# Effect of Nitrogen on the Growth of (100)-, (110)-, and (111)-Oriented Diamond Films
## 3 Results and Discussion  
The hydrogen extraction energies from diamond (100), (110), and (111) surfaces with and without nitrogen doping are listed in Table 1. The calculated hydrogen extraction energies for diamond (100), (110), and (111) surfaces were \(-0.53\), \(-0.84\), and \(-0.64\) eV, respectively. The (110) diamond surface had the lowest hydrogen extraction energy of \(-0.84\) eV. When the inner layer is nitrogen doped, the hydrogen extraction energy decreased. For example, if the second layer is nitrogen doped, then the hydrogen extraction energies from diamond (100), (110), and (111) surfaces were \(-2.35\), \(-2.03\), and \(-2.45\) eV, respectively. \(E_{ex}^{H}\) was one order of magnitude smaller than the corresponding value on the diamond surface. The lowest hydrogen extraction energy of \(-2.95\) eV was obtained when the third layer is nitrogen doped, which indicated that nitrogen-doped diamond (111) is favorable for hydrogen surface extraction. In general, hydrogen extraction energy considerably decreased after nitrogen doping. Table 2 lists the methyl molecule adsorption energies \(E_{ad}^{CH_{3}}\) for the diamond (100), (110), and (111) surfaces. The \(E_{ad}^{CH_{3}}\) values were \(-4.66\), \(-3.39\), and \(-4.18\) eV for the diamond (100), (110), and (111) surfaces, respectively. The lowest \(E_{ad}^{CH_{3}}\) value was obtained for the diamond (100) surface, indicating that attachment of \(CH_{3}\) to the diamond (100) surface was favorable. A previous study reported a lower result of \(E_{ad}^{CH_{3}}\) for the diamond (100) surface, with \(E_{ad}^{CH_{3}}=-3.72\) eV [14]. When the diamond layer was nitrogen doped, \(E_{ad}^{CH_{3}}\) substantially increased. This suggested that nitrogen doping does not favor the methyl molecule adsorption. Nevertheless, methyl group adsorption is crucial for the growth of artificial diamonds. On the basis of the hydrogen extraction energy and methyl group adsorption energy, we determined the total energy required for hydrogen abstraction and methyl molecule adsorption. The lowest sum of \(-5.19\) eV was obtained for the diamond (100) surface. However, nitrogen is the most common impurity in diamonds. In this situation, when nitrogen was doped to position \(C\) of the diamond (100) surface, this energy was \(-4.18\) eV (Figure 2; Tables 1 and 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Hydrogen Extraction Energy (eV)**} \\ \cline{2-4}  & **(100)** & **(110)** & **(111)** \\ \hline No doped & \(-0.53\) & \(-0.84\) & \(-0.64\) \\ N in position \(A\) & \(-2.35\) & \(-2.03\) & \(-2.45\) \\ N in position \(B\) & \(-1.52\) & \(-1.65\) & \(-2.95\) \\ N in position \(C\) & \(-2.43\) & \(-2.01\) & \\ N in position \(D\) & & & \(-1.67\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hydrogen extraction energy \(E_{ex}^{H}\) for the diamond (100), (110), and (111) surfaces with or without nitrogen doping at positions \(A\), \(B\), \(C\), and \(D\). The lowest \(E^{H}_{abstr}\) value of \(-\)3.05 eV was recorded with nitrogen doping in position \(A\) on the diamond (100) surface. \(E^{H}_{abstr}\) was calculated as \(-\)0.72 and \(-\)0.54 eV for the diamond (100) and (111) surfaces, respectively, which were in close agreement with previous theoretical results of \(-\)0.27 and \(-\)0.22 eV [14], respectively. Table 4 lists the total energies of hydrogen abstraction from the diamond surface \(E^{H}_{ex}\), methyl molecule adsorption on the diamond surface \(E^{CH_{3}}_{abstr}\), and hydrogen abstraction from the methylated diamond surface \(E^{H}_{abstr}\) (i.e., \(E^{H}_{ex}+E^{CH_{3}}_{abstr}+E^{H}_{abstr}\)). The diamond (100) surface yielded the lowest total energy of \(-\)5.91 eV. After nitrogen doping at position \(A\), the total energies of the diamond (100) or (111) surfaces decreased, indicating that nitrogen impurities are beneficial for diamond growth. The lowest total energy of \(-\)7.24 eV was obtained for nitrogen doping at position \(A\) on the diamond (100) surface.