The effects of vacancy and heteroatoms-doping on the stability, electronic and magnetic properties of blue phosphorene

At the first step, we have applied the first principles to calculate the electronic structure of the pristine blue phosphorene. As shown in figure 1, the P atoms are placed in a plane-hexagon lattice, where there are two P atoms at 1 × 1 supercell. Figure 1(a) shows the optimized structure of 7 × 7 × 1 supercell blue phosphorene, including 1 × 1 supercell is surrounded by a purple diamond shape, the relaxed lattice constant, buckling parameters and the length of P−P bond of the 1 × 1 units cell is 3.278 Å, 1.234 Å and 2.261 Å, respectively, the obtained simulation results were in very good accordance with the experimental results [43]. The band structures of pristine blue phosphorene spin-up and spin-down is presented in figures 2(a) and (c), and it is obviously that the lowest point of the conduction band and the highest point of the valence band correspond to different K points. As shown in figure 2, the consistency of the spin-up and spin-down trajectories is found to be non-magnetic. In conclusion, it is shown that blue phosphorene is a non-magnetic semiconductor with indirect bandgap, and the band gap is 2.03 eV. These characteristics have limited the study of blue phosphorene in some areas such as optoelectronics, nano-electronics and spintronic, so vacancy defects and heteroatom-doping have been introduced to improve their capabilities in our study.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

It is very important to investigate defect states for the developments and applications of semiconductor materials. In order to imitate the vacancy defect of blue phosphorene, we consider the four models that includes single vacancy (SV), two types of double vacancy (DV1 and DV2), six vacancy (SIXV) case. The optimized structure of the defect is shown as figures 2(b)–(c) and (e)–(f), which is different from previous defect states. In our works, single vacancy is formed by removing one P atom and the SV defect is found to be an unstable structure after removing one P atom, which is subject to Jahn–Teller distortion, P1 and P2 atoms form a chemical bond on the blue phosphorene surface with a bond length of 2.58 Å, so one five-atom ring and one nine-atom ring are formed at the defect site (see figure 1(b)). Meanwhile, two types of defects are considered: DV1 by deleting two adjacent P atoms while the DV2 is formed by missing the two atoms on opposite sides of the hexagon. DV1 defects form two five-atom rings and one eight-atom ring, all dangling bonds are saturated by forming the 2.52 Å P1–P2 bond (see figure 1(c)). The remaining four atoms of DV2 form a quadrilateral after optimization, the bond length of P1-P2, P2-P3 is 2.32 Å, 2.35 Å, respectively, so DV2 possess two nine-atom rings and one four-atom ring (see figure 1(e)). The SIXV by removing the six atoms that make up the hexagon in the 7 × 7 blue phosphorene (see figure 1(f)). The charge density (figure S2 and table S2) shows that P-P bonds of SV, DV1 have weakly chemical bond. It can be found that the initial defect is very unstable and produces a new stable structure after optimization.

To test the stability of the vacancy defects with blue phosphorene, we calculated the formation and binding energy. The formation energy ${E}_{f},$ and the binding energy ${E}_{b},$ were defined as [44]:

$$\begin{eqnarray*}&&{E}_{f}=\displaystyle \frac{1}{m}\left({E}_{bluep}-{E}_{defect}\right)-{E}_{p}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{E}_{b}=\displaystyle \frac{1}{n}\left({E}_{defect}-n\times {E}_{p}\right),\end{eqnarray*}$$

where ${E}_{bluep},$ ${E}_{defect}$ and ${E}_{p}$ are the total energy of pristine blue phosphorene, the energy of SV, DV1, DV2 and SIXV, the energy of one P atom, respectively. The $m$ and $n$ are the number of defect atoms and the P atom number of the blue phosphorene supercell with SV, DV1, DV2 and SIXV as shown in table 1 and figure S1. The greater the absolute value of the binding and formation energies of the defect-blue phosphorene, the more stable the structure is. Based on the equation, the calculated formation energy of blue phosphorene with SV, DV1, DV2 and SIXV are −5.68 eV, −4.63 eV, −5.47 eV and −4.29 eV, respectively. The results indicate that the blue phosphorene with defects is a stable structure.

Table 1. Structural parameters of the optimized blue phosphorene including band gaps, magnetic moment M (${\mu }_{B}$) and binding energy (${E}_{b}$).

Defect	Band gap (eV) Up Down		M (${\mu }_{B}$)	${E}_{b}({\rm{eV}})$	Properties
Perfect	2.026 62		0	−3.331	Indirect
SV-(5∣9)	0.9197	0.9283	0.999 992	−3.307	—
DV-(5∣8∣5)	1.2575		0	−3.304	Indirect
DV-(9∣4∣9)	0.5066		0	−3.287	Indirect
SIXV-(18)	1.677	1.024	5.999 974	−3.268	—

Next, in order to discuss the electronic characteristics of blue phosphorene with SV, DV1, DV2 and SIXV defects, we investigate DOS for SV, DV1, DV2 and SIXV systems. Note that in figure 3, red and blue represent spin-up and spin-down DOS, respectively. From figure 3, it can be found that the spin-up are consistent with spin-down band structures in DV1- and DV2- blue phosphorene, and the spin DOS are symmetrical, which indicates that blue phosphorene with DV1 and DV2 possess nonmagnetic ground states. Whereas the structures of SV and SIXV are just the opposite, they have different band structure and different DOS for spin-up and spin-down. This indicates that blue phosphorene with SV and SIXV exist magnetic state. According to the table 1, the band gaps are all smaller after introducing the defect, the bandgap of DV2 is only 0.5066 eV. It is easy to find DV1- and DV2-defects blue phosphorene exhibit an indirectly bandgap. However, SV and SIXV produced magnetic moments of about 1 μ_B and 6 μ_B . In order to describe the magnetism of SV and SIXV in more detail, we went on to plot the spin charge density (see figure 4), and it is clear that there is a spin-up charge all around the defect state, considering that it is the dangling bond around the defect that induces the magnetism.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To investigate the electronic structure and magnetism of blue phosphorene with heteroatom doping, we plotted the band structure, spin DOS and magnetic moment of heteroatom doping (Li, Na, Al, Si, Fe, Co, Sn) in blue phosphorene. We named the substitution of one P atom, two P atoms, and six P atoms by heteroatoms in blue phosphorene as P₉₇ATOM₁, P₉₆ATOM₂-1, P₉₆ATOM₂-2 and P₉₂ATOM₆, respectively, and the pattern of the heteroatom substitution is shown in figure S3. In order to clarify the stability of the defects in blue phosphorene, we calculated the formation and binding energy of heteroatom doping in blue phosphorene. The formation energy ${E}_{f},$ and the binding energy ${E}_{b},$ are calculated as follows [44]:

$$\begin{eqnarray*}&&{E}_{f}=\displaystyle \frac{1}{M}\left({E}_{M-defect}-{E}_{defect}\right)-{E}_{M}\end{eqnarray*}$$

where ${E}_{M-bluep},$ ${E}_{defect},$ ${E}_{M}\,$and ${E}_{p}$ are the total energy of heteroatom doping P_97/96/92ATOM_1/2/6- blue phosphorene, defects-blue phosphorene, the energy of doping atom and the energy of one P atom, respectively. The M and N are the number of doping atoms and P atom in the blue phosphorene supercell. The formation energy is shown in figure 5, and it can be found that heteroatoms substitutional doping in the blue phosphorene are able to achieve a stable structure, the larger the binding energy, the more stable the structure is. Si atoms doping in blue phosphorene has the largest formation energy and are the most stable structures, followed by Al and Fe atoms are doping in blue phosphorene.

Zoom In Zoom Out Reset image size

Then we calculate magnetic moments of the heteroatom (Li, Na, Al, Si, Fe, Co, Sn) substitutional doping in blue phosphorene. The numerical results indicate that different atoms can induce different magnetic moments in the blue phosphorene when heteroatom doping in P_97/96/92ATOM_1/2/6-blue phosphorene. The calculated results indicate that Li, Na, Al, Si, Fe, Co and Sn atoms possess magnetic moments of 1 μ_B , 1 μ_B , 1 μ_B , 2 μ_B , 4 μ_B , 3 μ_B and 2 μ_B , respectively.

According to the magnetic moments as shown in table 2, the s-orbitals of Li, Na, Si atoms are strongly hybridized with P atoms in P₉₇ATOM₁-, P₉₆ATOM₂-2-blue phosphorene, the d-orbital of Fe, Co are strongly hybridized with P atoms in P₉₆ATOM₂-1-, P₉₂ATOM₆-blue phosphorene, which determine the magnetic moments of blue phosphorene. For Li, Na, Al- doping in P₉₇ATOM₁- and P₉₆ATOM₂-2 blue phosphorene cases, the calculated magnetic moments are 1.999 712 μ_B , 1.999 816 μ_B , 1.987 73 μ_B , 1.997 385 μ_B , 1.000 001 μ_B and 1.999 986 μ_B , respectively. For Li, Na, and Si atoms doping in P₉₇ATOM₁-blue phosphorene, Li atom has one valence electron, the P atom has five valence electrons and forms a pair of Li–P bonds after Li atom are doping in a blue phosphorene, but the two nearby P atom is not saturated and thus generates magnetic moment. The same reason for generation of magnetic moment with Na atoms. For Si atom, there are four valence electrons, which form three pairs of Si–P bonds, and one valence electron that is not saturated, so the magnetic moment is generated. For Li, Na, Si substitutional doping in P₉₆ATOM₂-2-blue phosphorene, which produces the magnetic moment as same as P₉₇ATOM₁-blue phosphorous. The Li, Na atoms is hybridized with surrounding P atom to generate magnetic moments. After the two Si atoms doping in the P₉₆ATOM₂-2-blue phosphorene, the remaining two valence electrons of Si are not saturated, and the magnetic moment is generated.

For Li, Na, Si doping in P₉₆ATOM₂-1- and P₉₂ATOM₆-cases, the calculated magnetic moments are 0 μ_B . The reason is that Li and Na atoms hybridize with each two Li atoms and two Na atoms doping P₉₆ATOM₂-1-, P₉₂ATOM₆-blue phosphorene, and there is no interaction with the nearby P atom resulting in the Li–Li bond, and the Na–Na bond is saturated. After the substitutional doping of the Si atom, the two valence electrons of Si interact with the two P atoms, and the two remaining valence electrons of Si are paired, thus both Si atoms are saturated with zero magnetic moment. For Li-, Na-doping in P₉₂ATOM₆-blue phosphorene, Li and Na have only one valence electron, and the ring corresponds to exactly six Li/Na atoms make up a pair of Li–P bonds and Na–P bonds with six P atoms, so no magnetic moment is produced. For Si atoms, there are four valence electrons, which combine with the adjacent P atoms to form Si–P bonds. Other two valence electrons of Si hybridize with the neighboring Si atoms, and finally one valence electron remains for each Si atom, constructing three pairs of Si-Si double bonds.

For Al atoms doping in the blue phosphorene, the three valence electrons of P form an Al–P bond with three valence electrons of Al atoms, in other words, the three valence electrons of Al replace the three valence electrons of P to reach saturation and do not produce magnetic moment. Sn atoms are similar with Al substitutional doping in the blue phosphorene. For Fe doping in P₉₇ATOM₁-blue phosphorene, three Fe–P bonds are formed and the remaining three valence electrons are not saturated. For Fe atoms doping in the P₉₆ATOM₂-2-blue phosphorene, two Fe–P and one P–P bonds are formed, and the remaining valence electrons are not saturated. For Fe doping in P₉₂ATOM₆-blue phosphorene, the same reasoning as above, no saturation is reached. For Co substitutional doping in P₉₇ATOM₁-blue phosphorene have no magnetic moment, the reason is that Co-P bond is formed. For Co doping in P₉₆ATOM₂-1-, P₉₆ATOM₂-2-blue phosphorene, no saturation is reached. Therefore, substitutional doping of Li, Na, Si, Fe and Co atoms into the blue phosphorene can be an effective technique to induce magnetism, which expand the applications of blue phosphorene in spintronics fields.

In order to further investigate the magnetic properties in the Li, Na, Si, Fe and Co atoms doping in blue phosphorene, the spin density distribution is shown in figures 6 and 7. In figure 6, Li, Na, and Si atoms are doping in P₉₇ATOM₁- and P₉₆ATOM₂-2-blue phosphorene, resulting in spin polarization. From Li, Na doping in P₉₇ATOM₁- and P₉₆ATOM₂-2-, spin-up electrons are wrapped around the Li atom, in line with the above analysis. The result shows that the formation of Na's spin density is consistent with Li atoms. For Fe doping in blue phosphorene, the spin-up density surrounds Fe atoms, which is consistent with the above analysis. The substitutional doping of two Fe atoms as shown in figure 7(a), the spin-down density is generally greater than that in spin-up density. The Co atom is also surrounded by spin-down charges as shown in figures 7(c). Figure 7(b) is the opposite of figure 7(a), Fe atoms have more charge in the spin-up direction than in the spin-down direction, thus showing an overall spin-down. Overall, the spin charge density diagrams are consistent with the magnetic moments.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Now we turn to investigate the electronic characteristics of heteroatom substitutional doping into blue phosphorene. Pristine blue phosphorene has an indirect bandgap of approximately 2.026 eV, as shown in figure 2. It can be seen from the Li, Na, Si, Fe atoms doping in P₉₇ATOM₁-case that the spin-up and the spin-down are asymmetric, which indicates that the Li, Na, Si, Fe substitutional doping in P₉₇ATOM₁- system has a magnetic ground state as displayed in figure S4 and which is agrees with the above magnetism calculations. In figures S4 and 8 (P₉₇Al₁), it can be found that the spin-up and spin-down are symmetric for Al, Fe substitutional doping in P₉₇ATOM₁, which is agree with the above magnetism calculations. For the nonmagnetic Al, Co doping in P₉₇ATOM₁-, it is displayed indirect bandgap and P₉₇Al₁ is displayed direct bandgap. The reason is that hybridization occurs after Al substitutional doping in P₉₇ATOM₁- and the band gap is reduced by nearly 0.2 eV compared with the pristine blue phosphorene. After hybridization it changed from an indirect bandgap to a direct bandgap.

For the heteroatom substitutional doping in P₉₆ATOM₂-1, Fe atom have magnetism properties due to the asymmetric of DOS with spin-up and spin-down (see figure S5). For the magnetic Li, Na, Co and Sn substitutional doping in P₉₆ATOM₂-1 systems, they still possess semiconductors properties which are similar to above analysis. In the band structure of the P₉₆Al₂-1 system, the CBM and CVM are located at G point, showing a direct band gap of 1.256 eV; the conduction band minimum and valence band maximum are located at M point in the band structure of the P₉₆Al₂-1 system, showing that the direct bandgap is 1.25 eV. The doping of Co atoms results in a smaller bandgap, and the bandgap is 0.4 eV, which has a conduction band minimum and a valence band minimum at the G point. The reason is that other atoms (Al/Si/Co) occurs orbital hybridized with P atoms (see figure 8 P₉₆Al₂-1, P₉₆Si₂-1 and P₉₆Co₂-1).

Zoom In Zoom Out Reset image size

For the Li, Na and Si doping in P₉₆ATOM₂-2 case, figure S6 shows that the spin-up and spin-down density are asymmetrical because of the presence of magnetism. For the Al, Fe, Sn and Co atoms substitutional doping in P₉₆ATOM₂-2 case, the spin-up and spin-down density are symmetrical. In the figure 8, it can be found that the spin-up and spin-down are locate on G points for the P₉₆Al₂-2. After Fe, Co atoms are doping in P₉₂ATOM₆-blue phosphorene, the orbits of spin-up and spin-down in the DOS are inconsistent, showing magnetic properties as plot in figure S7. Other heteroatoms substitutional doping in blue phosphorene shows the non-magnetic state ascribe to the asymmetry of spin-up and spin-down state density. Atomic intercalation induces the magnetic properties of blue phosphorene, and the bandgap characteristics of blue phosphorene is found to change after some atoms are substitutional doped. The results further demonstrate the important effect of heteroatom substitutional doping on the electronic structure of P₉₇ATOM₁-, P₉₆ATOM₂-1-, P₉₆ATOM₂-2- and P₉₂ATOM₆-blue phosphorene.