Mechanistic insights in phosphorene degradation

The structural and chemical degradations of phosphorene severely limit its practical applications despite the enormous promise. In this regard, we investigate a cohort of microscopic kinetic mechanisms and develop a degradation phase diagram using first-principles calculations. At 400 K, the degradation and the competing self-annealing proceeds through the merger and annihilation of vacancies, respectively, which are triggered via itinerant vacancies and adatoms. A further increase in temperature beyond 650 K, the structural degradation results through the emission of the undercoordinated atoms from the defect and the concurrent pairwise sublimation. The role of interlayer vacancy diffusion is discarded in the context of structural degradation. The chemical degradation proceeds through the dissociation of an oxygen molecule that is activated at the room temperature on the pristine surface or spontaneous at the single-vacancy site. The present results are in agreement with the few available experimental conjectures and will motivate further efforts.

Figure 1

The top and side views of the single-vacancy in phosphorene in its two possible configurations (a) $\mathrm{SV}\left(5\right|9)$ and (b) $\mathrm{SV}\left(55\right|66)$. Atoms in the two half-layers are coloured in blue and black. The polygons in the vacancy are shaded with different colours. (c) Formation energies $E^f$ of the $\mathrm{SV}\left(5\right|9)$ and $\mathrm{SV}\left(55\right|66)$ defects at the apical layer with varied layer thickness. The $E^f$ for the subsurface vacancy (blue circles) and bulk are also shown. The formation energy decreases with increasing layer thickness. While in single layer, the $\mathrm{SV}\left(5\right|9)$ is thermodynamically favourable over the $\mathrm{SV}\left(55\right|66)$ configuration by 350 meV, and the difference in energy between the defects also decreases with the thickness to 45 meV for the bulk black phosphorus. Note that the vacancy formation is much easier in the few-layer phosphorene owing to the much lower $E^f$ compared to graphene and other monoelemental bulk semiconductors [33, 55, 56].

Figure 2

The intralayer $\mathrm{SV}\left(5\right|9)$ migration mechanisms along the (a) armchair and (b) zigzag crystallographic directions. The respective initial state (IS), transition state (TS) and final state (FS) are shown. The TS configurations are markedly different from each other, which leads to distinct activation barriers along the armchair and zigzag directions (Table 1). (c) The interlayer $\mathrm{SV}\left(5\right|9)$ migration is studied by considering two different pathways, where either of the nearest and next-nearest-neighbor atoms from the undefected half-layer jumps to the defected layer. The migrating atoms are encircled in red color, and the grey atoms belong to the defected layer. (d) The side view showing the interlayer $\mathrm{P}–\mathrm{P}$ bonding for the corresponding transition state.

Figure 3

Activation barriers for the in-plane diffusion of $\mathrm{SV}\left(5\right|9)$ vacancy at the surface and subsurface. The anisotropic crystal structure of phosphorene results in two distinct migration pathways along the armchair and zigzag directions with different activation barriers. Calculated barriers for the surface vacancy depend on the layer thickness. Further, the barriers are much smaller for the subsurface migration compared to the vacancy at the surface.

Figure 4

(a) The energy profiles for the mechanisms leading to the larger defect formation, $\mathrm{SV}\left(5\right|9)+\mathrm{SV}(9\left|5\right)\to \mathrm{DV}\left(5\right|8\left|5\right)$ and $\mathrm{SV}\left(5\right|9)\to \mathrm{DV}\left(5\right|8\left|5\right)+{\mathrm{P}}_{\mathrm{A}}$. Owing to a lower 0.68 eV barrier, $\mathrm{DV}\left(5\right|8\left|5\right)$ is generated via coalescence of itinerant $\mathrm{SV}\left(5\right|9)$ vacancies. While the forward $\mathrm{SV}\left(5\right|9)\to \mathrm{DV}\left(5\right|8\left|5\right)+{\mathrm{P}}_{\mathrm{A}}$ process has a high barrier, note that the reverse self-healing process has a much lower barrier of 0.46 eV. [(b) and (c)] The corresponding initial and final structures. (b) The merger of mono-vacancies into $\mathrm{DV}\left(5\right|8\left|5\right)$ through bond rotation (encircled in red). (c) The structures for the $\mathrm{SV}\left(5\right|9)\to \mathrm{DV}\left(5\right|8\left|5\right)+{\mathrm{P}}_{\mathrm{A}}$ mechanism.

Figure 5

Self-healing mechanisms of a vacancy via the recombination with P interstitial ${\mathrm{P}}_{\mathrm{I}}$ (encircled by red color), which are rate-limited by 0.69 eV activation barrier (Table 1). Frenkel defects (a) $\mathrm{SV}\left(55\right|66)+{\mathrm{P}}_{\mathrm{I}}$ and (b) $\mathrm{SV}\left(5\right|9)+{\mathrm{P}}_{\mathrm{I}}$ recombine to form pristine lattice in (c). The numbers in blue color indicate the corresponding activation barrier. The interstitial ${\mathrm{P}}_{\mathrm{I}}$ in the Frenkel defects preferentially binds along the zigzag direction, and these complexes are thermodynamically stable at room temperature. Meanwhile, the $\mathrm{DV}\left(5\right|8\left|5\right)$ is partially healed first to an $\mathrm{SV}\left(5\right|9)$ defect by absorbing an itinerant ${\mathrm{P}}_{\mathrm{A}}$ adatom, which requires 0.46 eV energy (Table 1 and Fig. 4).

Figure 6

The chemical degradation of phosphorene through oxidation. The top and side views for ${\mathrm{O}}_2$ dissociation are shown (a) on the pristine surface; and at the (b) $\mathrm{SV}\left(5\right|9)$ and (c) $\mathrm{DV}\left(5\right|8\left|5\right)$ defect sites. While the entire physisorption $\to$ chemisorption $\to$ dissociation process is activated on the pristine surface with 0.48 eV rate-limiting barrier, the same is spontaneous at the $\mathrm{SV}\left(5\right|9)$ vacancy. We did not find any chemisorbed configuration at the $\mathrm{DV}\left(5\right|8\left|5\right)$ defect, and the ${\mathrm{O}}_2$ dissociation directly proceeds from the physisorbed structure with 0.56-eV barrier. For all cases, the dissociated O atoms bind strongly with the phosphorene, and would thus be impossible to remove from the lattice. The numbers in blue color indicate the corresponding activation barrier.

Figure 7

Arrhenius rate $\mathrm{\Gamma }$ calculated for the various microscopic mechanisms leading to oxidation, annealing, degradation and sublimation. A typical prefactor of ${10}^{13}{\mathrm{s}}^{-1}$ is assumed. The $\mathrm{SV}\left(5\right|9)$ and ${\mathrm{P}}_{\mathrm{A}}$ are highly itinerant even below 100 K, which triggers the competing self-healing of vacancy and itinerant $\mathrm{SV}\left(5\right|9)$ mergers above 450 K. The degradation is accelerated above 650 K through the emission and sublimation of ${\mathrm{P}}_{\mathrm{A}}$. The chemical degradation through oxidation of pristine SLP takes place above 250 K. The overall phase diagram is in excellent agreement with the recent experimental observations [28, 34, 35].