the curves describing the normal electrical polarization of the PO configurations in terms of applied strain are linear. With respect to pure phosphorene, the piezoelectric stress parameters increase under 50% oxidation while the piezoelectric strain coefficients d11 are three times lower than 2D BP [80].
When axial deformation is implemented, the electronic features of the POs become modulated. The band gap of dangling and bridge structures increases with low tensile strain, then it reduces to achieve a metallic state for large deformations. Besides, both groups of POs can maintain the semi-conductor behavior along the armchair direction for a strain ranging from 20% to 40% [81]. One can deduce that the adjustment of the phosphorene oxides features makes this class of materials potential candidates for advanced devices.
1.3.3 Surface Oxidation on Phosphorene
In contrast to the functionals H, F, and −OH which work like scissors by breaking down phosphorene into nanoribbons [82], a complete oxidation maintains the initial phosphorene configuration and shifts the lattice constants without breaking the Phosphorous bonds connecting the two P-half-layers, namely, the upper and lower ones [30].
1.3.3.1 Optoelectronic Features
At high concentration, oxidation leads to new derivatives of oxided phosphorene. As shown in Figure 1.14, up to fully oxidation, the interatomic P-P lengths increase to 2.32 and 2.37 Å while the direct gap located at point Γ reduces with respect to pure phosphorene. VBM is characterized by py orbitals of P- and O-atoms, while the P-s and O-pz orbitals dominate the conduction band minimum (CBM) [30]. Both interstitial and dangling oxygen form no states in the middle of the gap, while the horizontal and diagonal oxygen introduce levels in the gap, which deals with a deep acceptor state at near the conduction band. Furthermore, the planar phosphorene oxides exhibit a monotonic increase to reach a maximum value with a deoxidation degree of 0.25, then start to decrease to attempt the value of 0.6 eV in a fully oxidized PO structure. For the tubular structure, the band gaps take the values from 0.4 (1.62) to 5.56 (7.78) eV at PBE (HSE level) [32]. Interestingly, the GW corrected band gap shows that the increasing oxygen coverage leads to an increase in the band energy from 4 eV to 10 eV, indicating that the VBM and CBM part become more localized [83].
Figure 1.14 (a) Top and (b) side views of phosphorene oxides PO.
The application of electric field reduces the gap energy of PO to a minimum of about 0.4 eV for a field E = 1.5 V/Å. The band gap fluctuates also from direct found for 100% to indirect for O-concentrations of 12.5%, 25%, and 50 %. Also, the work function in phosphorene increases linearly with the increased of the oxidation degree. The calculated values for PO0.125, PO0.25, and PO0.5, are 4.9, 5.2, and 5.8, respectively, compared to PO that has 7.2 eV [30].
Under ambient conditions, phosphorene oxide is a stable material that did not exhibit any negative frequencies in its phonon dispersion curve [30]. Moreover, the simulation indicates that oxided structure is still robust and intact at low temperature, confirming its stability, while the material cut for large temperature values [84]. Unlike pure phosphorene, the phonon dispersion of PO exhibits three main regions as displayed in Figure 1.15b, namely, (i) the acoustic region, (ii) the middle region, and (iii) the high frequency range. Moreover, in contrast to the electron effective mass, the effective masses of holes are anisotrope [30].
Besides the band structure modification, the oxidation tunes also the optical features of phosphorene. In PO systems, the absorption spectrum reveals that the 1st absorption peak is located at 2.7 eV, in P4O2, it is also found that both phosphorus and oxygen atoms contribute in the transition and extend the wavefunction along the AC-axis (see Figure 1.16a). Further, in the P4O10 system, the absorption peak moves to high energy with a peak located at 7.0 eV. The wavefunction only localized on oxygen atoms adsorbed at the surface (see Figure 1.16b). This changes the binding energy Eb from −1.4 eV to reach −3.0 eV for P4O2 and P4O10. The electronic and optical band gap as well as the binding energy of P4O2 and P4O10 are very close to those of benzene [83].
Figure 1.15 Phosphorene oxide (a) band structure and density of states, (b) phonon dispersion curves and density of states.
Figure 1.16 Absorption spectrum and exciton wavefunction for the first transition peak for (a) P4O2 and (b) P4O10 structures.
1.3.3.2 Stress vs Strain
When the surface is oxidized, the electrons get transferred forming ions in phosphorene which influences mainly the mechanical response of the material describe by its stiffness against externally applied strains. It results that the oxidation changes the elastic moduli leading to a higher flexible structure [31]. This is also the case for reduced concentrations. Indeed, phosphorene with an oxidation degree of 12.5% can resist to a deformation up to 32% and 35% in AC- and ZZ-axes, respectively, which are higher than that corresponding to pure phosphorene [31]. Moreover, with respect to the pure material, the ideal strength in phosphorene oxide is reduced owing to the enhancement of interatomic distance in the oxide lattice [30, 31] in good agreement with the process of hydrogenating single-layer h-BN [85]. Therefore, the oxidation causes a two times reductions in the value of ideal strength [31].
For a tensile strain varying from −8% to 8%, the band gap in PO increases under compressive strain and decreases with tensile strain, ranging from 0.85 to 0.1 eV for the strain values of [30]. The variation of the gap width results only from the CBM since the VBM is not influenced by the elastic strength. For small tensile strain interval of [−0.006, 0.006], the linear change of polarizations of PO reveals two values of stress piezoelectric responses, namely, e11= 20.13 10−10C/m and e31= 4.06 10−10C/m that correspond to the piezoelectric coefficients given in [86]. All these results indicate that phosphorene oxide are excellent candidates for potential applications requiring the conversion of energy [86].
1.3.3.3 Thermal Conductivity
Compared with pure phosphorene (P), phosphorene oxide (PO) exhibits a much lower thermal conductivity over the whole temperature range [87]. Indeed, the values of the thermal conductivityfor both P and PO along the armchair axis, namely
