## 3 Results  
### Reaction Mechanisms of TMG Adsorption on NH\({}_{2}\) Passivated Si(100) Surface  
The reaction mechanisms of TMG adsorption on the Si-NH\({}_{2}\) and Si\({}_{2}\)-NH surfaces during the ALD steps are explained in Figure 5. The corresponding molecular structures are labeled (a)-(g) for adsorption on the Si-NH\({}_{2}\) surface and (h)-(n) for adsorption on the Si\({}_{2}\)-NH surface, as shown at the bottom of the figure. The TMG adsorbed the silicon surface by consuming two adsorption sites and releasing two by-product molecules (CH\({}_{4}\)). The GaN\({}_{2}\) species was located between two neighboring silicon dimers. The reaction was initiated by the adsorption step when the TMG molecule approached the Si-NH\({}_{2}\) surface. Then, at the first transition state (TS 1-1), the Ga-C1 bond was broken at a distance of 2.73 A while the Ga-N1 bond formed. The CH\({}_{3}\) released in this step attacked one of the H atoms that was released from the NH\({}_{2}\) adsorption site to form a CH4 by-product molecule in the next step (product 1). In the PC 1-1 + CH4 stage, a CH4 molecule was removed, while the Ga-N1 bond formed with a length of 1.92 A. There was an interaction between a Ga atom and an N2 atom of the NH\({}_{2}\) adsorption site, leading to the second transition state  
Figure 4: Reaction pathway of TMG adsorption on the Si\({}_{15}\)H\({}_{18}\)-(NH\({}_{2}\))\({}_{2}\) substrate using various basis sets. The pathways calculated with 6-31G(d), 6-311G(d,p), 6-311+G(2d,p), and 6-311+G(2 df,2p) basis sets are illustrated by the blue, orange, yellow, and gray lines, respectively. (TS 2-1). At TS 2-1, the Ga-C2 bond was broken at a distance of 2.25 A while the Ga-N2 bond formed. In the final step (PC 2-1 + CH4), the Ga-N2 species formed completely while the second CH4 by-product was removed. The N2 Ga-CH3 species was the new surface. In addition, we observed that the Ga-C1 bond was broken while the Ga-N1 bond formed during the TS 2-1 stage; however, the N-H bond of the Si-NH2 surface site still remained. This showed that the Ga-C bond was broken together with the formation of the Ga-N1 bond, followed by the rupture of the N-H bond in the first adsorption. Knowing the order of breaking and forming in chemical bonds during the adsorption step is the key factor in ALD processes. We considered that the energy of precursor decomposition defined the process temperature of ALD. In the current work, the H atom of the Si-NH2 surface did not contribute to dissociation of the Ga-C bond (within a TMG precursor) in the transition states (TS 1-1 and Ts 2-1). Therefore, large activation barriers (2.00 eV) are needed to break the Ga-C bond directly, resulting in the relative energy for this stage being 1.65 eV above the reactant level. Therefore, the ALD-GaN thin film TMG precursor must be deposited at a high temperature (above 375 \({}^{\circ}\)C) [47]. These computational results were comparable to previous experimental reports. For example, in 2015, [PERSON] et al. [32] reported the mechanisms of TMG adsorbed on a GaN surface in the ALD process. The reaction mechanisms were characterized using infrared (IR) spectroscopy. In the adsorption step, TMG was adsorbed on the Ga-NH2 surface site by consuming one- or two-surface adsorption site(s). The adsorption on two-adsorption sites is considered more favorable. CH3 and H2 molecules were released as by-products. These results were consistent with [PERSON]'s work reported in 2016 [30]. However, in [PERSON]'s study, the CH4 molecule was released as a by-product, similar to the current work, where TMG was adsorbed on the one- and two-adsorption sites of the Si-NH2 surface species, respectively. Then, the Ga-CH3 species was a new surface species, while CH4 molecules were released as by-products. In the current work, we considered that the CH3 groups were released during transition states and were not always combined with an H atom to form the CH4 molecule because the H atom did not contribute to breaking the Ga-C bond during the TS stages.