The adsorptions of trimethygallium (TMG) and arsine (As$H_3$) on H/Si(100)-2x1 surface were theoretically investigated. In the case of TMG adsorption, methane loss reaction, surface methylation, hydrogen loss reaction and ring closing reaction channels were found. The mechanism of As$H_3$ adsorption on the surface was also identified. Among these, the methane loss reaction depositing ?Ga(C$H_3)_2$ was found to be the major channel due to its low barrier height and the large exothermicity. The surface methylation reaction is the second most favorable channel. In contrast, arsine turned out to be less reactive on the surface, implying that Arsine surface reaction would be the rate limiting step in the overall ALD process.