Superbound Excitons in 2D Phosphorene Oxides - The Journal of

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Superbound Excitons in 2D Phosphorene Oxides Yihua Lu, and Xi Zhu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b09683 • Publication Date (Web): 06 Dec 2018 Downloaded from http://pubs.acs.org on December 11, 2018

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The Journal of Physical Chemistry

Superbound Excitons in 2D Phosphorene Oxides Yihua Lu and Xi Zhu* School of Science and Engineering, the Chinese University of Hong Kong Shenzhen, Shenzhen, Guangdong, 518172, China Email: [email protected] Abstract The optical excitations in layered phosphorene oxides are studied via ab initio calculation together with GW approximation for the self-energy and solving the Bethe–Salpeter equation (BSE) for the excitations. It is found that the electronic structure of phosphorene oxides closely depend on the oxygen concentration, for the high oxygen coverage structure P4O10, it shows a strong localized molecular like electronic structure with exciton binding (Eb) energy up to 3.0 eV, which is several times larger than the ordinary Eb value in various low dimensional materials. This study may provide an alternative way to design functional layered materials with large exciton binding energy by controlling the oxidation level in phosphorene oxides. Introduction Since the discovery of graphene1, enormous researches have been focused on the two-dimensional (2D) due to their novel electrical optical or photoelectrical properties2. It is well known that the optical spectra of two-dimensional (2D) materials are mainly dominated by excitonic effects. The high stability of electrons in such materials is both due to the confinement of electron and hole and the reduced screening of the Coulomb interaction.3 A prime example is exciton in transition metal dichalcogenides, which possess exciton binding energies as high as 0.7 eV in WS2 and 1.1 eV in MoS2,4 normally reduced to about 0.30.4 eV for sulfides and 0.6 eV for selenides on dielectric substrates,

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which are much larger than their

corresponding bulk structures(∼ 0.1 eV).6 In free-standing phosphorene, despite the relatively smaller band gap, the exciton binding energy has also been reported to be 0.8 eV7. However, little is known about the excitonic properties of most layered oxides. Some bulk transparent oxides have exciton binding energies that are high enough to stabilize excitons up to room temperature (eg. 50 meV for ZnO8, 130 meV for TiO29). Similarly, we expect to find excitons in 2D oxides that can stably bound. Phosphorene oxide, as a kind of layered 2D oxide, attract much attention for their potential application in the field of optics and optoelectronics. This kind of material contains at least four stable allotropes, three of them are layered, with the composition of P2O5.10 It can be formed spontaneously as a product of the phosphorene oxidation in the absence of water11. Its production can also be accelerated by focused laser 1

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beam treatment, a technique allowing the control of the fraction of oxygen.12 Phosphorene oxide and its derivate can be viewed as the 2D analogue of phosphate glasses, with the glass forming substrate P2O5, which are commonly used as transparent windows in the ultraviolet range13. 2D phosphorene oxide and its sub-oxides possess bandgaps varying from 2 eV to about 10 eV13. Therefore, it may also be used as a transparent insulating layer in phosphorene-based optoelectronics. In this letter, the optical spectra of phosphorene oxide and its sub-oxides are systematically analyzed, it is notable for the high bandgap and tightly bound excitons. Computation Methods The oxide derived directly from phoshorene has been modeled by assuming oxygen adsorption at the phosphorus lone pairs and the P-P bond centers, which is consistent with XPS measurements in experiment11. Figure 1 shows the most stable configurations found for P4On with n ≤ 10.14 For the suboxides (n < 10), there are multiple configurations with similar energies, and those are expected to coexist in the real materials. For the efficiency of optical spectra simulation, only configurations with the lowest energy are considered in our study.

Figure. 1. Structures of phosphorene oxide and sub-oxides (P4On).The pink represents the phosphorous , the red and blue represent the oxygen with two fold and one fold bonding types respectively. Firstly, the ground state wavefunctions are determined by using the Perdew−Burke−Ernzerhof (PBE)

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exchange-correlation functional in Abinit code. 16 the scalar-relativistic norm-conserving pseudopotentials are used with 60 Ry kinetic energy cutoff. The atoms and lattices are fully relaxed until the force convergence within 0.001 eV/Å and the stress convergence within 0.1 GPa respectively. To mimic the quasi 2D layer structures, we apply a 20 Å vacuum slab in the non-periodic direction. A 0.02 Å ―1 K-point spacing is used to sample the Brillouin zone. The G0W0 approximation is used to treat the self-energy operator. The

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quasi-particle corrections is used to correct the underestimated band gaps in PBE calculation. The plasmonpole approximation17 is applied to deal with the screening effect. The Bethe−Salpeter equation (BSE) approach is used to resolve the electron−hole interactions for the many body Green function18.The BSE can be defined as below,

(𝐸𝑐𝑘 ― 𝐸𝑣𝑘)𝐴𝑆𝑣𝑐𝑘 + ∑𝑘′𝑣′𝑐′⟨𝑣𝑐𝑘│𝐾𝑒ℎ│𝑣′𝑐′𝑘′⟩𝐴𝑆𝑣𝑐𝑘 = Ω𝑆𝐴𝑆𝑣𝑐𝑘

(1)

where 𝐴𝑆𝑣𝑐𝑘 is the amplitude of exciton, 𝐾𝑒ℎ is the electron–hole interaction kernel, |𝑐𝑘〉 and |𝑣𝑘〉 are the quasi-particle states (electron and hole) respectively. Ω𝑆 is the excitation energy, 𝐸𝑐𝑘 and 𝐸𝑣𝑘 are the quasi particle energies. A box-shape truncated Coulomb interaction is applied to the simulation cell to avoid problematic image effects caused by proximate supercells. All the G0W0 and BSE calculations are performed with YAMBO code.19 Results and discussion The optimal structures of 2D layered Phosphorene and its corresponding oxides are shown in figure 1, clearly, oxygen atoms in P4On are of two different bonding types, namely type I and II. The type I oxygen atom connects two nearby phosphorus atoms by two single bonds, with bond length 1.67 Å, whereas type II is the oxygen atom forms a coordinate bond with one phosphorus atom, with bond length 1.48 Å. The ratio of type I and II oxygen changes with increasing oxygen coverage. In P4O2, there is only one type I and one type II oxygen atoms, the type I oxygen atoms inserted and connected every four phosphorus atoms, the delocalized P-P bond network is broken after oxidization. There are 6 type I and 4 type II oxygen atoms in P4O10. Moreover, the nearby phosphorus atoms are separated by the type I oxygen atoms, there is no PP bonds any more. The electronic structure of P4On is closely dependent on the number of type I and type II oxygen atoms either. Figure 2 (a), (b) shows the G0W0 corrected electronic band structures and projected density of states (PDOS) of P4O2 and P4O10 respectively.ForP4O2, it has indirect band gap around 4 eV, The valence band maximal (VBM) is mainly contributed by type II oxygen and phosphorus’s p orbital For P4O10, as shown in Figure 2 (b), it has direct band gap 5.36 eV by PBE and 10.0 eV after G0W0 correction, this band gap value is very close to molecular benzene 20, indicating a very localized electronic states, as shown the flat bands in the VBM part of band structure, and this localized band is from the type II oxygen’ s p orbital as plot in the DOS. In order to show the electronic structure of P4O2 and P4O10 better, figure 2(c), (d) present the real space wavefunction distribution of the VBM and CBM of the two systems, Similar trends can be observed here. The major difference between P4O2 and P4O10 is there is no P-P bonds in P4O10 at all, all the bridge site and edge site are occupied by oxygen atoms. Similar to the graphene epoxy (GE) structures,21 from P4O2 to P4O10, The influence of oxygen atoms on the VBM and CBM become more pronounced with the increasing oxygen coverage, the character of the VBM part changes can be observed in Figure 2(c) and (d) . In P4O2, it is a mixture of type II oxygen and the phosphorus’ p orbitals, meanwhile 3



there is still small type I oxygen’s p part involved. When it comes to P4O10, the type II oxygen dominant in the VBM, the electronic structure becomes more localized and molecular like, which significantly enlarge the band gap.

Figure 2: (a) and (b) show the G0W0 corrected electronic band structures and projected density of states (DOS) of the P4O2 and P4O10 structures, (c) and (d) shows the valence band maximal (VBM) and conduction band minimal (CBM) of the P4O2 and P4O10 structures respectively. Next, we turn to the optical properties. Figure 3 summarized the G0W0 corrected band gap 𝐸𝐺0𝑊0, the 1st BSE transition energy 𝐸𝐵𝑆𝐸 and the exciton binding energy 𝐸𝑏 (defined as 𝐸𝑏 = 𝐸𝐺0𝑊0-𝐸𝐵𝑆𝐸).From P4O2 to P4O10, with the increasing oxygen coverage , 𝐸𝐺0𝑊0 increase from 4 eV to 10 eV, indicating the VBM and CBM part become more localized and implying an characteristic change as discussed in last section. The oxygen atomic size is even smaller than that in benzene molecule. This kind of character changing reflected in the 𝐸𝑏 as well, the value of 𝐸𝑏 increases from 1.4 eV to 3.0 eV, this 3.0 eV exciton binding energy is extreme rare in ordinary semiconductors and low dimensional materials, for the quasi 1D single wall carbon nanotubes (SWCNTs), 𝐸𝑏 is below 1.0 eV 22, for the quasi 1D armchair graphene nanoribbon (AGNRs), 4


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except some extra narrow cases, 𝐸𝑏 is usually below 1.5 eV23,both the SWCNTs and AGNRs have nonlocalized exciton wavefunction, and the exciton types are non-Frenkel 24 .For the quasi 2D materials, the 𝐸𝑏 in the mono-layer MoS2 , monolayer black phosphorus mono-layer boron nitride is about 1.1 eV4a, 0.86 eV7c ,and 2.1 eV 25 respectively. Due to the truncated dimension, the screening effect outside the layer is extremely weak, which boosted the Frenkel type exciton in quasi 2D. Another quasi 2 D material GE, with the increasing oxygen coverage, the distribution of VBM shifting from the carbon domain to the oxygen domain21 and exciton type can change from Frenkel type to charge-transfer type.

Figure 3: G0W0 energy gap, (𝐸𝐺0𝑊0), the 1st BSE transition energy (𝐸𝐵𝑆𝐸 1𝑠𝑡 ) and the exciton binding energy (𝐸𝑏) for the P4O2, P4O4, P4O6, P4O8, P4O10 and the Benzene structures. The band structure and transition spectrums of each structure are shown in supporting information S1. For Benzene, 𝐸𝐵𝑆𝐸 1𝑠𝑡 is chosen for the first bright exciton at 7.2 eV. 20b In PO system, as discussed above, the VBM becomes more localized in the type II oxygen’s p orbital in P4O10. In GE system, the excitation character changes from Frenkel type to Charge-Transfer type after the VBM domain changes, which lower the 𝐸𝑏 value as well. however, the VBMs only become more localized around the oxygen atom in PO system, there is no domain changing, and the excitation type still follows the confinement picture as in SWCNTs 22 and AGNRs. 23 Figure 4 (a) plots the absorption spectrum with the exciton wavefunction of the 1st absorption peak at 2.7 eV, in P4O2, it is observed that both phosphorus and oxygen are involved in the transition and the wavefunction extends about 1.5 nm in X direction. Figure 4 (b) plots the absorption spectrum with the exciton wavefunction of the 1st absorption peak at 7.0 eV for P4O10, we can see the wavefunction only localized on the type II oxygen’s p orbitals, and there is no leakage nor inter-domain penetration for the exciton wavefunction as in GE, this strong localization induced by the oxygen coverage, pushes the 𝐸𝑏 from 1.4 eV to 3.0 eV from P4O2 to P4O10, both the band gap and binding energy are very close to benzene, as benchmarked in Figure 3, which confirmed the molecule like electronic

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structure from the optical property. Meanwhile, from the effective screening effect calculation shown in supporting information S2, the dielectric constant of Y direction is smaller than that in X direction, indicating a strong screening strength in X direction and shorter size in wavefunction distribution, as illustrated in the exciton wavefunction plot in Figure 4 (a) and (b). The decrease of the screening effect origins from about 6 eV band gap rises from P4O2 to P4O10 as shown by 𝐸𝐺0𝑊0 in Figure 3.

Figure 4: Absorption spectrum obtained by BSE for (a) P4O2 and (b) P4O10 structures, the exciton wavefunction for the first transition peak in (a) and (b) is shown below respectively, with iso-value 0.015. Conclusion To conclude, in this work we perfume first principle ab initio calculation for the electronic and optical properties of phosphorene oxides P4On, we found that the oxygen coverage affect the electronic and optoelectronic properties. In summary，the electronic and optical properties of phosphorene oxides P4On are studied via ab initio calculation. The results indicate that electronic and optoelectronic properties of this system is controlled by the oxygen coverage. Supplementary Material See supplementary materials for the G0W0 corrected band structure and BSE absorption spectrum for the PO structures, and the effective dielectric constant calculations.

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Acknowledgment This work is supported by Shenzhen Fundamental Research foundation (JCYJ20170818103918295) China Nature Science Foundation (Grant.No.21805234) and President’s funds from CUHK-Shenzhen (PF00728).

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Superbound Excitons in 2D Phosphorene Oxides - The Journal of

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