# Effect of Nitrogen on the Growth of (100)-, (110)-, and (111)-Oriented Diamond Films
## 2 Structure and Computational Methods  
To study the reaction energy of a nitrogen-doped diamond surface, we used the implementation of density-functional theory in the Vienna ab initio simulation package (VASP) [15; 16] with the generalized gradient approximation (GGA) [17; 18] for the exchange correlation functional. We prepared supercell C\({}_{72}\)H\({}_{24}\) containing 72 carbon atoms and terminated with 24 hydrogen atoms on both sides, as depicted in Figure 2, for the (100)-, (110)-, and (111)-oriented surfaces. The Monkhorst-Pack scheme included \(k\)-meshes of 4 \(\times\) 3 \(\times\) 1, 3 \(\times\) 3 \(\times\) 1, and 3 \(\times\) 2 \(\times\) 1 for the (100), (110), and (111) surfaces, respectively. The cut-off energy was set to 400 eV, and the self-consistent total energy criterion was 10\({}^{-5}\) eV.  
To calculate the hydrogen extraction energy \(E_{ex}^{H}\) (eV), we used the following formula:  
\[E_{ex}^{H} =\Big{(}E_{product}+E_{iso}^{H_{2}}\Big{)}-\big{(}E_{reactant}+E_{ iso}^{H}\Big{)}, \tag{1}\]  
where \(E_{product}\) is the total energy produced by extracting a hydrogen atom from the surface of a H-terminated diamond slab C\({}_{72-x}\)H\({}_{23}\)N\({}_{x}\) (x = 0, 1), \(E_{iso}^{H_{2}}\) is the total energy of an isolated H\({}_{2}\) molecule, \(E_{reactant}\) is the total energy of a H-terminated diamond slab C\({}_{72-x}\)H\({}_{24}\)N\({}_{x}\) (x = 0, 1), and \(E_{iso}^{H}\) is the total energy of an isolated hydrogen atom. We calculated \(E_{ex}^{H}\) for the substitution of a nitrogen atom in positions \(A\), \(B\), \(C\), or \(D\) for the diamond (100), (110), and (111) surfaces shown in Figure 2. After the hydrogen atom escaped from the diamond surface, we calculated \(E_{ad}^{CH_{3}}\), the molecule adsorption energy of \(CH_{3}\) as follows:  
\[E_{ad}^{CH_{3}} =E_{surface-CH_{3}}-\Big{(}E_{product}+E_{iso}^{CH_{3}}\Big{)}, \tag{2}\]  
where \(E_{surface-CH_{3}}\) is the total energy of a diamond slab after reacting with a methyl radical C\({}_{73-x}\)H\({}_{26}\)N\({}_{x}\) (x = 0, 1), and \(E_{iso}^{CH_{3}}\) is the total energy of an isolated \(CH_{3}\) molecule.  
Figure 2: (Color online) Supercell structures used for diamond (100) surface, diamond (110) surface, and diamond (111) surfaces. Each surface contains 24 hydrogen atoms and 72 carbon atoms. The letters \(A\), \(B\), \(C\), and \(D\) denote positions of nitrogen atoms. White and gray spheres represent H and C atoms, respectively.  
We also calculated \(E_{ad}^{CH_{3}}\) for situations in which a nitrogen atom is absorbed into the inner layer of the diamond slab. Furthermore, we calculated \(E_{abstr}^{H}\), the energy required for hydrogen abstraction from the methylated diamond surface, as follows:  
\[E_{abstr}^{H}=\left(E_{surface-CH_{2}}+E_{iso}^{H_{2}}\right)-\left(E_{surface- CH_{3}}+E_{iso}^{H}\right), \tag{3}\]  
where \(E_{surface-CH_{2}}\) is the total energy of a diamond slab after reacting with a methyl radical (\(CH_{2}\)), \(C_{73-x}H_{25}N_{x}\) (\(x=0\), 1). Finally, we also calculated the hydrogen extraction energy for a \(CH_{3}\) molecule for various nitrogen-substitution positions.