## 3 Results and Discussion
### Surface Structural Deformation
#### 3.2.2 Structural Deformation Caused by PV and PVH Complexes  
Changes of bond lengths of the PV and PVH complex are listed in Tables 3 and 4, respectively. The P-C bonds around PV complex change by more than 20%, and some P-C bonds around PVH complex even change by over 30%. Clearly seeing from Tables 3 and 4, some of the P-C bonds are compressed and some of them are stretched which means the dopant P atom moves toward the vacancy, stretching the original P-C bond, decreasing the distance between P and C that needs to bond, and forming new P-C bonds. Because PV complex breaks one C-C bond for each of the six surrounding C atoms, the doped P atom finally bonds with the six surrounding C atoms, as shown in Figure 4. Adding the P atom, which is larger in size than the C atom, causes the surrounding structure to expand, and due to the presence of vacancy, the P atom moves towards this place with less constraining force. In the site of vacancy, the C-C bonds formed between the original C atom and the surrounding C atoms are broken. Because the P atom moves toward the vacancy and there are three carbon atoms near the vacancy lose a covalent bond, the P \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Surface**} & \multirow{2}{*}{**Layer**} & \multirow{2}{*}{**Position of P**} & \multicolumn{5}{c}{**Change in Bond Length (\%)**} \\  & & & **d\({}_{1}\)** & **d\({}_{2}\)** & **d\({}_{3}\)** & **d\({}_{4}\)** \\ \hline \multirow{6}{*}{**(001)**} & **2** & **A** & 14.4 & 24.2 & 13.5 & 13.5 \\  & **3** & **A** & 10.9 & 10.9 & 10.7 & 10.7 \\  & **B** & 9.5 & 9.5 & 10.5 & 10.5 \\  & **A** & 10.0 & 9.5 & 9.8 & 9.8 \\  & **B** & 9.5 & 9.5 & 9.6 & 9.6 \\  & **5** & **A** & 10.2 & 8.8 & 9.7 & 9.7 \\  & **6** & **A** & 9.4 & 9.6 & 9.5 & 9.5 \\ \hline \multirow{6}{*}{**(111)**} & **2** & **A** & 14.4 & 11.0 & 10.6 & 10.6 \\  & **3** & **A** & 11.5 & 9.8 & 9.9 & 9.9 \\ \cline{1-1}  & **4** & **A** & 10.2 & 9.3 & 9.3 & 9.3 \\ \cline{1-1}  & **5** & **A** & 10.0 & 9.9 & 9.5 & 9.5 \\ \cline{1-1}  & **6** & **A** & 10.1 & 9.7 & 9.4 & 9.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Change of typical bond lengths of a single P atom with its surrounding C atoms. The result of changing in bond length comes from: (length after doping\(-\)length before doping)/ length before doping. atom ends up bonding with those three C atoms. For the PVH complex, because the P has five valence electrons and due to the presence of H atoms, doped P atoms form five covalent bonds with five neighboring C atoms and the remaining carbon bonds with the H atoms. This is different from the P-H complex, as P covalently bonds with H atoms [17]. The C-H bond lengths are almost constant around 1.1 A. Although the vacancy of PV and PVH complex eventually disappears, in order to describe the influence of different complex on the surface structure more intuitively, we still use PV and PVH complex to name the optimized structure. Doping PV and PVH complex causes a deformation that is much larger than that of doping one P atom, and this can explain the formation energies of doping PV and PVH complex are larger than that of doping one P atom in almost every layer of (001) surface, except the situation of doping PVH complex in fourth layer. It is harder for the PV complex and PVH to form than doping a single P atom in the surface layers of (001) surface. However, in the deeper layer of (111) surface, although a larger deformation is produced, the formation energy of doping PV and PVH complex becomes even smaller than that of doping one P atom. A reason for this phenomenon appears to originate from the different arrangement of atom in two surfaces: the atoms are arranged more neatly and closely in (111) surface. When doping P atom in deeper layer of (111) surface, the surrounding compact structure prevents the formation of structure deformation, and the doping site is under compressive stress which is larger than that of (001) surface.