Enhanced out-of-plane piezoelectricity in two-dimensional TlP by surface hydrogenation

Piezoelectric materials have triggered a wide range of interest from condensed matter physicists, chemists, semiconductor device engineers, and materials scientists in recent years. At the same time, it draws the scientific community’s attention toward these low-dimensional piezoelectric materials. Piezoelectricity is an extraordinary material property that converts mechanical energy into electric energy and vice versa. Piezoelectricity is only possible in semiconductor materials that have broken their inversion and mirror symmetry. For example, in layered materials, such as TMDCs^1–4 and group III and IV monochalcogenides,^5–13 reduction to a single layer disrupts the centrosymmetric structure, revealing and enhancing piezoelectric properties. In the transition from bulk to a single layer, the piezoelectric coefficients of bulk SnSe increase as the number of layers decreases in odd-layer configurations.¹⁴ Recent advances in 2D materials have demonstrated diverse strategies to engineer piezoelectricity, such as the flexoelectric effect¹⁵ and inducing piezoelectricity by creating pores with specific symmetries in graphene.¹⁶ In contrast to conventional piezoelectric materials requiring non-centrosymmetric structures, recent studies on strain-gradient-induced polarization in graphene highlight the critical role of symmetry-breaking mechanisms in centrosymmetric systems for achieving electromechanical coupling.¹⁷ However, it is common knowledge that few 2D materials have a significant piezoelectric effect in the out-of-plane.

Most recently, there have been some studies on out-of-plane piezoelectric coefficients. For instance, Gao et al. have reported out-of-plane piezoelectric coefficients of 0.07–0.46 pm/V in Janus group-III chalcogenide monolayers.¹⁸ Guo et al. have shown a large piezoelectric coefficient (e₃₁ = 96.88 pC/m) in the hydrofluorination of penta-graphene (PG).¹⁹ Li et al. have shown a d₃₁ value of 6.28 pm/V in Li-doped black P (P₄Li₂).²⁰ Ong and Reed have selected F and Li atoms to be adsorbed on graphene, thereby inducing a maximum d₃₁ coefficient (d₃₁ = 0.30 pm/V).²¹ Shang et al. have shown a piezoelectric strain coefficient d₃₃ value of −5.33 pm/V in the C₃HF–Si1_FS monolayer.²² Nevertheless, TlP has an inversion center and does not possess intrinsic piezoelectricity. Amazingly, we found that TlP of surface hydrogenation (TlPH₂) exhibits a larger piezoelectric coefficient than the reported GaP and InP. After a deep understanding of piezoelectricity, plenty of strategies can be used to enhance the piezoelectric effect, such as chemical doping, adatoms, and defects. Typically, we propose that TlP can be designed to be piezoelectric through selective surface atomic adsorption.

In this article, we systematically investigate the configuration’s structures, stabilities, and electronic properties for surface-hydrogenated TlP. A new ground state based on the surface hydrogenation configuration of TlP (TlPH₂) is uncovered. Moreover, the new TlPH₂ is a potential piezoelectric material due to its non-centrosymmetry, similar to the hexagonal group III–V compounds GaP and InP,⁷ which are suitable piezoelectric materials. The piezoelectric coefficients d₁₁ and d₃₁ for TlPH₂ are evaluated as −24.73 and −0.79 pm/V, respectively. We found that the piezoelectricity in TlPH₂ is more notable than that of the theoretically viable hydrofluorination of penta-graphene¹⁹ and Janus group-III chalcogenide monolayers,¹⁸ indicating that it is expected that TlPH₂ can be synthesized for sensors, actuators, electric field generators, and any other applications that require electrical and mechanical energy conversion.

The first-principles calculations for the optimization of the structure and investigation of properties are performed using the Vienna ab initio Simulation Package (VASP),^23,24 in which a set of plane wave bases is used to expand the wave functions of the system. The interactions between nuclei and valence electrons are described by the projector augmented wave (PAW) method.²⁵ Interactions between valence electrons are counted using the generalized gradient approximation (GGA).²⁶ The cutoff energy is 500 eV, and a 5 × 9 × 1 k-point mesh is used in the calculation process. The crystal structures are fully relaxed until the residual force on each atom is less than 10⁻³ eV/Å and the total energy change is less than 10⁻⁶ eV. In all our calculating models, the vacuum distance is set to be greater than 20 Å to eliminate the interaction between adjacent layers. For the newly discovered ground state of TlPH₂, the vibrational spectra are simulated through the phonopy code^27,28 with forces calculated from VASP to evaluate its dynamical stability. The hybrid functional method (HSE06) was used to calculate the band structures.²⁹ 

The crystalline structure of TlP [shown in Fig. 1(a)] is very similar to that of h-BN reported previously.³⁰ It belongs to the non-centrosymmetric buckled honeycomb structure (space group P3m1, No. 156) with optimized lattice constants of a = 7.61 Å and b = 4.39 Å. After surface hydrogenation, the same configuration can be obtained, as shown in Fig. 1(b). The in situ surface adsorption keeps the system [TlPH₂ in Fig. 1(b)] with the same space group of P3m1 as TlP. After complete optimization, the lattice constants of TlPH₂ are correspondingly transformed to be a = 7.62 Å and b = 4.40 Å, which are in excellent agreement with the lattice constants of TlP. Subsequently, in Fig. 1(c), the minor imaginary frequencies caused by the inaccuracy of the fast Fourier transform grid only appear near the Γ point, which manifests that the phonon frequencies of TlPH₂ are all positive in the Brillouin zone and the phonon branches are almost free of any imaginary frequencies. This indicates that TlPH₂ is dynamically stable.

The formation energy E_f characterizes the relative stability of the TlPH₂ system. The formation energy E_f of the system was calculated using the formula E_f = (E_total − E_TlP − 2E_H2)/8, where E_total is the total energy of the system, E_TlP is the energy of the TlP unit cell, and E_H2 is the energy of the free hydrogen molecule. The denominator 8 denotes the total number of atoms in the unit cell. The formation energy value of the TlPH₂ system is calculated to be −1.11 eV per atom, and a negative value indicates an exothermic process, indicating that it is the stable structure of the H atom to be adsorbed on TlP. In other words, the TlPH₂ system has a lower energy than the pristine TlP system and the H₂ molecule.

Our calculated planar stiffness coefficients C₁₁, C₂₂, and C₁₂ for GaP and InP are 62.23 and 62.23, 21.06 and 45.09, and 45.14 and 18.77 N/m, respectively. These results are in excellent agreement with those reported in the previous literature,⁷ verifying the reasonability of our calculation settings. As shown in Fig. 3(a), the energy vs TlPH2 function of external strains is determined by Eq. (1). Through a quadratic fitting of the results in Fig. 3(a), we can obtain the planar stiffness coefficients C₁₁, C₂₂, and C₁₂ of TlPH₂. They are 24.82, 24.90, and 11.88 N/m, respectively, as listed in Table I, together with those of TlP, GaP, and InP for comparison. We calculate C₁₃, C₁₄, C₃₃, and C₄₄ of TlPH₂ using DFPT. The results are 0.31, −0.05, 0.22, and 0.002 N/m, respectively. Our calculations, C₁₁ > |C₁₂|, $C132<12C33(C11+C12)$⁠, and $C142<12C44(C11−C12)$⁠,^31,32 indicate that TlPH₂ is also mechanically stable. The elastic stiffness of TlPH₂ is greater than that of the corresponding group-III phosphide, as listed in Table I. The changes in elastic stiffness can be understood by shortening the in-layer Tl–P bonds after surface hydrogenation, which induces ionic features in the system through electron transfer. Similar changes can also be noticed in hydrogenating a single layer of h-BN.³³ 

Based on first-principles calculations, we identified a new ground-state configuration (TlPH₂) for surface-hydrogenated TlP. TlPH₂ possesses remarkable energetic and mechanical stability and is confirmed to be dynamically stable. Our results demonstrate that it is a direct bandgap semiconductor with a bandgap of about 0.801 and 1.402 eV calculated from DFT-PBE and HSE06 methods, respectively. Because of its remarkable out-of-plane piezoelectric coefficients d₃₁, TlPH₂ is predicted to be an excellent piezoelectric material comparable to other known 2D materials. Its calculated piezoelectric coefficients are more impressive than the theoretical value of the surface-modified penta-graphene and group-III phosphides. These results indicate that TlPH₂ is a desirable target for synthesis experiments, with potential applications in sensors, actuators, electric field generators, and any other nano-devices for electrical–mechanical energy conversion. Similar to carbon-bridged oligo(p-phenylenevinylene)s achieving photostable and broadly tunable organic lasers through molecular design,³⁶ our surface hydrogenation strategy demonstrates the effectiveness of chemical modification in tailoring functional properties of low-dimensional materials. Our results confirm that surface modification, namely hydrogen absorption, effectively enhances piezoelectricity in 2D TlP.

This work was financially supported by the Natural Science Foundation of Shanxi Province (Grant No. 202303021222282), the Science and Technology Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2023L415), and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020A1515110627).

The authors have no conflicts to disclose.

Jia-Bin Li: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review and editing (equal). Yonghua Tang: Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.