Stability and Electronic Properties of Phosphorene Oxides: from 0-dimensional to Amorphous 2-dimensional Structures Oleksandr I. Malyi1, Kostiantyn V. Sopiha2, Claudia Draxl3, and Clas Persson4 1 – School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798 Singapore, Singapore 2 – Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore, Singapore 3 – Physics Department and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Groβen Windkanal 6, D-12489 Berlin, Germany 4 – Department of Physics, University of Oslo, P. O. Box 1048 Blindern, NO-0316 Oslo, Norway Combining screening by first-principles calculations and Born-Oppenheimer molecular dynamics simulations, we fully reconsider phosphorene oxidation and formation of lowdimensional phosphorus oxides (PxOy). It is found that previously reported 2-dimensional PxOy (2d-PxOy) structures cannot provide a full understanding of 2d-PxOy properties. We show that P-O interaction can result in highly stable 0d-PxOy and 2d-PxOy structures with close energetics, but noticeable difference in band-gap energies. Here, the possibility for formation of amorphous 2d-PxOy structures and their unique electronic properties are also studied in detail.
Emails:
[email protected] (O.I.M),
[email protected] (K.V.S)
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Introduction Owing to high stability,1, 2 a direct band gap of about 1.2-2 eV,3, 4 and high anisotropy,5, 6
single-layer black phosphorus named phosphorene has become one of the most promising 2-
dimensional (2d) materials for different semiconductor applications.7 In particular, phosphorene has already proven its great potential for metal-ion batteries,8,
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transistors,2
sensors,10 etc. However, in contrast to graphene, black phosphorene can exhibit a drastic change of its properties in different environments, which is due to its high reactivity.11-13 Because of this, and since P-O interaction can induce degradation of desirable optoelectronic properties,12,
14-24
controlling of phosphorene oxidation is one of the main challenges in
developing phosphorene-based technologies further. To overcome the oxidation problem, and thereby reach air-stable performance, the encapsulation of phosphorene using BN14, 22 or AlOx layers23, 24 is widely applied. Phosphorene oxidation can also be considered as a way for both band-gap engineering and opening perspectives towards novel materials. Wang et al. first proposed a new class of 2d materials based on the density-functional theory (DFT) analysis of O coverage of black phosphorene.17 This work inspired extensive theoretical studies of 2-dimensional phosphorus oxides (2d-PxOy) in different forms.18-21 Ziletti et al. expanded the mechanisms for P-O interaction by exploring planar and tubular PxOy forms18 and provided a more complete picture of 2d-PxOy properties in their following studies.15,
16
Recently, using laser oxidation, the
concept of band-gap engineering was proved experimentally.16 However, from a theoretical perspective, there are still many open issues. Despite previous works reporting some fundamental understanding of P-O interaction, surface and planar models for 2d-PxOy yield very different trends for the dependence of the electronic properties on phosphorene oxidation.18 Although the planar model provided basic insight into the experimental results, it does not allow for explaining the origin of experimentally observed defect-induced states.16 In
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all previous theoretical studies, the stability of proposed 2d-PxOy materials was predicted by analyzing binding energies and phonon frequencies, which allowed for excluding highly metastable structures. However, many semiconductor surfaces tend to reconstruct in order to minimize the number of dangling bonds. This is essential for an understanding of long-term behavior for the proposed 2d-PxOy. Moreover, to the best of our knowledge, the energetics of 0d-PxOy has not been investigated in detail despite actual van der Waals (vdW)-bonded PxOy polymorphs with clearly defined 0d-PxOy building blocks.25-27 Taking into account recently synthesized blue phosphorene28 and the possibility for P amorphization, it is highly important to expand our knowledge on low-dimensional PxOy. Motivated by this, here, we fully reconsider phosphorene oxidation by combining screening by first-principles calculations and Born-Oppenheimer molecular dynamics (BOMD) simulations.
Methods DFT calculations are carried out using the Vienna Ab Initio Simulation Package (VASP) with projector augmented wave (PAW) pseudopotentials29,
30
and Perdew-Burke-
Ernzerhof (PBE)31 exchange-correlation functional. Since PBE is expected to provide underestimated band-gap energies, for the most stable PBE structures, we also perform calculations with the range-separated hybrid functional HSE32 which is known to be a wellestablished and accurate for describing electronic properties.33 The cutoff energies for the plane-wave basis are set to 300, 400, 600 eV for BOMD simulations, HSE calculations, and all other DFT calculations, respectively. Г-centered Monkhorst-Pack34 grids of different sizes (see Table S1) are used to perform the Brillouin-zone integrations. For the studied systems, all atoms are relaxed until the internal forces are smaller than 0.01 eV/Å. The BOMD simulations are performed using the Nose thermostat35, 36 with a time step of 2 fs. Details on supercell sizes
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used in BOMD simulations are given in Table S2. The computed results are analyzed using Vesta37 and pymatgen.38
Results and discussion First, we form a dataset of 0d-PxOy and 2d-PxOy structures based on the analysis of different group-15 and 16 compounds available in the Materials Project database39 and previously reported 2d-PxOy (see Supplementary Information). Next, for each system in the dataset, recursive O adsorption and reduction are considered until the lowest energy configurations for all compositions are found. The simplified picture of the screening protocol is shown in Fig. 1a. To analyze the material’s stability, we calculate the binding energy as
Eb EP4Oy EP yEO2 / 2 , where EP4Oy , E P , and EO2 are the energies of phosphorene oxide scaled to that of P4Oy containing y O atoms, black phosphorene containing 4 P atoms, and an isolated spin-polarized O2 molecule, respectively. In total, over 6500 unique PxOy systems are analyzed in the screening calculations. Here, our simulations have a limitation, as they do not take into account the formation of 1d-PxOy and 2d-PxOy from 0d-PxOy building blocks. Such study requires a proper description of vdW interactions, which is a big challenge for some lowdimensional materials. In particular, significant inaccuracy of vdW-DF functionals in the description of phosphorene-based systems was shown.40,
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Nevertheless, the current
methodology allows for summarizing the key properties of the most representative lowdimensional PxOy compounds as well as for understanding their stability and electronic properties. Due to the high variety of possible structures, there is still a possibility for more complex polymorphs to exist. Because of this, to ensure that the found structures do not reconstruct for every lowest energy 2d-PxOy material found in this work, we also perform BOMD simulations as discussed below.
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The oxidation of bulk P results in the formation of various PxOy polymorphs having similar building blocks.42, 43 In the highest oxidation state, each P atom takes 2.5 O atoms. Here, the resulted P-O interaction even can lead to the formation of layered structure.43 Thus, it is reasonable to assume that a single layer of the layered P4O10 polymorph represents the lowest energy 2d-P4O10 structure. However, Ziletti et al. proposed planar 2d-P4O10 with a higher stability as compared to the isolated layer.18 Indeed, despite different computational setups, our calculations confirm the relative energetics. The computed binding energy for the planar 2dP4O10 is -27.12 eV/unit-cell, while for the isolated layer it is -27.09 eV/unit-cell. Nevertheless, the isolated P4O10 layer is unstable to minor structural perturbations, resulting in the lower energy structure. Moreover, the perturbed 2d-P4O10 layer is by 0.1 eV/unit-cell more stable than the planar 2d-P4O10. Note that this energy difference is within typical energy range for coexisting phases and hence both systems may exist under experimental conditions. The cohesion of both 2d-P4O10 and 0d-P4O10 (discussed below) is determined by bonding PO4 tetrahedra, and two types of O atoms (dangling and bridging) are identified in the systems (see Figs. 1b,c). The dangling O forms a single bond with the neighboring P atom, while the bridging O is bonded to two P atoms. Analysis of the equilibrium configurations and their energetics suggests that for O-rich 2d-P4Oy, the dangling O forms weaker bonds than the bridging O. This is well illustrated by a Bader charge analysis. For instance, for 2d-P4O10, the average Bader charge on the dangling O atoms is -1.38e, while for the bridging O atoms it is 1.53e. Moreover, the lowest energy 2d-P4O6 and 2d-P4O9 can be considered as 2d-P4O10 with the number of dangling O atoms removed from the system (see Fig. 2a). Here, the found 2dP4O6 system is the same to that isolated from bulk (P21/c) As2Se3. It should also be noted that 2d-P4O7 and 2d-P4O8 systems received from the step-by-step reduction of 2d-P4O10 are within 0.05 eV/unit-cell to the lowest energy systems found from the step-by-step oxidation of 2dP4O6 isolated from bulk (P21/c) As2O3 structure (see Supplementary Information).
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O-poor 2d-PxOy compounds were previously studied using surface17 and planar18 models. Applying the screening protocol to blue and black phosphorene, we find that O-poor systems proposed in the previous studies are metastable. For instance, reported 2d-P4O1 and 2d-P4O2 can be considered as black phosphorene modified by O adsorption. We manage to reproduce these structures using our screening protocol applied to black phosphorene. Here, the computed binding energies for planar 2d-P4O1 and 2d-P4O2 are -2.01 and -4.41 eV/unit cell, respectively. However, aside from black phosphorene, experimental stabilization of blue phosphorene was recently reported.28 Taking into account that the cohesive energy per atom for blue phosphorene is only a few meV higher than for black phosphorene,44 the oxidation may result in stabilization of blue phosphorene-like polymorphs. Indeed, O interaction with blue phosphorene results in the most stable 2d-P4O1 and 2d-P4O2 with the binding energies of 2.42 and -4.98 eV/unit-cell (see Fig. 2a), respectively. In these structures, O adsorption leads to the formation of 1d building blocks weakly bonded in the 2d material. For the 2d-P4O2 system, the interaction energy between 1d building blocks computed as the difference in binding energies of the 2d-P4O2 and 1d-P4O2 systems is -0.25 eV/unit-cell, whereas for 1dP4O1 it is only -0.02 eV/unit-cell. This implies that various 2d-P4O1 structures can be formed by the observed 1d building blocks. The difference of P-O interaction for blue and black phosphorene is a very interesting observation and may give ideas on how to synthesize blue phosphorene-like systems. However, a more detail study is needed. To predict long-term behavior of each 2d-PxOy system found above, we carry out BOMD simulations with a canonical ensemble using two different types of temperature protocols (see Fig. 2b). For the first type, we perform a 20-ps annealing at 500 or 800 K. For each simulation, one structure is taken every 5 ps to analyze its energetics further. The second type involves 20-40 ps annealing at 500 or 800 K followed by a quenching to 1 K during 20 ps. Here, only the systems obtained after the quenching are used in the stability analysis. It is
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important to note that the simulations involving the 40-ps annealing are carried out only for the systems having the tendency to reconstruct. For both types of the temperature protocols, BOMD simulations do not result in further stabilization of O-poor (2d-P4O1 and 2d-P4O2) and O-rich (2d-P4O6, 2d-P4O7, 2d-P4O8, 2d-P4O9, and 2d-P4O10) structures. In fact, for O-rich structures, the P-O bonds are strong. As an illustration, the difference in binding energies for 2d-P4O9 and 2d-P4O10 is 2.68 eV. At low O concentration, P-P bonds play a significant role in the material’s stability. However, 2d-P4O3, 2d-P4O4, and 2d-P4O5 reconstruct during BOMD simulations and indeed can be considered as amorphous (see Supplementary Information). The typical energy profiles for 2d-P4O4 and 2d-P4O10 are shown in Figs. 2с,d. Here, the potential energy of 2d-P4O10 remains roughly constant during the BOMD simulation. In contrast to that, lowering of the potential energy due to clearly defined structural transformations is observed for 2d-P4O4. Moreover, the binding energies for amorphous 2d-P4O3, 2d-P4O4, and 2d-P4O5 are lower than for those found from the screening process. It can be speculated that, since PO4 tetrahedra play a significant role in the stability of O-rich 2d-PxOy, similar to known oxides with tetrahedral building blocks,45, 46 it might be possible to realize a variety of amorphous and crystalline structures even for high O concentrations by rearranging the PO4 tetrahedral network. We also carry out BOMD simulations for previously reported 2d-PxOy systems. As an example, the energy profiles for the planar 2d-P4O2 and 2d-P4O4 surface forms at 500 K are shown in Figs. 3a,b. For planar 2d-P4O2, the potential energy remains constant during the simulation (see Fig. 3a). This indicates that despite existing a lower energy structure, the equilibrium cannot be reached due to potentially slow kinetics. In contrast, the surface form of 2d-P4O4 can undergo drastic transformations even at the picosecond scale, resulting in lowering of the potential energy (see Fig. 3b). Since the system has a strong tendency to reconstruct in a more stable amorphous 2d-P4O4 structure, under normal conditions, the surface model gives
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limited information on P-O interaction and its effect on phosphorene properties. For planar 2dPxOy reported by Ziletti et al.,18 we also find that most systems from BOMD simulations have lower binding energies than the previously reported structures. However, it should be noted that the change in binding energies is much smaller there, and the resulted systems are not stable with respect to the lowest energy polymorphs found in this work. We find 0d-PxOy with the energetics close to that for 2d-PxOy (see Figs. 4a,b). Here, 0d-P4O10 is the lowest binding energy 0d system and can be considered as 4 PO4 tetrahedra combined into a pyramid-like structure. This is also an isolated building block of bulk (R3c) P4O10 (see Fig. 1c).25 The energy difference between O-rich 0d-PxOy and 2d-PxOy is as low as 0.004 eV/atom, which is much smaller compared to that between fullerene and graphene (0.370.44 eV/atom).47, 48 Because of this, it is highly likely that 0d-PxOy can be synthesized in the future. Similar to the 2d-PxOy materials, 0d-P4O6, 0d-P4O7, 0d-P4O8, and 0d-P4O9 are just minor modifications of 0d-P4O10. The structures can be obtained by removal of the dangling O atoms, indicating that similar to 2d-P4O10, the dangling O atoms form weaker bonds than the bridging O atoms. We are also able to reproduce 0d-P4O6 and 0d-P4O7 isolated directly from bulk P4O626 and P4O7.27 Further reduction of the O concentration increases the energy difference between 0d-PxOy and 2d-PxOy. For instance, the difference in binding energies of 0d-P4O2 and 2d-P4O2 is 1.67 eV, suggesting that it can be difficult to isolate O-poor 0d-PxOy. For both 0d-PxOy and 2d-PxOy, the binding energy decreases (the structure becomes more stable) with the increase in O content, reaching its minimum for 0d-P4O10 and 2d-P4O10 (see Fig. 4a). Further oxidation increases the binding energy implying that it is hard to adsorb more O for both 0d-P4O10 and 2d-P4O10 under normal conditions. The energy cost for O adsorption on 0d-P4O10 and 2d-P4O10 is more than 1.1 eV, and it comes from the need to break two strong bridging O-P bonds forming two weaker dangling O-P bonds. Comparing the energetics of 0d-PxOy, 2d-PxOy, and previously reported 2d-PxOy17, 18 as shown in Fig. 4b
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indicates that the structures found in this work have noticeably lower binding energies. The largest difference of about 3 eV/unit-cell is found for comparison with the surface form of 2dP4O4. This energy difference leads to the fast amorphization demonstrated in Fig. 3b. The planar 2d-PxOy systems reported by Ziletti et al.18 are more stable, and indeed some of them provide understanding of 2d-PxOy properties. However, for some compositions, the difference in binding energy can still reach noticeable 1.3 eV/unit-cell (see Fig. 4b). To understand the effect of oxidation on the electronic properties of phosphorene, we perform a detailed analysis of band-gap energies and densities of states (DOS) for 0d-PxOy and 2d-PxOy. We find that O adsorption induces a significant widening of the energy gap (see Figs. 5a,b and Fig. S3). As an example, the band-gap energy for 0d-P4O10 is 7.88 eV (5.98 eV for PBE), while for black phosphorene it is 1.60 eV (0.91 eV for PBE). Due to the existence of 0d, planar-, tubular-, and amorphous-like 2d structures, the overall dependence of electronic properties on the O concentration is very complicated. In particular, it was reported before that 1d-tubular structures do not have a monotonic dependence of the band-gap energy.18 Moreover, for 2d-P4O1, due to the different arrangement of weakly bonded 1d-P4O1, a variation of PBE band-gap energies within about 0.5 eV is observed. For other compositions, minor structural variations resulting in close energy systems can also induce a noticeable change in electronic properties. For instance, for two 2d-P4O6 systems isolated from bulk (P21/c) As2Se3 and As2O3 structures, the difference in binding energy is only about 0.02 eV/unit-cell, while the difference in computed PBE band-gap energy is 0.28 eV. Nevertheless, we still find a near-linear behavior of the energy gap on O concentration for the lowest energy systems from the screening calculations for 2d-PxOy (see Figs. 5a,b). For 0d-PxOy, the band-gap energy increases with the O concentration. However, for the most stable 0d-P4O4, a local reduction of the energy gap is observed. This is mainly due to the existence of the highly stable 0d-P4O4 structure with clearly defined PO4 tetrahedra containing a single dangling O atom, while the lowest energy
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configurations of 0d-P4O3 and 0d-P4O5 are limited to the bridging O-P bonding (see Supplementary Information). At low O concentration, P atoms have a significant contribution to both the valenceband maximum (VBM) and conduction-band minimum (CBM) as shown in Fig. 5c. For Orich systems, O states dominate at the VBM. For all structures except 2d-P4O1 and 2d-P4O2, P atoms with a smaller number of P-O bonds (O-poor region) have a larger contribution to the VBM than P atoms from O-rich regions. This is well illustrated for the most stable 2d-P4O9 (Figs. 2a and 5d). Because of this, an accurate description of O-poor and O-rich regions is critical. Since the surface model for 2d-PxOy is limited only to the dangling O-P bonds, it cannot provide a complete understanding of 2d-PxOy properties. For instance, the HSE band-gap energy for the surface form of 2d-P4O2 is 1.70 eV (0.85 eV for PBE), while it is 3.15 eV (2.21 eV for PBE) for the lowest energy 2d-P4O2. The results for screening calculations (see Figs. 5a,b) are similar to those reported by Ziletti et al.18 who explained the predicted near-linear dependence by the increasingly ionic character of the bonds and the resulting wave-function localization. Here, the computed band-gap energy for the most stable 2d-P4O10 is 7.29 eV (5.39 eV for PBE), while for previously reported planar 2d-P4O10 it is 7.23 eV (5.35 eV for PBE). Despite this, the difference in the energy gaps of the planar and the lowest energy structures for some composition reaches more than 1 eV (see Figs. 5a,b). The difference is even more obvious when amorphous 2d-PxOy systems are taken into account. Nevertheless, the nature of amorphous structures is complicated. In particular, for 2d-P4O3, 2d-P4O4, and 2d-P4O5, the computed band-gap energies from HSE calculations are 2.08, 2.52, and 2.30 eV (1.34, 1.59, and 1.48 eV for PBE), respectively. Detailed analysis of DOS and charge density indicates that the reduction in band-gap energy comes from in-gap states originated from P-rich regions (see Figs. 5e,f). Similar to other amorphous materials with in-gap states, the P-rich regions can be considered as defects, which do not determine the overall electronic properties. However, these
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regions are indeed critical for the understanding the features of experimental absorption spectra16, which cannot be explained based on planar and surface 2d-PxOy models.
Conclusions Using first-principles calculations, we reconsidered the phosphorene oxidation by screening over 6500 possible 0d-PxOy and 2d-PxOy structures and BOMD simulations. We found that previous studies have some limitations in the description of 2d-PxOy due to considering metastable structures. P-O interaction results in the formation of new systems with binding energies strongly dependent on the O concentrations. At low O concentrations, the energy difference of 0d-PxOy and 2d-PxOy is significant. However, for high O concentrations, the found 0d-PxOy systems are highly stable. We also obtained highly stable amorphous 2dP4O3, 2d-P4O4, and 2d-P4O5 structures with unique properties due to the formation of O-rich and O-poor substructures. P-O interaction induces a significant increase in the band-gap energy from 1.60 eV (0.91 eV for PBE) for black phosphorene to 7.88 and 7.29 eV (5.98 and 5.39 eV for PBE) for 0d-P4O10 and 2d-P4O10, respectively. We believe that the fundamental understanding developed in this work can be used to design new tailor-made PxOy-based systems with tunable electronic properties.
Acknowledgments The authors acknowledge support from the Research Council of Norway (Project: 221469). The majority of this work was performed on the Abel cluster, owned by the University of Oslo and the Norwegian Metacenter for Computational Science (NOTUR), and operated by the Department for Research Computing at USIT, the University of Oslo IT-department. The authors also acknowledge PRACE for awarding access to resource MareNostrum based in
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Spain at BSC-CNS. O.I. Malyi thank Dr. Alexandra Carvalho (National University of Singapore) for useful discussions and providing original structures reported in their works.
Electronic Supplementary Information (ESI) available: details on supercell sizes used in BOMD simulations, screening protocol, Monkhorst-Pack grids, electronic properties, and all key structures.
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Figures and Captions
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Figure 1. (a) Schematic illustration of the screening protocol used in this work shown with the example of 0d-P4O6 isolated from the bulk P4O6 with space group P21/m. The reduction and oxidation correspond to a screening of possible vacancy and adsorption sites. Blue and red spheres represent P and O atoms, respectively. Adsorption and vacancy sites considered in this work are shown as green and yellow spheres, respectively. The lowest energy (b) 2d-P4O10 and (c) 0d-P4O10 found in this work. Atoms D and B represent dangling and bridging O, respectively. 17
Figure 2. (a) Schematic illustration of the lowest energy 2d-PxOy structures found in this work from the screening calculations. (b) BOMD temperature protocols used in this work. The inset represents a temperature protocol where every 5 ps one structure is taken to analyze the material’s stability further. Typical energy profile for annealing of (c) 2d-P4O4 at 800 K and (d) 2d-P4O10 at 500 K. For the BOMD simulation of 2d-P4O4, fully relaxed initial and final 2dP4O4 structures are shown in the inset.
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Figure 3. Energy profiles observed from BOMD simulations of (a) planar 2d-P4O2 and (b) surface form of 2d-P4O4 at 500 K. For 2d-P4O2, the inset represents the initial system. For 2dP4O4, structures at the beginning and at the end of BOMD simulation are shown.
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Figure 4. (a) Binding energy as a function of O concentration for the most stable 0d-PxOy and 2d-PxOy systems. (b) Relative energy computed as the difference in binding energies for previously reported 2d-PxOy, 0d-PxOy, and 2d-PxOy structures found from the screening calculations, and the lowest energy systems at corresponding concentrations.
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Figure 5. (a) PBE and (b) HSE band-gap energies computed for the lowest energy 0d-PxOy, 2d-PxOy, and those reported in previous studies. DOS computed using HSE for (c) 2d-P4O2, (d) 2d-P4O9, and (e) amorphous 2d-P4O4. (f) Lowest energy amorphous 2d-P4O5 with charge density at valence-band maximum (yellow region) and conduction-band minimum (blue region).
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