## 3 Results and Discussion
### Single Substitutional Silicon Impurity in H-, O-, and N-Terminated C (001) Surfaces  
Single substitutional silicon (Si) impurity in a diamond (001) surface was modeled by replacing one C atom with a silicon atom near the surface. According to the analysis of the symmetry of surface structures, two different possible silicon-substituting positions were considered in the third, fourth, and seventh C layers of the H-terminated surface; and in the second, third, sixth, and seventh C layers of the N-terminated surface: under dimeric rows (_Lm-1_, where \(m\) refers to the C layer number) and between rows (_Lm-2_). For the O-terminated surface, there was only one possible site in every single C layer. The possible silicon-substituting positions (in _L2_ to _L7_) under H, O, and N terminations are shown in Figure 2. The structures chosen here were used in our existing work [2; 46], as they were the most normal and stable configurations among fully H-, O-, and N-terminated diamond (001) surfaces. Figure 2: Structural illustrations of the studied diamond (001) surfaces under (**a**) H termination, (**b**) O termination, and (**c**) N termination. Possible Si or V sites from the second to the seventh C layer (_L2_ to _L7_) near the diamond (001) surface are presented as different colored spheres. The formation energy \(E_{f}\) of single Si positioned in various C layers of H-, O-, or N-terminated diamond (001) surfaces and in a 216-atom bulk diamond, calculated using Equation (1), is illustrated in Figure 3. The formation energies of Si substituting one C atom under the dimer rows (_configuration_ 1) and between (_configuration_ 2) conform to Figure 2.  
As indicated in Figure 3, none of these configurations showed a negative formation energy value, which implied the presence of energy barriers against their formation from the perfectly terminated diamond (001) surface. However, we can see that the structure of Si replacing the C atom in the second C layer at _configuration 2_ under N termination led to the smallest formation energy of 2.64 eV. Si replacing the _L2_ and the _L3_-2 C sites under H termination also showed similar small formation energies of 2.70 eV. For all possible configurations under O termination, large formation energies of more than 4.5 eV were found, which meant, as compared with H and N terminations, that an O-terminated diamond (001) surface introduced the effect of preventing the formation of silicon impurity. Regarding the drastic difference between the formation energies of single Si in _configuration 1_ and 2 within the first four C layers under H and N terminations, this potentially occurred because of the local structural and electronic environments near the surface being significantly different between _configurations 1_ and 2. As shown in Table 1, bond lengths around _configuration 2_ in the first four C layers were much longer than those in _configuration 1_ under H and N terminations. However, for the O-terminated surface, there was only one possible Si-doping site in each C layer because of its high symmetry, and as indicated in Table 1, its bond lengths were almost the same below the second C layer; and thus its formation energies for single Si, positioned in various C layers, were similar when below the second C layer, as shown in Figure 3.  
Additionally, for silicon impurities positioned deeper than the fifth C layer (including the fifth layer) from the surface, their formation energies were close to 4.7 eV, regardless of their termination state, which indicated that surface effects decayed to nearly negligible levels below the fifth C layer under diamond (001) surfaces. This conclusion was confirmed in Table 1, where the bond lengths between C atoms below the fifth C layer under H, O, or N termination were nearly constant at roughly 1.54 A, which was the calculated C-C bond length value in the 216-atom bulk diamond. This value was in excellent agreement with the well-accepted value of 1.544 A [47].