Thickness-dependent atomic structures of two-dimensional few-layer ZnO: A density functional theory study

Dong Han, Xian-Bin Li, Nian-Ke Chen, Dan Wang, Sheng-Yi Xie, Xue-Jiao Chen, and De-Zhen Shen

Phys. Rev. B 109, 014105 – Published 19 January 2024

Abstract

The thickness-dependent atomic structures of two-dimensional (2D) few-layer (FL) ZnO are systematically investigated by the first-principles calculations. It is found that the structural transformation between thinner FL ZnO with graphitic structure $(FL g ZnO)$ and thicker FL ZnO with wurtzite structure $(FL w ZnO)$ takes place at the critical thickness of 9–12 Zn-O atomic layers. At the thickness of 9–12 layers, both graphitic and wurtzite structures can coexist at room temperature. In FL $g ZnO$ , the interlayer interaction is a long-range Coulomb interaction, and the charge population of Zn and O inside does not change during the structural transformation. Moreover, we demonstrate that the structural transformation of FL ZnO originates from the competition between the high energy of the O $2 p_{z}$ orbital in the graphitic structure and the polar-surface-induced dipole energy in the wurtzite structure. Our microscopic understanding guides a clear direction of regulating the atomic structure of FL ZnO, further optimizing its electronic properties, which benefits developing function-advanced 2D stacked devices.

Received 24 July 2023
Accepted 5 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.014105

Physics Subject Headings (PhySH)

Crystal structure

II-VI semiconductors Multilayer thin films

Density functional calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dong Han ^1,*, Xian-Bin Li ², Nian-Ke Chen², Dan Wang³, Sheng-Yi Xie ⁴, Xue-Jiao Chen⁵, and De-Zhen Shen^1,†

¹State Key Laboratory of Luminescence and Applications, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, People's Republic of China
²State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, People's Republic of China
³School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, People's Republic of China
⁴School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
⁵CAS Key Laboratory of Magnetic Materials, Devices and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, People's Republic of China

^*hand@ciomp.ac.cn
^†shendz@ciomp.ac.cn

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Issue

Vol. 109, Iss. 1 — 1 January 2024

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Images

Figure 1
Binding energies as a function of interlayer distance in (a) graphite, (b) $h BN$ , and (c) BK $g ZnO$ . The insets show their unit cells, respectively. The total energies of them in their monolayer forms are set to zero, respectively. The dashed lines show the lattice constant $c$ of the optimized unit cell of graphite, $h BN$ , and BK $w ZnO$ , respectively. The 2D slice (light-blue slice in unit cells) of the charge-density difference of (d) graphite, (e) $h BN$ , and (f) BK $g ZnO$ between when the layers adjoin at their equilibrium distances and the corresponding isolated layers. The position of atoms on 2D slices are labeled in each material, respectively. (The vesta software package was used to generate all figures [50].)
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Figure 2
(a) The equilibrium lattice constants $a$ of FL ZnOs ( $a^{G}$ , $a^{W}$ for graphitic and wurtzite structures) vary along with the layers from 2 to 15 layers. The equilibrium lattice constants $a$ of BK $g ZnO$ , monolayer ZnO, and BK $w ZnO$ are shown in red, pink, and blue dashed lines, respectively. (b) The $z$ -directional displacement $R_{1}$ between the intralayer Zn and O in FL ZnOs from 2 to 15 layers. The height of the bar is the $z$ -directional displacement $R_{1}$ , where the scale of $Y$ axis varies from 0 ( $R_{1}$ in BK $g ZnO$ ) to 0.644 Å ( $R_{1}$ in BK $w ZnO$ ). The bar located in the $X$ axis stands the average $z$ -directional position of the Zn-O layer in the supercell model. Two corresponding optimized atomic structures are illustrated in the 6 and 11 layers.
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Figure 3
(a) The average binding energies ( $E_{b}$ ) of FL ZnOs with graphitic and wurtzite structures vary along with the layers, respectively. The total energy of monolayer ZnO is set to zero. (b) The energy barriers of FL ZnOs between graphitic and wurtzite structures as a function of the layers. FL ZnO with graphitic geometry is set to zero.
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Figure 4
The Zn- and O-orbital energy levels (cyan and red) of FL $g ZnO$ and FL $w ZnO$ (11 layers). The dashed lines are the corresponding orbital energy levels calculated in BK $g ZnO$ and BK $w ZnO$ , respectively. These orbital energy levels are the weighted average of PDOS in Fig. S2 in the Ref. [40]. Note that the orbital energy levels in FL $w ZnO$ have been corrected to eliminate the effect of internal electric field induced by polar surface, as shown in Fig. S3 in the Ref. [40]. The ideal vacuum [48, 49] of BK ZnO is set to zero, and the O $2 s$ -orbital energy level of FL $g ZnO$ (FL $w ZnO$ ) is aligned to the O $2 s$ -orbital energy level of BK $g ZnO$ (BK $w ZnO$ ).
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