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Biaxial strain and external electric field effects on the electronic structure of hydrogenated GaN monolayer
Journal Pre-proof Biaxial strain and external electric field effects on the electronic structure of hydrogenated GaN monolayer D.M. Hoat, Mosayeb Naseri, Tuan V. Vu, Hai L. Luong, Nguyen N. Hieu, R. Ponce-Pérez, J.F. Rivas-Silva, Gregorio H. Cocoletzi
PII: DOI: Reference:
S0749-6036(19)31400-4 https://doi.org/10.1016/j.spmi.2019.106270 YSPMI 106270
To appear in:
Superlattices and Microstructures
Received date : 7 August 2019 Revised date : 6 September 2019 Accepted date : 9 September 2019 Please cite this article as: D.M. Hoat, M. Naseri, T.V. Vu et al., Biaxial strain and external electric field effects on the electronic structure of hydrogenated GaN monolayer, Superlattices and Microstructures (2019), doi: https://doi.org/10.1016/j.spmi.2019.106270. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Biaxial Strain and External Electric Field Effects on the Electronic Structure of Hydrogenated GaN Monolayer D. M. Hoata,b,∗, Mosayeb Naseric , Tuan V. Vud,e , Hai L. Luongf , Nguyen N. Hieug,∗∗, R. Ponce-P´erezh , J. F. Rivas-Silvai , Gregorio H. Cocoletzii a Computational
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Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam b Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Physics, Kermanshah Branch, Islamic Azad University, P.O. Box 6718997551, Kermanshah, Iran d Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam e Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam f Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam g Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam h Universidad Aut´ onoma de Coahuila, Facultad de Ciencias Qu´ımicas, Ing. J. C´ardenas Valdez, Republica, 25280 Saltillo, Coahuila, Mexico i Benem´ erita Universidad Aut´onoma de Puebla, Instituto de F´ısica, Apartado Postal J-48, Puebla 72570, Mexico
Abstract
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We investigate systematically the electronic properties of fully hydrogenated GaN (HGaNH) monolayer under effects of the biaxial strain and external electric field. Results assert that the pristine GaN monolayer is an indirect semiconductor with a band gap of 1.933 eV. Band structures indicate that the N-p and Ga-p states are the main contributors to the valence and conduction bands near Fermi level, respectively. The full hydrogenation can induce an increase of this parameter to 3.019 eV, with H-s state being present in both valence and conduction bands. Interestingly, the HGaNH monolayer transforms from indirect to direct gap as a consequence of GaN hydrogenation. Based on results, the electronic band gap of HGaNH monolayer shows sensitivity to the biaxial strain and external electric field. Therefore, these factors can be used to effectively tune the electronic properties of HGaNH monolayer in order to make it more suitable for optoelectronic applications.
1. Introduction
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Keywords: Hydrogenated GaN monolayer, Electronic properties, Strain engineering, External electric field, Optoelectronic applications.
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Since its discovery in 2004 [1], Graphene, a sp2 hybridized compound with honeycomb-like hexagonal structure, has attracted huge attention of the researchers due to its extremely intriguing properties such as high surface area, high electric conductivity, good optical absorption, mechanical strength, and the chemical stability [2, 3], among others. Undoubtedly, this 2D layer has become the center of the nanoscience and nanotechnology, being proven to have potential applications in optoelectronic devices [4, 5], sensors [6, 7], production and storage of energy [8, 9], photonics [10, 11], and the medical and biopharmaceutical fields [12, 13], and so on. The success of graphene has motivated special interest of the scientific community in low-dimensional materials, provided that some extremely superior physical and chemical properties emerge as compared with their bulk counterpart. Recently, extensive investigations have been devoted to the 2D nanosheets of transition metal monochalcogenides and dichalcogenides [14–16], metal oxides [17, 18], IV-IV group [19, 20], and III-V group [20–24]. Within this group ∗ Corresponding
author author Email addresses: [email protected] (D. M. Hoat), [email protected] (Mosayeb Naseri), [email protected] (Tuan V. Vu), [email protected] (Hai L. Luong), [email protected] (Nguyen N. Hieu), [email protected] (R. Ponce-P´erez), [email protected] (Gregorio H. Cocoletzi) ∗∗ Corresponding
Preprint submitted to Elsevier
September 6, 2019
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of 2D systems, the existence of the III-Nitride monolayers such as BN, AlN and GaN have attracted the attention. In bulk, these compounds may crystallize in a wurtzite-type hexagonal and/or cubic structure, they have wide band gap and potential optoelectronic applications [25, 26]. In 2D forms, they have been proven to have potential applicability, even equivalent to graphene, due to some intriguing properties such as wide electronic band gap, resistance to oxidation, mechanical and chemical stability. It is understood that the GaN monolayer can be exfoliated from the 3D wurtzite structure invoking the (0001) plane. So far, the electronic and optical properties of this monolayer have been the subject of some investigations. O. Dakir et al [27] studied the electronic and absorption properties of GaAs and GaN monolayers using first-principles calculations based on FP-LAPW method. Results show a band gap of 2.328 eV of the GaN monolayer. Employing the same method, Razieh Beiranvand et al [28] investigated the electronic and optical properties of BN, AlN and GaN monolayers and found that GaN monolayer is an indirect semiconductor with a band gap of 1.95 eV.
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To the best of our knowledge, the effect of full hydrogenation on the structural and electronic properties of GaN monolayer has not been investigated well yet. Moreover, it is well known that the strain and external electric field are two factors that can effectively tune the electronic structure of 2D materials [29–31]. Thus, in this work, our main aim is to examine the effectiveness of electronic structure engineering of the fully hydrogenated GaN (HGaNH) monolayer using biaxial strains and external electric fields. Results show that the HGaNH monolayer band gap is sensitive to the mentioned external factors, so that, they can be used to optimize the electronic properties in order to make the 2D layer more suitable for optoelectronic applications. 2. Computational details
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First-principles calculations based on the density functional theory (DFT) [32], as embedded in the CASTEP package [33], have been performed to investigate comprehensively the effect of biaxial strain and external electric field on the hydrogenated GaN (HGaNH) monolayer electronic properties. Norm-conserving pseudopotential and the Perdew-Burke-Ernzerhof (PBE) scheme within the Generalized Gradient Approximation are employed to describe the exchange-correlation energy functional [34]. Moreover, the Grimme scheme [35, 36] within the DFT-2D correction is adopted to take into account the weak van der Waals interactions. 4s2 4p1 states of Al atom, 2s2 2p3 states of N atom and 1s1 state of H atom are treated as valence states. The kinetic energy cut-off of the plane wave expansion is set to 500 eV. The self-consistent iterations will be stopped once the energy tolerance of 2 × 10−7 eV/atom has been reached. The k-mesh of 6 × 6 × 1 and 12 × 12 × 1 are adopted to integrate in the Brillouin zone for the structural optimization and electronic properties, respectively. In order to prevent the interactions between two consecutive layers, a vacuum space larger than 20 Åin the direction perpendicular to the monolayer is employed.
Figure 1: Total energy as a function of lattice constant and optimized atomic structure of pristine GaN monolayer (brown ball: Ga; blue ball: N.
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Figure 2: Optimized atomic structure of the hydrogenated GaN monolayer (brown ball: Ga; blue ball: N; gray ball: H).
3. Results and discussion
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3.1. Structural properties
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GaN wurtzite adopts a hexagonal structure belonging to the space group P63 /mc (no. 186), in which Ga and N atoms are situated at (1/3; 2/3; 0) and (1/3; 2/3; 0.375), respectively. Whose lattice constants are a = 3.190 Åand c = 5.189 Å[37]. In this 3D compound, the bond length Ga-N is dGa−N = 1.953 Å. The atomic structure of the 2D GaN monolayer can be generated from the wurtzite structure maintaining the hexagonal symmetry, however, it adopts a new space group P6m2 (no. 187). The structural optimization of pristine GaN monolayer is carried out by relaxing freely all atoms in the unit cell and then, finding the optimal geometry. In the second step, the energy-dependence of the volume is described through the Birch-Murnaghan equation of state [38]: 2 3 2 V 23 0 V0 23 9V0 B V0 3 0 E (V) = E0 + − 1 B + − 1 6 − 4 16 V V V
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Fig.1 depicts the total energy of the pristine monolayer calculated as a function of the lattice constant. According to our calculations, the lattice constants of GaN monolayer are a = b = 3.256 Å. These results are in good agreement with other theoretical values available in the literature [27, 28]. The optimized atomic structure of this monolayer is exhibited in the right panel of Fig.1. One can note that it has a planar graphene-like structure. The calculated interatomic distance Ga-N is dGa−N = 1.888 Å, which is about 3.32% smaller than that in bulk. The increase of the bonding strength from sp3 in bulk to sp2 in the monolayer results in the reduction of the interatomic distance. However, the bond nature in the GaN monolayer is predominantly ionic due to the large electronegativity difference between Ga and N atoms, similar to other III-V monolayers. Fig.2 displays a supercell 4 × 4 × 1 of the optimized atomic structure of fully hydrogenated GaN (HGaNH) monolayer. It is observed that when the GaN monolayer is hydrogenated, its structural planarity is disappeared and a buckling is appeared. Specifically, the calculated buckling height is 0.705 Å. While the Ga-N bond length increases to 2.008 Å, with the Ga-H and N-H interatomic distances being 1.570 and 1.032 Å, respectively. Obviously, the appearance of buckling and difference between dGa−H and dN−H in the HGaNH monolayer are generated by the electronegativity difference between atom pairs Ga-H and N-H. 3.2. Electronic properties
In Fig.3, the calculated band structure, total and projected density of states (DOS) of the pristine GaN monolayer are given. The electronic band structure is calculated along high symmetry direction Γ − M − K − Γ for energies ranging from -4 to 8 eV. From the figure, it is clearly observed that the valence band maximum (VBM) and conduction 3
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Figure 3: Electronic band structure and density of states of pristine GaN monolayer.
Figure 4: Electronic band structure and density of states of hydrogenated GaN monolayer.
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Figure 5: Band structure of hydrogenated GaN monolayer under various biaxial strains.
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Figure 6: Band structure of hydrogenated GaN monolayer under various external electric fields.
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band minimum (CBM) are found at K and Γ points, respectively, indicating that GaN monolayer is an indirect semiconductor, whose band gap value is 1.933 eV. This value is found in good agreement with other previously obtained theoretical result reported in reference [28]. The exhibited DOS plots evidences that the valence band is dominated mainly by the N-p state, with a small contribution of Ga-p state in the energy range from -2.9 to 0 eV. While the very flat subband from 0 to 4.2 eV and dense subband from 5.5 to 8 eV of conduction band are formed mainly from the Ga-s state. Whereas, the Ga-p state is the main contributor of the subband from 4.2 to 5.5 eV, in which a remarkable contribution of N-p state is also noted.
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Fig.4 shows the calculated band structure, total and projected density of state (DOS) of the HGaNH monolayer. Compared with the band structure of the pristine GaN monolayer, two differences can be clearly noted: (1) HGaNH monolayer is a direct semiconductor as both the VBM and CBM are located at Γ point, this result indicates the transition from indirect to direct semiconductor of the GaN monolayer as induced by the full hydrogenation, and (2) The overlapping of some electronic states along Γ − M and K − Γ high symmetry directions in conduction band is destroyed. The calculated band gap of HGaNH monolayer is 3.019 eV, which corresponds to an increase of the order of 56.18% from that of the pristine monolayer. Analyzing the DOS plots of HGaNH monolayer, one can note that the lower part from -4 to -2 eV of the valence band is mainly formed by the N-p state. While, the upper part is mainly dominated by the Ga-p, N-p, and H-s states. The same DOS values also suggest the strong states hybridization. On the other hand, the conduction band is built mainly by the Ga-s and Ga-p states, in which a small contribution from the N-p and H-s states is also noted. Comparing Fig.3 and Fig.4, we can conclude that the overlapping in the conduction band of the pristine GaN monolayer at energies higher than 5 eV is due to the Ga-s and N-p states. However, in the HGaNH monolayer, the observed overlapping disappears becauses the Ga-p state contribution becomes significant, which is a result of the hybridization of Ga-p state with H-s state. Next, we examine the biaxial strain influence on the electronic structure of the HGaNH monolayer. The biaxial 5
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Figure 7: Band gap of hydrogenated GaN monolayer as a function of (a) biaxial strain and (b) external electric field.
4. Conclusions
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0 strain is defined as follows: = a−a a0 × 100%, where a and a0 are lattice constant of the monolayer with and without strain, respectively. This study considers the biaxial strain ranging from -4% to 4%, herein the negative and positive values stand for the compressive and tensile strains, respectively. The calculated band structures of the HGaNH monolayer under various strains are displayed in Fig.5, in which the band structure at unstrained state is also presented for comparison. The figure shows that the applied strains does not change the direct nature of the monolayer, and the profile of entire band structure remains almost unchanged. The strain-dependence of the electronic band gap is illustrated in Fig.7a. It can be perceived that the band gap of HGaNH monolayer shows a sensitivity with the applied strain and it behaves differently under the compression and tension. To precise, this parameter decreases in overall considered tensile strain, at = 4%, its value is 2.845 eV. However, it increases with a small compressive strain up to 3.036 eV when = −1%. Further compression will decrease the band gap value to 2.958 eV at = −4%. Finally, we assess the effect of the external electric field on the HGaNH monolayer electronic properties. The external electric field is applied in z-direction perpendicular to the monolayer with values ranging from -0.5 to 0.5 (eV/Å/e), herein, the negative and positive values refer to the z-downward and z-upward directions, respectively. Band structures of the HGaNH monolayer under different electric fields are given in Fig.6. From the figure, one can see that both VBM and CBM are found at the Γ point, indicating that the direct nature of HGaNH monolayer is not affected by the presence of external electric field. However, its electronic band gap is very sensitive to this factor and shows a strong dependence. This parameter is plotted as a function of the electric field strength in Fig.7b. The figure shows that the band gap of HGaNH monolayer increases nearly linearly in the case of z-downward direction up to E = −0.3 (eV/Å/e) (3.224 eV), and a stronger electric field will decrease its value to 3.126 eV at E = −0.4 (eV/Å/e) and 2.270 eV at E = −0.5 (eV/Å/e). In contrast, this value decreases in overall considered external electric field range in the case of z-upward direction. Specifically, a nearly linear decreasing trend is observed up to E = 0.3 (eV/Å/e) (2.615 eV), from which the changing rate becomes higher giving values of 2.050 and 1.204 eV at E = 0.4 and E = 0.5 (eV/Å/e), respectively. Clearly, the band gap of HGaNH monolayer is strongly dependent on the electric field strength and direction application, this result is due to the fact that the spontaneous polarization is considerably changed when the first factor is varied or the second one is switched.
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In summary, we have carried out a comprehensive investigation of the electronic structure of HGaNH monolayer under biaxial strain and external electric field using the pseudopotential plane-wave method within the framework of density functional theory . Pristine GaN monolayer has a planar honeycomb-like structure. However, the structural planarity is destroyed by the full hydrogenation with a buckling height of 0.705 Åbeing produced as result of the electronegativity difference between atom pairs Ga-H and N-H. Our results asserted that GaN monolayer in an indirect gap semiconductor and the indirect-to-direct nature transition can be reached through the full hydrogenation. Based on our calculations, the band gap of HGaNH monolayer increases from the tensile strain to compressive strain of = −1%, and a larger compression will decrease its value. Moreover, this parameter decreases with an applied zupward direction external electric field, while it shows an increasing trend in the case of z-downward direction with strength up to -0.3 (eV/Å/e), a stronger electric field will decrease its value. Also, it has been demonstrated that the strain nature (compressive or tensile) and the application direction of the external electric field (upward or downward) 6
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play an important role due to the spontaneous polarization of the monolayer. We hope that results presented here will be helpful for the practical applications of GaN and HGaN monolayers in optoelectronic devices. References
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Journal Pre-proof Biaxial Strain and External Electric Field Effects on the Electronic Structure of Hydrogenated GaN Monolayer D. M. Hoat a,b,∗ , Mosayeb Naseri c , Tuan V. Vu d,e , Hai L. Luongf , Nguyen N. Hieu g,∗∗,R. Ponce-Pérez h , J. F. Rivas-Silva i , Gregorio H. Cocoletzi i a
Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam b
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Department of Physics, Kermanshah Branch, Islamic Azad University, P.O. Box 6718997551, Kermanshah, Iran d
Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam f
Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
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Universidad Autónoma de Coahuila, Facultad de Ciencias Quı́micas, Ing. J. Cárdenas Valdez, Republica, 25280 Saltillo, Coahuila, Mexico
Benemérita Universidad Autónoma de Puebla, Instituto de Fı́sica, Apartado Postal J-48, Puebla 72570, Mexico
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Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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email: [email protected]
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GaN monolayer has a planar graphene-like structure and the hydrogenation generates a buckling height of 0.705 Å. GaN monolayer is a semiconductor with a band gap of 1.933 eV and the hydrogenated has a band gap of 3.019 eV. The effect of biaxial strain and external electric field on the electronic properties of the hydrogenated GaN monolayer is studied in details. The hydrogenated GaN monolayer band gap is sensitive to biaxial strain and external electric field.
PII: DOI: Reference:
S0749-6036(19)31400-4 https://doi.org/10.1016/j.spmi.2019.106270 YSPMI 106270
To appear in:
Superlattices and Microstructures
Received date : 7 August 2019 Revised date : 6 September 2019 Accepted date : 9 September 2019 Please cite this article as: D.M. Hoat, M. Naseri, T.V. Vu et al., Biaxial strain and external electric field effects on the electronic structure of hydrogenated GaN monolayer, Superlattices and Microstructures (2019), doi: https://doi.org/10.1016/j.spmi.2019.106270. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
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Biaxial Strain and External Electric Field Effects on the Electronic Structure of Hydrogenated GaN Monolayer D. M. Hoata,b,∗, Mosayeb Naseric , Tuan V. Vud,e , Hai L. Luongf , Nguyen N. Hieug,∗∗, R. Ponce-P´erezh , J. F. Rivas-Silvai , Gregorio H. Cocoletzii a Computational
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Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam b Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Physics, Kermanshah Branch, Islamic Azad University, P.O. Box 6718997551, Kermanshah, Iran d Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam e Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam f Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam g Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam h Universidad Aut´ onoma de Coahuila, Facultad de Ciencias Qu´ımicas, Ing. J. C´ardenas Valdez, Republica, 25280 Saltillo, Coahuila, Mexico i Benem´ erita Universidad Aut´onoma de Puebla, Instituto de F´ısica, Apartado Postal J-48, Puebla 72570, Mexico
Abstract
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We investigate systematically the electronic properties of fully hydrogenated GaN (HGaNH) monolayer under effects of the biaxial strain and external electric field. Results assert that the pristine GaN monolayer is an indirect semiconductor with a band gap of 1.933 eV. Band structures indicate that the N-p and Ga-p states are the main contributors to the valence and conduction bands near Fermi level, respectively. The full hydrogenation can induce an increase of this parameter to 3.019 eV, with H-s state being present in both valence and conduction bands. Interestingly, the HGaNH monolayer transforms from indirect to direct gap as a consequence of GaN hydrogenation. Based on results, the electronic band gap of HGaNH monolayer shows sensitivity to the biaxial strain and external electric field. Therefore, these factors can be used to effectively tune the electronic properties of HGaNH monolayer in order to make it more suitable for optoelectronic applications.
1. Introduction
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Keywords: Hydrogenated GaN monolayer, Electronic properties, Strain engineering, External electric field, Optoelectronic applications.
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Since its discovery in 2004 [1], Graphene, a sp2 hybridized compound with honeycomb-like hexagonal structure, has attracted huge attention of the researchers due to its extremely intriguing properties such as high surface area, high electric conductivity, good optical absorption, mechanical strength, and the chemical stability [2, 3], among others. Undoubtedly, this 2D layer has become the center of the nanoscience and nanotechnology, being proven to have potential applications in optoelectronic devices [4, 5], sensors [6, 7], production and storage of energy [8, 9], photonics [10, 11], and the medical and biopharmaceutical fields [12, 13], and so on. The success of graphene has motivated special interest of the scientific community in low-dimensional materials, provided that some extremely superior physical and chemical properties emerge as compared with their bulk counterpart. Recently, extensive investigations have been devoted to the 2D nanosheets of transition metal monochalcogenides and dichalcogenides [14–16], metal oxides [17, 18], IV-IV group [19, 20], and III-V group [20–24]. Within this group ∗ Corresponding
author author Email addresses: [email protected] (D. M. Hoat), [email protected] (Mosayeb Naseri), [email protected] (Tuan V. Vu), [email protected] (Hai L. Luong), [email protected] (Nguyen N. Hieu), [email protected] (R. Ponce-P´erez), [email protected] (Gregorio H. Cocoletzi) ∗∗ Corresponding
Preprint submitted to Elsevier
September 6, 2019
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of 2D systems, the existence of the III-Nitride monolayers such as BN, AlN and GaN have attracted the attention. In bulk, these compounds may crystallize in a wurtzite-type hexagonal and/or cubic structure, they have wide band gap and potential optoelectronic applications [25, 26]. In 2D forms, they have been proven to have potential applicability, even equivalent to graphene, due to some intriguing properties such as wide electronic band gap, resistance to oxidation, mechanical and chemical stability. It is understood that the GaN monolayer can be exfoliated from the 3D wurtzite structure invoking the (0001) plane. So far, the electronic and optical properties of this monolayer have been the subject of some investigations. O. Dakir et al [27] studied the electronic and absorption properties of GaAs and GaN monolayers using first-principles calculations based on FP-LAPW method. Results show a band gap of 2.328 eV of the GaN monolayer. Employing the same method, Razieh Beiranvand et al [28] investigated the electronic and optical properties of BN, AlN and GaN monolayers and found that GaN monolayer is an indirect semiconductor with a band gap of 1.95 eV.
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To the best of our knowledge, the effect of full hydrogenation on the structural and electronic properties of GaN monolayer has not been investigated well yet. Moreover, it is well known that the strain and external electric field are two factors that can effectively tune the electronic structure of 2D materials [29–31]. Thus, in this work, our main aim is to examine the effectiveness of electronic structure engineering of the fully hydrogenated GaN (HGaNH) monolayer using biaxial strains and external electric fields. Results show that the HGaNH monolayer band gap is sensitive to the mentioned external factors, so that, they can be used to optimize the electronic properties in order to make the 2D layer more suitable for optoelectronic applications. 2. Computational details
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First-principles calculations based on the density functional theory (DFT) [32], as embedded in the CASTEP package [33], have been performed to investigate comprehensively the effect of biaxial strain and external electric field on the hydrogenated GaN (HGaNH) monolayer electronic properties. Norm-conserving pseudopotential and the Perdew-Burke-Ernzerhof (PBE) scheme within the Generalized Gradient Approximation are employed to describe the exchange-correlation energy functional [34]. Moreover, the Grimme scheme [35, 36] within the DFT-2D correction is adopted to take into account the weak van der Waals interactions. 4s2 4p1 states of Al atom, 2s2 2p3 states of N atom and 1s1 state of H atom are treated as valence states. The kinetic energy cut-off of the plane wave expansion is set to 500 eV. The self-consistent iterations will be stopped once the energy tolerance of 2 × 10−7 eV/atom has been reached. The k-mesh of 6 × 6 × 1 and 12 × 12 × 1 are adopted to integrate in the Brillouin zone for the structural optimization and electronic properties, respectively. In order to prevent the interactions between two consecutive layers, a vacuum space larger than 20 Åin the direction perpendicular to the monolayer is employed.
Figure 1: Total energy as a function of lattice constant and optimized atomic structure of pristine GaN monolayer (brown ball: Ga; blue ball: N.
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Figure 2: Optimized atomic structure of the hydrogenated GaN monolayer (brown ball: Ga; blue ball: N; gray ball: H).
3. Results and discussion
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3.1. Structural properties
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GaN wurtzite adopts a hexagonal structure belonging to the space group P63 /mc (no. 186), in which Ga and N atoms are situated at (1/3; 2/3; 0) and (1/3; 2/3; 0.375), respectively. Whose lattice constants are a = 3.190 Åand c = 5.189 Å[37]. In this 3D compound, the bond length Ga-N is dGa−N = 1.953 Å. The atomic structure of the 2D GaN monolayer can be generated from the wurtzite structure maintaining the hexagonal symmetry, however, it adopts a new space group P6m2 (no. 187). The structural optimization of pristine GaN monolayer is carried out by relaxing freely all atoms in the unit cell and then, finding the optimal geometry. In the second step, the energy-dependence of the volume is described through the Birch-Murnaghan equation of state [38]: 2 3 2 V 23 0 V0 23 9V0 B V0 3 0 E (V) = E0 + − 1 B + − 1 6 − 4 16 V V V
(1)
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Fig.1 depicts the total energy of the pristine monolayer calculated as a function of the lattice constant. According to our calculations, the lattice constants of GaN monolayer are a = b = 3.256 Å. These results are in good agreement with other theoretical values available in the literature [27, 28]. The optimized atomic structure of this monolayer is exhibited in the right panel of Fig.1. One can note that it has a planar graphene-like structure. The calculated interatomic distance Ga-N is dGa−N = 1.888 Å, which is about 3.32% smaller than that in bulk. The increase of the bonding strength from sp3 in bulk to sp2 in the monolayer results in the reduction of the interatomic distance. However, the bond nature in the GaN monolayer is predominantly ionic due to the large electronegativity difference between Ga and N atoms, similar to other III-V monolayers. Fig.2 displays a supercell 4 × 4 × 1 of the optimized atomic structure of fully hydrogenated GaN (HGaNH) monolayer. It is observed that when the GaN monolayer is hydrogenated, its structural planarity is disappeared and a buckling is appeared. Specifically, the calculated buckling height is 0.705 Å. While the Ga-N bond length increases to 2.008 Å, with the Ga-H and N-H interatomic distances being 1.570 and 1.032 Å, respectively. Obviously, the appearance of buckling and difference between dGa−H and dN−H in the HGaNH monolayer are generated by the electronegativity difference between atom pairs Ga-H and N-H. 3.2. Electronic properties
In Fig.3, the calculated band structure, total and projected density of states (DOS) of the pristine GaN monolayer are given. The electronic band structure is calculated along high symmetry direction Γ − M − K − Γ for energies ranging from -4 to 8 eV. From the figure, it is clearly observed that the valence band maximum (VBM) and conduction 3
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Figure 3: Electronic band structure and density of states of pristine GaN monolayer.
Figure 4: Electronic band structure and density of states of hydrogenated GaN monolayer.
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Figure 5: Band structure of hydrogenated GaN monolayer under various biaxial strains.
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Figure 6: Band structure of hydrogenated GaN monolayer under various external electric fields.
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band minimum (CBM) are found at K and Γ points, respectively, indicating that GaN monolayer is an indirect semiconductor, whose band gap value is 1.933 eV. This value is found in good agreement with other previously obtained theoretical result reported in reference [28]. The exhibited DOS plots evidences that the valence band is dominated mainly by the N-p state, with a small contribution of Ga-p state in the energy range from -2.9 to 0 eV. While the very flat subband from 0 to 4.2 eV and dense subband from 5.5 to 8 eV of conduction band are formed mainly from the Ga-s state. Whereas, the Ga-p state is the main contributor of the subband from 4.2 to 5.5 eV, in which a remarkable contribution of N-p state is also noted.
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Fig.4 shows the calculated band structure, total and projected density of state (DOS) of the HGaNH monolayer. Compared with the band structure of the pristine GaN monolayer, two differences can be clearly noted: (1) HGaNH monolayer is a direct semiconductor as both the VBM and CBM are located at Γ point, this result indicates the transition from indirect to direct semiconductor of the GaN monolayer as induced by the full hydrogenation, and (2) The overlapping of some electronic states along Γ − M and K − Γ high symmetry directions in conduction band is destroyed. The calculated band gap of HGaNH monolayer is 3.019 eV, which corresponds to an increase of the order of 56.18% from that of the pristine monolayer. Analyzing the DOS plots of HGaNH monolayer, one can note that the lower part from -4 to -2 eV of the valence band is mainly formed by the N-p state. While, the upper part is mainly dominated by the Ga-p, N-p, and H-s states. The same DOS values also suggest the strong states hybridization. On the other hand, the conduction band is built mainly by the Ga-s and Ga-p states, in which a small contribution from the N-p and H-s states is also noted. Comparing Fig.3 and Fig.4, we can conclude that the overlapping in the conduction band of the pristine GaN monolayer at energies higher than 5 eV is due to the Ga-s and N-p states. However, in the HGaNH monolayer, the observed overlapping disappears becauses the Ga-p state contribution becomes significant, which is a result of the hybridization of Ga-p state with H-s state. Next, we examine the biaxial strain influence on the electronic structure of the HGaNH monolayer. The biaxial 5
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Figure 7: Band gap of hydrogenated GaN monolayer as a function of (a) biaxial strain and (b) external electric field.
4. Conclusions
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0 strain is defined as follows: = a−a a0 × 100%, where a and a0 are lattice constant of the monolayer with and without strain, respectively. This study considers the biaxial strain ranging from -4% to 4%, herein the negative and positive values stand for the compressive and tensile strains, respectively. The calculated band structures of the HGaNH monolayer under various strains are displayed in Fig.5, in which the band structure at unstrained state is also presented for comparison. The figure shows that the applied strains does not change the direct nature of the monolayer, and the profile of entire band structure remains almost unchanged. The strain-dependence of the electronic band gap is illustrated in Fig.7a. It can be perceived that the band gap of HGaNH monolayer shows a sensitivity with the applied strain and it behaves differently under the compression and tension. To precise, this parameter decreases in overall considered tensile strain, at = 4%, its value is 2.845 eV. However, it increases with a small compressive strain up to 3.036 eV when = −1%. Further compression will decrease the band gap value to 2.958 eV at = −4%. Finally, we assess the effect of the external electric field on the HGaNH monolayer electronic properties. The external electric field is applied in z-direction perpendicular to the monolayer with values ranging from -0.5 to 0.5 (eV/Å/e), herein, the negative and positive values refer to the z-downward and z-upward directions, respectively. Band structures of the HGaNH monolayer under different electric fields are given in Fig.6. From the figure, one can see that both VBM and CBM are found at the Γ point, indicating that the direct nature of HGaNH monolayer is not affected by the presence of external electric field. However, its electronic band gap is very sensitive to this factor and shows a strong dependence. This parameter is plotted as a function of the electric field strength in Fig.7b. The figure shows that the band gap of HGaNH monolayer increases nearly linearly in the case of z-downward direction up to E = −0.3 (eV/Å/e) (3.224 eV), and a stronger electric field will decrease its value to 3.126 eV at E = −0.4 (eV/Å/e) and 2.270 eV at E = −0.5 (eV/Å/e). In contrast, this value decreases in overall considered external electric field range in the case of z-upward direction. Specifically, a nearly linear decreasing trend is observed up to E = 0.3 (eV/Å/e) (2.615 eV), from which the changing rate becomes higher giving values of 2.050 and 1.204 eV at E = 0.4 and E = 0.5 (eV/Å/e), respectively. Clearly, the band gap of HGaNH monolayer is strongly dependent on the electric field strength and direction application, this result is due to the fact that the spontaneous polarization is considerably changed when the first factor is varied or the second one is switched.
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In summary, we have carried out a comprehensive investigation of the electronic structure of HGaNH monolayer under biaxial strain and external electric field using the pseudopotential plane-wave method within the framework of density functional theory . Pristine GaN monolayer has a planar honeycomb-like structure. However, the structural planarity is destroyed by the full hydrogenation with a buckling height of 0.705 Åbeing produced as result of the electronegativity difference between atom pairs Ga-H and N-H. Our results asserted that GaN monolayer in an indirect gap semiconductor and the indirect-to-direct nature transition can be reached through the full hydrogenation. Based on our calculations, the band gap of HGaNH monolayer increases from the tensile strain to compressive strain of = −1%, and a larger compression will decrease its value. Moreover, this parameter decreases with an applied zupward direction external electric field, while it shows an increasing trend in the case of z-downward direction with strength up to -0.3 (eV/Å/e), a stronger electric field will decrease its value. Also, it has been demonstrated that the strain nature (compressive or tensile) and the application direction of the external electric field (upward or downward) 6
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play an important role due to the spontaneous polarization of the monolayer. We hope that results presented here will be helpful for the practical applications of GaN and HGaN monolayers in optoelectronic devices. References
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Journal Pre-proof Biaxial Strain and External Electric Field Effects on the Electronic Structure of Hydrogenated GaN Monolayer D. M. Hoat a,b,∗ , Mosayeb Naseri c , Tuan V. Vu d,e , Hai L. Luongf , Nguyen N. Hieu g,∗∗,R. Ponce-Pérez h , J. F. Rivas-Silva i , Gregorio H. Cocoletzi i a
Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam b
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Department of Physics, Kermanshah Branch, Islamic Azad University, P.O. Box 6718997551, Kermanshah, Iran d
Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam f
Department of Physics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
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Universidad Autónoma de Coahuila, Facultad de Ciencias Quı́micas, Ing. J. Cárdenas Valdez, Republica, 25280 Saltillo, Coahuila, Mexico
Benemérita Universidad Autónoma de Puebla, Instituto de Fı́sica, Apartado Postal J-48, Puebla 72570, Mexico
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Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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email: [email protected]
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GaN monolayer has a planar graphene-like structure and the hydrogenation generates a buckling height of 0.705 Å. GaN monolayer is a semiconductor with a band gap of 1.933 eV and the hydrogenated has a band gap of 3.019 eV. The effect of biaxial strain and external electric field on the electronic properties of the hydrogenated GaN monolayer is studied in details. The hydrogenated GaN monolayer band gap is sensitive to biaxial strain and external electric field.