Thermodynamic, Structural, and Piezoelectric Properties of Adatom-Doped Phosphorene and Its Applications in Smart Surfaces

Lou Li, Huiying Cao, Bo Xu, Junkai Deng, Jingran Liu, Yilun Liu, Xiangdong Ding, Jun Sun, and Jefferson Zhe Liu

Phys. Rev. Applied 13, 054061 – Published 26 May 2020

Abstract

Engineering the surface morphology is an effective way to obtain specific functionalities in applications of smart surfaces. Developing two-dimensional (2D) smart materials, which can undergo morphology changes under appropriate external stimuli, is a promising route to pursue for smart-surface design. In the work presented here, using density-functional-theory calculations, we systematically study the thermodynamic stability, crystal structure, and piezoelectric properties of black phosphorene (black $P$ ) doped with metallic atoms on one side with different concentrations. Particularly, $Li$ -doped black $P$ ( $P_{4} {Li}_{2}$ ) has a $d_{31}$ value of 6.28 pm/V, which is at least 4 times larger than that of any other 2D piezoelectric material. Via finite-element-method simulations, we show a $P_{4} {Li}_{2}$ -based prototype design for obtaining a surface-morphology change under a vertical electric field. The surface swelling pattern can be detected by human fingers with an appropriate design of the geometry. This demonstrates the promise of 2D piezoelectric materials for use in smart-surface applications.

Received 15 August 2019
Revised 16 March 2020
Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.054061

Physics Subject Headings (PhySH)

Adsorption Piezoelectricity

2-dimensional systems Alkali metals Elemental semiconductors Smart materials

Density functional calculations Finite-element method

Interdisciplinary PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Lou Li¹, Huiying Cao¹, Bo Xu¹, Junkai Deng ^1,*, Jingran Liu², Yilun Liu², Xiangdong Ding¹, Jun Sun¹, and Jefferson Zhe Liu ^3,†

¹State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China
²State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China
³Department of Mechanical Engineering, The University of Melbourne, Parkville, VIC 3010, Australia

^*junkai.deng@mail.xjtu.edu.cn
^†zhe.liu@unimelb.edu.au

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Vol. 13, Iss. 5 — May 2020

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Images

Figure 1
Formation energy per adatom $E_{f}$ of $P_{48} X_{1}$ calculated using DFT with the PBE functional. All metallic adatoms in the first three rows of the Periodic Table are examined, as shown at the top of the figure. All alkali adatoms have a negative $E_{f}$ . For transition metals, only $Ni$ , in the middle of the Periodic Table, have a negative $E_{f}$ . The inset shows the most stable adsorption site, the hollow site.
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Figure 2
(a) Formation energy per adatom $E_{f}$ of $P_{4} X_{1}$ and $P_{4} X_{2}$ . All metallic adatoms in the first three rows of the Periodic Table are tested. The inset shows an enlarged view for the cases of $Li$ and $Na$ . (b) Crystal structure of $P_{4} X_{2}$ with adatoms on two hollow sites. (c) Crystal structure of $P_{4} X_{2}$ with adatoms on two top sites. Most alkali metals have a negative $E_{f}$ . With an increase in concentration, $E_{f}$ for transition-metal adatoms, $Al$ , and $Ga$ tends to shift to more negative values.
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Figure 3
In-plane piezoelectric strains in the $x$ and $y$ directions under an electric field applied perpendicular to the black- $P$ plane (along the $z$ direction) for $P_{4} X_{2}$ .
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Figure 4
Comparison of piezoelectric coefficients $d_{31}$ of our adatom-doped black $P$ with previously known values for 2D piezoelectric materials. The orange and green bars represent values of $d_{31}$ calculated using the PBE functional and the DFT-TS scheme, respectively. GO denotes the graphene oxide. The color-filled and unfilled bars represent adatom-induced piezoelectric materials and intrinsic piezoelectric materials, respectively. The superscript labels “(a),” “(b),” “(c),” “(d),” and “(e)” refer to Refs. [26], [33], [27], [31], and [32], respectively.
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Figure 5
Prototypical smart-surface design where $P_{4} {Li}_{2}$ is used to generate morphology changes under an external electric field, simulated via FEM. (a) Illustration of the design. A 2D $P_{4} {Li}_{2}$ monolayer thin film is placed on a rigid substrate with a vertical electric field applied locally. (b) Top view of our FEM model. The $P_{4} {Li}_{2}$ thin film has an edge length of $L$ . The four edges are fixed to the substrate. The vertical electric field is applied to a local region in the center with edge size $l$ . See the main text for details of our FEM model. The right part of (b) shows the surface swelling profile. (c) Maximum swelling height $H$ as a function of $L$ and $l / L$ . The piezoelectric strains are $ε_{11} = 0.628 %$ and $ε_{22} = 0.03 %$ . (d) Four arrays of $9 \times 9$ building blocks (pixels) assembled together. Each building block follows the prototypical design shown in (b). When a voltage is applied to selected blocks, the swollen blocks form patterns with special morphologies. In this case, the patterns are “X,” “J,” “T,” “U.”
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