New 2D penta-SiPN: A wide and indirect bandgap semiconductor

In recent years, two-dimensional (2D) pentagonal ternary monolayers have attracted much attention and emerged as a new class of materials because of their new feature and extensive applicability. Using first-principles density functional theory (DFT) calculations, we predict a new 2D pentagonal-SiPN or p-SiPN monolayer material. The new monolayer has shown to be structurally, thermodynamically, and dynamically stable. Our findings imply that p-SiPN is a wide and indirect bandgap semiconductor, with a highly tunable bandgap with applied equ-biaxial strain. This makes p-SiPN a promising candidate for futuristic optoelectronics and nanomechanics device applications.


Introduction
The first two-dimensional (2D) hexagonal honeycomb lattice-based material, Graphene [1], has shown extraordinary physiochemical properties, however, it lacks semiconducting functionality with zero bandgap, restricting its applications in optoelectronics and piezoelectric industries.Meanwhile, the newly discovered penta-Graphene [2,3], with semiconducting behavior, mechanical strength equivalent to that of Graphene, and very rare auxetic mechanics, has shed light into the importance of the new 2D Cairo-pentagonal lattice-based sheets (elementary, binary compounds) as promising future materials, which demonstrated exceptional physical and chemical properties.These properties have been identified mostly with theoretical and computational approaches [4,5,6,7,8], with promising possibility for experimental synthesis and experimental feasibility [9,10,11,12,13].They exhibit buckling/puckering nature combined with three virtual layers geometry, which enable them to parade phenomenal optoelectronic, mechanical, and thermal conductivity properties.In particular, period I-II group light-weight penta materials have garnered a lot of attention lately because of their tremendous abundance, light-mass, and environmental traits.Moreover, binary pentagonal monolayers [14,15,16] among many others have demonstrated multi-functional responses and exceptional mobility, thermal conductivity, transport, and optoelectronic properties, which make them excellent candidates for several applications involving thermoelectric devices and catalysis.In addition, the recently predicted ternary penta compounds [17,18] have demonstrated extraordinary auxetic mechanics, piezoelectricity, and kinetic stability properties superior to that of their binary counterpart.Motivated in part by the buckled configuration of the N, P, and Si atoms, together with the adaptable structure of the electronic configuration of the P atom, and similar bond lengths and bond angles, we design a new 2D p-SiPN monolayer material, which we find to be structurally, dynamically, and thermodynamically stable.

Computational Details
In our calculations, the SIESTA code [19] was used to carry-out all DFT calculations.The GGA approximation based on the PBE parametrization was used to account for the electronic exchange and correlation potentials.The electrons-core interactions as implemented in the Kleinman-Bylander form were calculated using the Troullier-Martins norm-conserving pseudopotentials within the semi-local form.Moreover, the electronic distribution of each atom was described using the double-ȗ polarized basis based on the numerical atomic orbitals.To establish the convergence criterion, we used a mesh of 20×20×1 k-points within the Monkhrost pack scheme, and a cutoff energy = 350 Ry.For geometry optimization, atomic forces < 0.01 e V / Å , self-consistent field = 10 −6 eV, and a vacuum-gap = 25 Å along the out-of-plane (zdirection) are used.We ensured chemical stability by calculating both the cohesive (E coh ) and formation (Ef ) energies using: (1) where Ep−SiPN, ESi, EP, and EN represent the energy of p-SiPN, and free/isolated Si, P, and N atoms, respectively, and: with ‫ܧ‬ ௌ ௨ , ‫ܧ‬ ௨ and ‫ܧ‬ ே ௨ being the energy at the most stable bulk geometry of Si, P, and N atoms, respectively.The finite displacement method implemented in the PHONOPY package [20] within the Viena Ab-initio Simulation Package (VASP) is utilized to calculate the phonon bands needed to ensure the p-SiPN dynamical stability.Moreover, we carried ab-initio molecular dynamics (AIMD) simulations at T = 300 K, i n a t i m e s t e p = 1 f s up to 2000 fs to investigate the p-SiPN thermodynamical stability.Both stability calculations were performed using a supercell of 7×7×1 in order to achieve convergence.

Structural Properties
Based on the arrangement of three and four carbon atoms in the bottom, upper, and middle layers of penta-Graphene, the p-SiPN shape is formed with a central layer of 4-coordinated Si (Si4c) and bottom/upper layers of 3-coordinated P/N (P/N3c).Moreover, we experimented with various versions of the 2D pentagonal structure and found that the Si4c structure was the most stable, as shown in Figure (1a).The final p-SiPN unit cell is composed of two atoms of Si, P, and N each, organized in three virtual layers within one monolayer.Next, we fine-tuned the p-SiPN configuration to achieve the minimum energy level, inter-atomic forces, and stresses.The resulting structure exhibits pentagonal symmetry in two dimensions, possessing P -21 crystal symmetry with space group No. 4. The supercell's aerial perspective reveals four well-defined and unique pentagonal Cairo structures, featuring optimized lattice parameters of a = 4.41 Å and b = 4.43 Å.The bond lengths measured for Si-P, P-N, and Si-N are 2.32 Å, 1.81 Å, and 1.78 Å, in that order.The thickness that was measured is h = 2.85 ˚A, which is greater than the thickness found in previous studies on 2D penta-monolayers (1.34 h 2.50) Å, because of the longer bond-lengths observed in p-SiPN.The bond angles for Į, ȕ, and Ȗ in the P-Si-P, Si-P-N, and P-N-Si structures are 109.30o , 97.21 o , and 119.67 o , respectively.To further comprehend the atomic charge distribution and bonding mechanism, we have conducted Mulliken charge density analysis.The valence charge density iso-surface plot in Fig. (1b) indicates that the charge is primarily concentrated around the N atom with some distribution along the Si-N and N-P bonds.This is clearly due to the increased N atom electronegativity.Figure (1c) displays a contour plot of 2D charge density, with green representing the highest intensity and red representing the lowest intensity.The presence of a greater electron charge in Si-N and P-N bonds, the green color, and the intersection of concentric lines with the merging of electronic wave functions validate covalency.The distinctive smaller wave functions overlapping along with the deformation of the conjoining contour lines, shown as dumbbell-shaped with smaller charge spread, faded-green, between P-N clearly suggest the ionic and covalent bonding formation, with the bonding of P-N and Si-N being the strongest compared to the Si-P bond.Further, the obtained negative cohesive energy Ecoh = −5.28eV/atom, calculated based on Eq. ( 1), confirms the structural stability.In addition, we found formation energy Ef = +1.56eV/atom, based on Eq. ( 2), which suggests the possible synthesis of the 2D p-SiPN monolayer through endothermic experimental process.The phonon band spectrum along the first Brillouin zone is also calculated.It contains only real frequencies with fifteen optical and three acoustic branches phonon frequencies, Fig. (1d), which further confirms dynamical stability.The shown AIMD simulation performed at T = 300 K, Fig. (1e), suggests that the p-SiPN monolayer is highly thermodynamically stable, and does not exhibit any distortion.We further investigate the modulation of the electronic bandgap and the tuning mechanism of p-SiPN, Fig. 3(a − b), when both an equ-biaxial tensile and compressive strain (−4% İxy +8%) are applied.In order to reach the state of minimum energy, we permitted the atomic positions to relax during the process.When subjected to a compressive strain of İxy = −2%, the bandgap expanded to 2.50 eV while maintaining its indirect nature.When the strain was at İxy = −4%, the bandgap reduced to 2.41 eV and exhibited a direct bandgap behavior at the Y point, likely attributed to the meta-stability of p-SiPN under applied strain.However, applying a tensile strain of İxy = + 2% results in obtaining an indirect bandgap of 2.41 eV, leading to the VBM shifting from the Y to the M point.By further increasing the tensile strain to a range of 4% İxy 8%, the bandgap decreases even more to 2.15 eV, 1.85 eV, and 1.55 eV for strain levels of 4%, 6%, and 8% respectively.Compared to being strain-free, the electronic bandgap value decreases by approximately 36% when stretched by 8%.This indicates that the electronic performance of p-SiPN can be easily adjusted by changing the applied strain, which is essential for various optoelectronic, nanomechanical, energy storage, and light harvesting devices [22,23,24].

Conclusions
In this work, DFT calculations were carried-out to predict a new 2D p-SiPN material.The new p-SiPN monolayer is verified to be structurally, dynamically, and thermodynamically stable.The p-SiPN obtained negative cohesive energy E coh = −5.28eV/atom and formation energy Ef = 1.56 eV/atom confirm the structural stability of the 2D p-SiPN monolayer suggesting its possible experimental synthesis using endothermic process.In addition, the performed AIMD simulation carried-out at T = 300 K confirms that the 2D p-SiPN monolayer is highly thermodynamically stable without any distortion.The plots of the valence charge density isosurface for p-SiPN reveal that the charge mostly clusters around the N atom, while also being widely distributed along the Si-N and N-P bonds, due to the N atom's greater electronegativity.Our calculations suggest that both the spin-up and spin-down bands show clear symmetry indicating a zero total magnetic moment with a non-magnetic ground state of the 2D p-SiPN.Moreover, p-SiPN seems to exhibit a wide and indirect bandgap semiconducting behavior with a bandgap value of E g = 2.43 eV (3.43 eV) as calculated based on the GGA (hybrid functional HSE06) approximation.It also shows high tunable bandgap against both applied biaxial and compressive strains in the range of −4% İxy +8%, making p-SiPN an attractive material for various applications such as energy-storage, optoelectronics, nanomechanics, and lightharvesting devices [22,23,24].

Figure 1 .
Figure 1.(Color online) (a) The final optimized p-SiPN monolayer is shown in the top and side views.The Si, P, and N atoms are shown in green, purple, and blue balls, respectively, (b) the valence charge-density iso-surface (light-magenta) with 0.11 e/ Å3 , (c) the 2D charge density contour plots of the inter-atomic charge distribution are shown in the top/right and side/left panel, (d) phonon band, and (e) energy fluctuation during the NVT ensemble at T = 300 K are based on AIMD simulation.The diagram displays the optimized geometry of p-SiPN from both top-view and side-view perspectives.

Figure 2 .
Figure 2. (Color online) (a) The band structure (electronic), (b) the PDOS with the VBM/CBM calculated using GGA approximation displayed in the top/bottom panels, (c) electronic band structure acquired from GGA approximation, and (d) comparison of band structure using HSE06 functional.The green box indicates the endpoint locations of the VBM and CBM bands.To understand the electronic structure of p-SiPN, the spin-polarized/unpolarized electronic bands, and PDOS are calculated, Figs.(2a-2b).Both the spin-up and spin-down bands show clear symmetry suggesting a zero total magnetic moment with a non-magnetic ground state.There is a high-symmetry observed in the first Brillouin zone (BZ) along the ī−X−M -Y−ī path as calculated using the NAO-basis implemented i n SIESTA, Fig. (2a), and the planewave approach used by VASP, Fig. (2c).Both the GGA and HSE06 approximations yield

Figure 3 .
Figure 3. (Color online) The change in the electronic band due to applied equi-biaxial tensile and compressive strain İxy.The shown dotted horizontal lines display the valence band maximum and conduction band minimum, and the solid arrow represents the nearest inter-band transition.