High-performance photocatalytic and piezoelectric properties of two-dimensional transition metal oxyhalide $\mathrm{ZrO}{X}_2 (X=\mathrm{Br},\mathrm{I})$ and their Janus structures

As an emerging type of two-dimensional (2D) family, transition metal oxyhalides with the chemical formula ${\mathrm{MOX}}_2$ have been studied in recent years. Inspired by the successful synthesis of $\mathrm{ZrO}{\mathrm{I}}_2$ monolayer with excellent photocatalytic and piezoelectric properties, we conducted a systematic and comprehensive investigation of $\mathrm{ZrO}{X}_2 (X=\mathrm{Br},\mathrm{I})$ and its Janus ZrOBrI monolayers using first-principles calculations. The results show that the mechanically, dynamically, and thermally stable $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI are indirect-gap semiconductors with band gaps ranging from 1.89 to 3.48 eV by the hybrid density functional HSE06 method. Besides, their valence-band minimum and conduction-band minimum can straddle the redox potential of water at $p\mathrm{H}=0$, respectively. Interestingly, due to the optimal band alignment mechanism, the band-edge position of Janus ZrOBrI with an intrinsic electric field does not expand. Moreover, biaxial compressive strain (within −6%) effects on the band alignments and band gaps are discussed. What is more, strong anisotropy and high optical absorption in the visible-ultraviolet region ($\sim {10}^5\mathrm{c}{\mathrm{m}}^{-1}$) render these monolayers fantastic polarizers and photoelectronic devices. Besides, the orientation-dependent carrier mobility of these monolayers is much higher than that of many other 2D semiconductors, making them potential electronic and photocatalytic devices. For piezoelectric performance, all of these monolayers exhibit a considerable in-plane transverse piezoelectric coefficient $d_{21}$, reaching about 20 pm/V. Furthermore, the Janus ZrOBrI possesses additional out-of-plane piezoelectric responses due to structural mirror asymmetry. Under AC stacking mode, multilayer Janus ZrOBrI has appreciable vertical piezoelectric coefficients $d_{31}$ and $d_{32}$, reaching 1.17 and 4.61 pm/V, respectively. Our findings highlight that all three monolayers are multifunctional devices, especially in the fields of photocatalysis and piezoelectricity.

Figure 1

(a) The optimized crystal structures of $\mathrm{ZrO}{X}_2$ ($X=\mathrm{Br}$, I) and Janus ZrOBrI monolayers, where the black dashed lines represent the unit cell. (b) Phonon spectra and (c) AIMD simulations at 300 K for $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers, where the blue lines and the red lines represent the variation of the total energy and temperature with time, respectively. (d) The original (left) and final (right) crystal structures after AIMD simulations with 8 ps. The blacked dashed lines represent the supercell by $4\times 4\times 1$.

Figure 2

(a) Projected band structures (left) and density of states (right) of the suborbitals of the Zr-$d$ and -$p_x$ orbitals of O/Br/I atoms calculated by the HSE06 method. (b) Plane-averaged electrostatic potential along the $z$ direction. (c) The charge distribution of CBM and VBM states, the isosurface value is $0.03\mathrm{e}/{\AA }^{-3}$. (d) Band-edge alignments from the HSE06 method compared with the water redox potential at $p\mathrm{H}=0$. The red dots represent the real position of CBM and VBM.

Figure 3

(a) Biaxial compressive strain effect on the band gap of $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers at the HSE06 level. (b) Biaxial compressive strain effect on the band alignment of $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers at $p\mathrm{H}=0$.

Figure 4

(a) The imaginary parts of the dielectric function calculated by the ${\mathrm{G}}_0{\mathrm{W}}_0+\mathrm{BSE}$ method for $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers, respectively. (b) The optical absorption coefficients computed by the ${\mathrm{G}}_0{\mathrm{W}}_0+\mathrm{BSE}$ method for $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers. (c) The optical anisotropy ratio as a function of photon energy for $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers.

Figure 5

(a) The anisotropic electron and hole mobility obtained by Lang-Zhang-Liu (LZL) method for $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers. (b) The anisotropic electron and hole mobility obtained by the Boltzmann transport equation (BTE) method for $\mathrm{ZrO}{X}_2$ and Janus ZrOBrI monolayers.

Figure 6

The direction-dependent Young's modulus (a) and Poisson's ratio (b). The schematic diagram of piezoelectric responses (c), where the blue thin arrows represent the direction of mechanical stress and the thick arrows (black, red, and green) denote the direction of charge polarization. (d) Seven high-symmetry stacking types of bilayer Janus ZrOBrI. For AA, AB, and AC stacking, the two Janus ZrOBrI monolayers are parallelly orientated. Br and I atoms in up layers are settled on the I-top site (AA), on the Zr-top site (AB), and on the O-top site (AC). For AA′, AB′, and AC′ stacking, the two Janus ZrOBrI monolayers are antiparallelly orientated. Br and I atoms in up layers are settled on the I-top site (AA′), on the Zr-top site (AB′), and on the O-top site (AC′). The BB′ stacking represents Zr atoms in the upper layer settled on the top of Zr atoms in the lower layer. (e) Four-layer Janus ZrOBrI under the AC stacking mode.

Figure 7

(a)–(c) The relationship between the elastic tensor, piezoelectric tensor, and piezoelectric coefficients with the number of layers in multilayer ZrOBrI under AC mode.