# Effect of Nitrogen on the Growth of (100)-, (110)-, and (111)-Oriented Diamond Films
## 3 Results and Discussion
The hydrogen extraction energy from the methyl molecule yielded the greatest contribution to this total. Furthermore, for the diamond (111) surface, the total energy was \(-\)6.68 eV after nitrogen doping in position \(A\). To further clarify the impact of near-to-surface nitrogen doping on the hydrogen extraction energy, we plotted four models of the nitrogen doping through substitutional nitrogen exchange with a neighboring vacancy in Figure 3. In Figure 3a, the reference energy is set for a free nitrogen atom and the diamond (100) surface with a single vacancy. In Figure 3b, the chemisorption of the nitrogen atom on the diamond (100) surface yields an energy gain of \(-\)0.56 eV. Then, the adsorbed nitrogen atom diffuses into the inner layer of the diamond (100) surface at position \(A\) or \(B\) (Figure 2), which requires a low energy addition of 0.07 eV, as illustrated in Figure 3c. Position \(A\) or \(B\) is a transition state with a low barrier height for the nitrogen migration towards the inside of the diamond layers for a favorable driving force of \(-\)1.11 eV as shown in Figure 3d, showing that the nitrogen atom \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Adsorption Energy (eV)**} \\ \cline{2-5}  & **(100)** & **(110)** & **(111)** & **(111)** \\ \hline No doped & \(-\)4.66 & \(-\)3.72 \({}^{\star}\) & \(-\)3.39 & \(-\)4.18 & \(-\)3.29 \({}^{\star}\) \\ N in position \(A\) & \(-\)1.84 & \(-\)1.78 \({}^{\star}\) & \(-\)1.26 & \(-\)1.54 & \(-\)1.30 \({}^{\star}\) \\ N in position \(B\) & \(-\)2.46 & \(-\)2.46 \({}^{\star}\) & \(-\)1.77 & \(-\)1.01 & \\ N in position \(C\) & \(-\)1.75 & & \(-\)1.38 & & \\ N in position \(D\) & & & & \(-\)2.32 & \\ \hline \hline \end{tabular} \({}^{\star}\) Ref. [14].  
\end{table} 
Table 2: Methyl molecule adsorption energy \(E^{CH_{3}}_{ad}\) for the diamond (100), (110), and (111) surfaces with or without nitrogen doping at positions \(A\), \(B\), \(C\), and \(D\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Hydroogen Extraction Energy \(E^{H}_{abstr}\) (eV)**} \\ \cline{2-5}  & **(100)** & **(110)** & **(111)** & **(111)** \\ \hline No doped & \(-\)0.72 & \(-\)0.27 \({}^{\star}\) & \(-\)0.81 & \(-\)0.54 & \(-\)0.22 \({}^{\star}\) \\ N in position \(A\) & \(-\)3.05 & \(-\)1.87 \({}^  
moves from position \(A\) or \(B\) to position \(C\) (Figure 2), with an energy gain of \(-1.11\) eV. This demonstrated that the energy of \(-1.11\) eV can promote the diffusion of doped nitrogen. Through the vacancy diffusion mechanism, this result is in full agreement with the previous experiments on nitrogen-doped diamond surfaces [12; 13; 14]. Figure 3: (Color online) (**a**) Nitrogen exposure and (**b**) chemisorption of a nitrogen atom on the diamond surface; nitrogen substitution on the (**c**) second and (**d**) third layers of the diamond surface. The stoichiometry of all super cells was fixed at \(C_{71}H_{23}N_{1}\). Blue, white, and gray spheres represent N, H, and C atoms, respectively. Dashed circles indicate vacancies.