuned through the polarity and surface reconstruction of nitride [28]. However, to our best knowledge, neither the graphene/g-AlN heterojunction itself nor the modulation of defect or strain on its physical properties have been theoretically reported. Thus, a systematic investigation on the graphene/g-AlN van de walls heterostructure is desirable.

_{Al}, and Gr/g-AlN-V

_{N}to be a p-type, p-type, and n-type Schottky contact, respectively. Furthermore, biaxial strain could effectively tune the contact type. The p-type contact of Gr/g-AlN would change into n-type under a negative biaxial strain and turn into ohmic under a positive biaxial strain. These important findings will provide valuable guidance for experimentalists to fabricate Gr/g-AlN-based devices.

## 2. Computational Details

^{−6}eV. vdW correction and dipole correction were both considered in all calculations. A 20 Å vacuum slab was added to avoid interaction between adjacent images. The band structure analysis was conducted while using VASPKIT, a pre- and post-processing program for the VASP code [33]. The heterojunction binding energy is used to describe the relative stability of the heterostructure, as defined by Equation (1):

## 3. Results and Discussion

#### 3.1. Sublayers and Heterostructures

_{Al}) or a nitrogen vacancy (g-AlN-V

_{N}) to better compare the electronic differences of graphene and g-AlN monolayer before and after contacting, as shown in Figure 1. Graphene shows a zero-gap nature with an obvious Dirac cone (shown in Figure 1a). The g-AlN shows an indirect band gap of 3.07 eV while using the PBE functional (Figure 1b), close to that in our previous work [38]. The nonmagnetic nature of both graphene and g-AlN is found.

_{Al}gap when an aluminum vacancy is introduced. Two of them are unoccupied and others are located just around the Fermi level (Figure 1c), indicating g-AlN-V

_{Al}is a half-metal. The band gap of g-AlN-V

_{Al}is slightly increased due to the nitrogen dangling bonds around the vacancy. In contrast, g-AlN-V

_{N}is still a semiconductor, but with a magnetic moment of 1 μ

_{B}. The defect levels are found in both spin channels, only one of which is occupied in spin-up (right panel) channel locating ~0.25 eV lower than the Fermi level. Noting that the band gap of g-AlN-V

_{N}is increased to ~3.4 eV due to the aluminum dangling bonds (Figure 1d). The electronic and magnetic properties of monolayer AlN with vacancy has been previously reported by us in detail [39].

_{Al}(V

_{N}), all within the vdW gap range that was similar to previous reports [19,40]. A negative binding energy calculated by Equation (1) is found in all heterostructures, indicating that the Gr/g-AlN contacts are energetically stable. The heterostructure properties, including interlayer spacing (d), bond lengths of C-C (${L}_{\mathrm{C}-\mathrm{C}}$), and Al-N (${L}_{\mathrm{Al}-\mathrm{N}})$ around vacancy, binding energy (${E}_{\mathrm{b}})$, gap, work function (WF), and Schottky barrier height (SBH) are listed in Table 1.

#### 3.2. Electronic Properties

_{2}heterojunctions [42]. The Fermi level exactly passes through the Dirac cone, which indicates that the charge transfer between graphene and g-AlN sublayers are negligible and barely affects the nature of graphene. Based on Equation (2), the formation energies of V

_{Al}(under N-rich limitation) and V

_{N}(under Al-rich limitation) are 8.14 and 3.16 eV, respectively. The positive formation energy means that it is hard to generate Al or N vacancy under the thermodynamic stability condition. However, Komsa et al. reported that vacancies can be produced by means of high-energy electron irradiation [43]. We expect that the same technology is applicable for artificially producing vacancies in the AlN monolayer. Only graphene could preserve the electronic properties when defects are introduced in g-AlN. Besides, the vacancy is inevitably induced in the high-temperature epitaxial growth chamber. The band gaps of the AlN sublayer in Gr/g-AlN, Gr/g-AlN-V

_{Al}, and Gr/g-AlN-V

_{N}are calculated as 3.18, 3.13, and 3.14 eV, respectively. An increase of 0.11, 0.06, and 0.07 eV are obtained, respectively, when compared with the pristine g-AlN monolayer. Heyd-Scuseria-Ernzerhof (HSE) [44] functional was also used for comparison to have a more accurate gap value. The HSE band gaps of g-AlN sublayer in Gr/g-AlN, Gr/g-AlN-V

_{Al,}and Gr/-g-AlN-V

_{N}are 3.93, 3.98, and 4.11 eV, respectively. The HSE gap of freestanding g-AlN is 4.04 eV [38]. When vacancy defects are introduced, the band structures with defects are different from that of freestanding g-AlN and g-AlN in heterostructures, as shown in Figure 1c,d and Figure 3b,c.

_{Al}structure has a total magnetic moment of 3 μ

_{B}, as induced by symmetry-breaking in the vacant system, which agrees with our previous reported paper [39]. In Gr/g-AlN- ${\mathrm{V}}_{\mathrm{Al}}$, two unoccupied defect levels in the spin-up channel are moved farther away from each other after contact with graphene. Some electrons are transferred to g-AlN from graphene, which leads the Dirac cone to shift above the Fermi level. Additionally, as seen in Figure 3b, the transferred electrons occupy the defect levels near the Fermi level, leading the states to become partially non-degenerated. However, the half-metal nature of g-AlN-V

_{Al}is preserved, which is similar to the results of Gr/g-GaN in Ref. [19] and, therein, the results are also confirmed in Figure 4. The defect states located close to the valance band are mainly contributed by the N-p orbitals (Figure 4b), acting as an acceptor. The density of states (DOS) of Gr/g-AlN-V

_{Al}near the Fermi level is very close to that of pristine Gr/g-AlN, where the PDOS of Al, N, and C hardly overlap with each other near the Fermi level. Thus, only weak interaction exists between the two sublayers. As a result, the interlayer distance (3.28 Å) is relatively larger than that of Gr/g-AlN-V

_{N}(3.08 Å).

_{N}can be more easily produced with a lower formation energy. Vacancies can induce gap states and magnetism, as shown in Figure 1b,d. By vertically contacting with graphene, the projected band structures of g-AlN sublayer in Gr/g-AlN-V

_{N}(Figure 3c) are tuned back to resemble that in the freestanding g-AlN monolayer (Figure 1b). Thus, we expect that the growing g-AlN monolayer on graphene is beneficial in preserving its intrinsic nature, even N vacancy is unintentionally introduced. Additionally, the magnetic nature in freestanding g-AlN-V

_{N}disappears after contacting graphene, which indicates that graphene could also tune the magnetism of g-AlN-V

_{N}, which shows potential application in electronic devices. The same phenomenon is also found by comparing the band structures of GaN-V

_{N}in [45] and Gr/g-GaN-V

_{N}in [18]. The disappearance of magnetism in Gr/g-AlN-V

_{N}is because electrons occupied on the vacancy induced defect states would transfer to graphene, which leads the defect levels to shift up to conduction bands and then become unoccupied. As shown in Figure 3c, the Dirac cone of graphene decreases about 1eV and it is lower than the Fermi level, which confirms the electrons transfer from g-AlN to graphene. As a result, graphene acts as an acceptor in Gr/g-AlN-V

_{N}. The unoccupied states near the conduction band in Gr/g-AlN-V

_{N}are mainly contributed by Al-s, Al-p, N-p, and C-p orbitals (Figure 4c). In addition, the PDOS of Al, N, and C atoms near the Fermi level have a similar shape, which results in strong orbital hybridization and interaction between the graphene and g-AlN sublayers. It agrees with the lowest interlayer distance (i.e., 3.08Å in Figure 2).

_{N}is shown in Figure 3d to further verify the results based on PBE functional, which is basically in accordance with that by PBE functional (Figure 3c), signifying that our other PBE band structures are also reliable. The reasons why we only use HSE functional to calculate Gr/g-AlN-V

_{N}band structures are: (1) the defect formation energy of V

_{N}is apparently lower than that of V

_{Al}, so it is more meaningful to discuss this more realistic contact in detail; (2) the band structures of Gr/g-AlN-V

_{N}obviously change when compared with Gr/g-AlN, so it is necessary to verify the reliability of PBE results by using the more accurate HSE functional; (3) the HSE band structure calculation for such large supercells costs too much, while the core purpose in this work is to study how the vacancies and strain engineering would tune SBH, rather than evaluating the accurate defect level position. The CBM and VBM are confirmed to be at the Γ and K position, as that obtained with PBE functional. Noting that the VBM eigenvalue difference between location Γ and K is about ~0.5 eV, which is in agreement with that in Ref [14]. While considering this correction, we can obtain the HSE gaps as well as SBHs of Gr/g-AlN and Gr/g-AlN-V

_{Al}by doing HSE self-consistent calculation, in which the Γ but not K point is included. This method is significantly more time saving than band calculation, and Table 1 lists the corresponding HSE results.

_{Al}, one can find that some electrons in graphene near aluminum vacancy would be depleted and then transform to g-AlN. While the graphene sublayer is found to act as an electron acceptor for Gr/g-AlN-V

_{N}.

_{z}-like orbitals in Gr/AlN and Gr/AlN-V

_{N}, while contributed by p

_{x(y)}-like orbitals in Gr/AlN-V

_{Al}, and the electrons that accumulated in graphene of Gr/AlN-V

_{N}are found to be mainly occupying the p

_{z}-like orbitals. The results are consistent with their band structures in Figure 3 and are confirmed in Figure 5g,h.

_{Al}(V

_{N}) are 0.26 and 0.24 (−0.50 eV) (Δ${\Phi}_{i}$, i = 1, 2, 3), indicating charge transfer and dipole formation at the interface. The potential differences in the sublayer regions are 1.00 and 1.90 (0.80) eV (shown in Figure 6 as Δ${\Phi}_{i}$, i = 4, 5, 6), respectively. The results prove that V

_{Al}would increase the potential difference, while ${\mathrm{V}}_{\mathrm{N}}$ would decrease it.

_{Al}, g-AlN-V

_{N}, Gr/g-AlN, Gr/g-AlN-V

_{Al}, and Gr/g-AlN-V

_{N}under strain-free condition are 4.26, 5.10, 5.44, 3.29, 4.41, 4.80, and 3.27 eV, respectively, and the work function of graphene agrees with that in Ref. [18]. The differences in WF between graphene and g-AlN, g-AlN-V

_{Al}, and g-AlN-V

_{N}are −0.84, −1.18, and 0.97 eV, respectively, once again proving that graphene would lose electrons (donor) in Gr/g-AlN and Gr/g-AlN-V

_{Al}, while obtaining electrons (acceptor) in Gr/g-AlN-V

_{N}.

#### 3.3. Schottky Barrier Height

_{Al}, respectively, also a p-type contact. However, the SBHs are obviously changed by aluminum vacancy. In the case of Gr/g-AlN-V

_{N}, it is n-type contact, owing to a 1.10 eV ${\Phi}_{\mathrm{B},\mathrm{n}}$. By band gap correcting with HSE functional, the ${\Phi}_{\mathrm{B},\mathrm{p}}$(${\Phi}_{\mathrm{B},\mathrm{n}})$ of Gr/g-AlN, Gr/g-AlN-V

_{Al}, and Gr/g-AlN-V

_{N}are 0.24 eV (3.69 eV), 3.23 eV (0.75 eV), and 3.13 eV (0.98 eV), respectively. The HSE results are in compliance with the PBE counterparts, indicating our PBE-level calculations are qualitatively reliable. These results prove that vacancies can tune the SBH of Gr/g-AlN heterojunctions. Table 1 also summarizes the SBH data calculated with both PBE and HSE functionals.

#### 3.4. Effects of Biaxial Strain on SBH

_{Al}changes little when the compressive biaxial strain is larger than 2.5% and decreases within the range of −2.5% to 10%. For Gr/g-AlN-V

_{N}, the AlN band gap almost monotonously decreases within the whole strain range, as shown by the total DOS in Figure 7c and the triangle-line in Figure 8c.

_{2}monolayer [49], as well as that in Gr/g-GaN heterostructure [18] and Gr/MoSe

_{2}heterostructure [42]. It is also observed in Figure 7 that the Fermi level shifts close to the VBM and away from the CBM for Gr/g-AlN and Gr/g-AlN-V

_{Al}, and an inverse phenomenon is found for Gr/g-AlN-V

_{N}.

_{Al}, even within a large strain range. Thus, it is the p-type Schottky contact with a stable SBH value of ~0.5 eV, despite the variations of strain.

_{N}, it is n-type contact. By applying a 7.5% tensile biaxial strain, it transforms from the n-type back into p-type contact. The discussions on the strain engineering provide theoretical guidance on Gr/g-AlN based flexible device applications.

_{Al}, the VBM and Fermi level both change slightly with the change of strain, while the CBM decreases fast, which leads to the decrease of ${\Phi}_{\mathrm{B},\mathrm{n}}$ in Figure 8b. In the case of Gr/g-AlN-V

_{N}, CBM, VBM, and Fermi level decrease at a different speed (Figure 9c), which leads to the Fermi level moving close to the CBM. As a result, contact-type transition occurs at a tensile strain of ~5% (Figure 8c).

## 4. Conclusions

_{N}is energy favorable, with the lowest binding energy of -2.90 eV and the smallest sublayer distance of 3.08 Å. Based on the results of the projected band structure and PDOS, we find the bandgap of g-AlN increasing slightly after contacting with graphene, and two unoccupied defect levels in the spin-up channel of Gr/g-AlN- ${\mathrm{V}}_{\mathrm{Al}}$ are moved farther away from each other after contacting with graphene. Graphene is found to act as a weak electron donor in Gr/g-AlN and Gr/g-AlN-V

_{Al}, and acceptor in Gr/g-AlN-V

_{N}heterostructure based on the charge transfer analysis. Besides, the magnetic nature in freestanding g-AlN-V

_{N}disappears after contacting graphene, which indicates that graphene could tune the magnetism of g-AlN-V

_{N}. The results prove that the vacancy in g-AlN would strengthen the heterostructure interaction. Finally, the results show that Schottky barrier height can be effectively modulated by applying biaxial strain. Under the free-strain condition, Gr/g-AlN is found to be a p-type Schottky contact with a ${\Phi}_{\mathrm{B},\mathrm{p}}$ of 0.83 eV and transform into an n-type contact by introducing a nitrogen vacancy. In contrast, aluminum vacancy would enhance the stability of the contact type of Gr/g-AlN under external strain. Our results can provide some trend-guidance for experimentalists, especially for those who want to modify the device characteristics by tuning the Schottky barrier. More specifically, our study is expected to promote the application of ultrathin Gr/g-AlN heterostructures that are based nanoelectronics devices with transparent and flexible nature, such as electric field effect transistor, tunneling transistor, Schottky devices, and so on [50,51].

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The band structures of (

**a**) graphene, (

**b**) g-AlN, (

**c**) g-AlN-V

_{Al}, and (

**d**) g-AlN-V

_{N}. The Fermi level is referred to zero energy. The spin-up and spin-down channels are marked with blue and red colors.

**Figure 2.**A schematic illustration of the Gr/g-AlN heterostructure with and without vacancy: (

**a**) pristine Gr/g-AlN heterostructure, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr/g-AlN-V

_{N}. (

**d**–

**f**) are the corresponding side views with the layer distance labeled.

**Figure 3.**The band structures of (

**a**) Gr/g-AlN, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr /g-AlN-V

_{N}. (

**d**) is the HSE band structure of Gr/g-AlN-V

_{N}. Fermi level is set to zero energy. The spin-up and spin-down channels are plotted in the right and the left panels, respectively.

**Figure 4.**The projected density of states (PDOS) of (

**a**) Gr/g-AlN, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr/g-AlN-V

_{N}configurations, respectively. Fermi level is set to zero energy.

**Figure 5.**The iso-surface of differential charge density for (

**a**) Gr/g-AlN, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr/g-AlN-V

_{N}, respectively. (

**d**–

**f**) are their corresponding side views. The purple and yellow color represent electron accumulation and depletion, respectively. The iso-surface is set to be $4\times {10}^{-4}$e/Å

^{3}. Differential density Δρ along the z-direction for (

**g**) Gr/g-AlN, (

**h**) Gr/g-AlN-V

_{Al}, and (

**i**) Gr/g-AlN-V

_{N.}

**Figure 6.**The planar averaged potential as a function of vacuum thickness in z-direction: (

**a**) for pristine Gr/g-AlN, (

**b**) for Gr/g-AlN-V

_{Al}, and (

**c**) for Gr/g-AlN-V

_{N}. The graphene sublayer is located at the right side and g-AlN sublayer at left.

**Figure 7.**The PDOS for (

**a**) Gr/g-AlN, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr/g-AlN-V

_{N}under −10% to 10% biaxial strain. The green and red colors present the spin-up and spin-down channels, respectively. The Fermi level is set to zero energy.

**Figure 8.**The evolution of the SBH as a function of the biaxial strain for (

**a**) Gr/g-AlN, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr/g-AlN-V

_{N}. The red, cyan, and deep blue color represent the ${\Phi}_{\mathrm{B},\mathrm{n}}$, ${\Phi}_{\mathrm{B},\mathrm{p}}$, and the AlN gap value in heterostructures, respectively.

**Figure 9.**The conduction band minimum (CBM), valence band maximum (VBM) of AlN monolayer in Gr/g-AlN contact, and Fermi level as a function of applied strain for (

**a**) Gr/g-AlN, (

**b**) Gr/g-AlN-V

_{Al}, and (

**c**) Gr/g-AlN-V

_{N}, respectively.

**Table 1.**Interlayer distance (d), bond length (L) around vacancy, binding energy (${E}_{\mathrm{b}}$), work function (WF), bandgap of AlN (or AlN in Gr/g-AlN), and Schottky barrier height (SBH). The Gap and SBH calculated by both Perdew-Burke-Ernzerhof (PBE) functional and Heyd-Scuseria-Ernzerhof (HSE) functional are shown for comparison.

Structures | d (Å) | ${\mathit{L}}_{C-C}\text{}(\AA )$ | ${\mathit{L}}_{Al-N}(\AA )$ | Gap (eV) | ${\mathit{E}}_{b}\text{}\left(\mathbf{eV}\right)$ | WF (eV) | SBH (eV) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

PBE | HSE | PBE | HSE | ${\Phi}_{B,n}$ | ${\Phi}_{B,p}$ | |||||||

PBE | HSE | PBE | HSE | |||||||||

Graphene | - | 1.43 | - | - | - | - | 4.26 | - | - | - | - | - |

g-AlN | - | - | 1.78 | 3.07 | - | - | 5.10 | - | - | - | - | - |

g-AlN-V_{Al} | - | - | 1.80 | 3.15 | - | - | 5.44 | - | - | - | - | - |

g-AlN-V_{N} | - | - | 1.81 | 3.40 | - | - | 3.29 | - | - | - | - | - |

Gr/g-AlN | 3.49 | 1.42 | 1.78 | 3.18 | 3.93 | −2.15 | 4.41 | 5.67 | 2.35 | 3.69 | 0.83 | 0.24 |

Gr/g-AlN-${\mathrm{V}}_{\mathrm{Al}}$ | 3.28 | 1.42 | 1.78 | 3.13 | 3.98 | −2.89 | 4.80 | 5.12 | 2.77 | 3.23 | 0.36 | 0.75 |

Gr/g-AlN-${\mathrm{V}}_{\mathrm{N}}$ | 3.08 | 1.43 | 1.78 | 3.14 | 4.11 | −2.90 | 3.27 | 3.16 | 1.10 | 0.98 | 2.04 | 3.13 |

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## Share and Cite

**MDPI and ACS Style**

Liu, X.; Zhang, Z.; Luo, Z.; Lv, B.; Ding, Z.
Tunable Electronic Properties of Graphene/g-AlN Heterostructure: The Effect of Vacancy and Strain Engineering. *Nanomaterials* **2019**, *9*, 1674.
https://doi.org/10.3390/nano9121674

**AMA Style**

Liu X, Zhang Z, Luo Z, Lv B, Ding Z.
Tunable Electronic Properties of Graphene/g-AlN Heterostructure: The Effect of Vacancy and Strain Engineering. *Nanomaterials*. 2019; 9(12):1674.
https://doi.org/10.3390/nano9121674

**Chicago/Turabian Style**

Liu, Xuefei, Zhaofu Zhang, Zijiang Luo, Bing Lv, and Zhao Ding.
2019. "Tunable Electronic Properties of Graphene/g-AlN Heterostructure: The Effect of Vacancy and Strain Engineering" *Nanomaterials* 9, no. 12: 1674.
https://doi.org/10.3390/nano9121674