# Effect of Nitrogen on the Growth of (100)-, (110)-, and (111)-Oriented Diamond Films  
[PERSON]  
1 Center for General Education, China Medical University, Taichung 402, Taiwan; [EMAIL_ADDRESS]
2 Program of Digital Health Innovation, China Medical University, Taichung 402, Taiwan 2  
[PERSON]  
3 Graduate Institute of Precision Engineering, National Chung Hsing University, Taichung 402, Taiwan; [EMAIL_ADDRESS] (T-C.L.); [EMAIL_ADDRESS] (Y-J.T).  
[PERSON]  
3 Graduate Institute of Precision Engineering, National Chung Hsing University, Taichung 402, Taiwan; [EMAIL_ADDRESS] (T-C.L.); [EMAIL_ADDRESS] (Y-J.T).  
[PERSON]  
3 Correspondence: [EMAIL_ADDRESS]; Tel.: +886-921-820915312  
diamond surface is the key factor influencing the growth rate of diamonds. In 2005, [PERSON] et al. studied nucleation on the diamond (100) surfaces with methyl molecules (\(CH_{3}\)) and hydrogen ions fabricated through CVD [10]. Their results revealed the three steps through which diamond nucleation occurs. The hydrogen abstraction from the diamond (100) surface is assumed to take place by using a hydrogen radical, resulting in a gaseous H\({}_{2}\) molecule. A schematic of this mechanism of nucleation is shown in Figure 1a-c. Second, a methyl molecule is adsorbed by the dangling surface bond, and a hydrogen atom of the methyl molecule is freed by atomic hydrogen in the chamber. Figure 1d-f show the schematic for hydrogen abstraction from a methyl molecule on the diamond surface. Finally, the C-C dimer breaks and forms a new ring with the methylene molecule on the diamond surface. A schematic of the breaking dimer and ring formation is shown in Figure 1g-i. According to these findings, the hydrogen extraction from methyl molecules on the diamond surface is crucial for the diamond growth rate. In 2011, [PERSON] et al. used the HFCVD technique to deposit diamond films with various methane concentrations [11]. Their experimental results suggested that methyl molecules are the main source of diamond growth.  
The primary impurity in diamonds is nitrogen [12]. In 2004, [PERSON] et al. first used 2.45-GHz MPCVD with methane at 60 standard cubic centimeters per minute (sccm) and hydrogen at 500 sccm. They observed that the diamond growth rate ranged from 30 to 120 \(\upmu\)m/h. Furthermore, to understand the effect of nitrogen on the growth of diamond  
Figure 1: (Color online) (**a**) A hydrogen atom approaches the hydrogen-terminated C–C dimer of the diamond surface; (**b**) The terminated hydrogen atom is extracted from the transition state; (**c**) This forms a hydrogen molecule away from the diamond surface. (**d**) A methyl molecule is bonded to the diamond surface; (**e**) The hydrogen atom of this methyl molecule is extracted from the transition state; (**f**) This forms a methylene molecule on the diamond surface and a hydrogen molecule away from the diamond surface. (**g**) Finally, a methylene molecule approaches; (**h**) This methylene molecule causes the C–C dimer in the pentagon carbon ring to break; (**i**) This pentagon carbon ring becomes a hexagon carbon ring. White and gray spheres represent H and C atoms, respectively.  
films, nitrogen gas was added at 1.8 sccm, which doubled the diamond growth rate. Therefore, nitrogen doping increases the growth rate of diamonds [13]. In 2008, [PERSON] et al. studied the effect of nitrogen on the initial stages of diamond growth using CVD and determined the reaction energies of nitrogen-doped diamond (100) and (111) surfaces [14]. Their results indicated that the hydrogen abstraction energy can be reduced when nitrogen is added to the system. Numerous experiments have been conducted on nitrogen-doped diamonds, but the influence of nitrogen doping on diamond growth is not yet fully understood. Therefore, on the basis of density-functional theory, we systematically studied the reaction energies of nitrogen-doped (100)-, (110)-, and (111)-oriented diamond films.