## 4 Conclusions  
Density functional theory (DFT) calculations were used to investigate the growth mechanism of GaN thin films via the ALD process, using trimethylgallium (TMG) and NH\({}_{3}\) as the gallium and nitrogen precursors, respectively. In the TMG adsorption step, TMG binds to both Si-NH\({}_{2}\) and Si\({}_{2}\)-NH surfaces by occupying one or two surface site(s). On the Si\({}_{2}\)-NH surface, the average activation barrier (1.59 eV) is significantly lower than that on the Si-NH\({}_{2}\) surface (1.72 eV) when TMG is adsorbed by occupying two surface sites. Moreover, the activation barrier further decreases to 1.11 eV when TMG is adsorbed by occupying only one surface site. This mechanism also improves the reactivity during subsequent NH\({}_{3}\) adsorption. The results clearly indicate that tuning the surface adsorption sites of the substrate directly influences both the reaction kinetics and the process temperature. The present study suggests that increasing the density of Si\({}_{2}\)-NH surface sites accelerates the initial ALD reactions, enabling lower deposition temperatures, shorter cycle times, and improved GaN film quality.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure** & \begin{tabular}{c} **Vibration Mode** \\ **(Symmetric Stretching)** \\ \end{tabular} & \
\begin{tabular}{c} **Wavenumber** \\ **(cm\({}^{-1}\))** \\ \end{tabular} &
\begin{tabular}{c} **Other Studies [11,32]** \\ **(cm\({}^{-1}\))** \\ \end{tabular} \\ \hline
**Products (first half)** & & & \\ PC 1–1 + CH\({}_{4}\) & Ga–N & 531 & 534 \\  & Ga–CH\({}_{3}\) & 2917 & 2912 \\ PC 2–1 + CH\({}_{4}\) & Ga–N & 530 & 534 \\  & Ga–CH\({}_{3}\) & 2917 & 2912 \\ PC 1-2 + CH\({}_{4}\) & Ga–N & 537 & 534 \\  & Ga–CH\({}_{3}\) & 2917 & 2912 \\ PC 2-2 + CH\({}_{4}\) & Ga–N & 574 & - \\  & Ga–CH\({}_{3}\) & 2939 & - \\
**Products (second half)** & & & \\ PC 1-3 + CH\({}_{4}\) & Ga–N & 557 & 534 \\ PC 1-4 + CH\({}_{4}\) & Ga–N & 509 & - \\ PC 3-1 + CH\({}_{4}\) & Ga–N & 547 & 534 \\ PC 3-2 + CH\({}_{4}\) & Ga–N & 539 & 534 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prediction of infrared frequencies of Ga–N and Ga–CH\({}_{3}\) species calculated from product structures compared to other experimental studies, with vibrational frequencies calculated at B3 LYP 6–31G(d) level and scaled using 0.96.  
**Author Contributions:** Conceptualization, P.P.P., T.P. and S.S. ([PERSON]); methodology, T.P. and P.P.P.; validation, T.P., S.S. ([PERSON]), W.S., S.S. ([PERSON]), W.T. and T.J.; formal analysis, P.P.P., T.P. and S.S. ([PERSON]); investigation, P.P.P. and T.P.; resources, P.P.P. and T.J.; data curation, T.P. and P.P.P.; writing--original draft preparation, T.P. and P.P.P.; writing--review and editing, P.P.P., S.S. ([PERSON]), S.S. ([PERSON]), W.S., T.J. and W.T.; visualization, T.P. and P.P.P.; supervision, P.P.P.; project administration, P.P.P. and T.P.; funding acquisition, P.P.P. and T.P. All authors have read and agreed to the published version of the manuscript.  
**Funding:** Thailand Research Fund (TRF), grant number MRG6180194.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Acknowledgments:** This work was supported by the Thailand Research Fund (TRF), currently integrated under the National Research Council of Thailand (NRCT), under project number MRG6180194. We gratefully acknowledge the Faculty of Science at Sriracha, Kasetsart University, for the partial financial support of the unit research project in 2022. The authors would also like to thank the anonymous referees for their helpful comments on this article.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this research paper.