3.4.1 AFM Oxidation Mechanism and Kinetics

In order to be able to predict and control the fabrication of nanostructures with LON, the mechanisms and kinetics behind the oxidation process must be understood. The first attempt to understand the mechanisms behind AFM oxidation was proposed by Gordon et al. [65] in 1995. There, it is suggested that the rate is limited by the initial density of surface OH$^-$ ions and that the oxide growth follows the Mott-Cabrera model [26], where the growth is consistent with electric field limited diffusion. Gordon et al. were also the first to identify that oxyion species (OH$^-$ or O$^-$) recombine with holes (h$^+$) present on the surface of the silicon sample.

Figure 3.10: Oxidation driven by oxyions, which are generated due to the presence of the strong electric field, interacting with the silicon surface.

It is now understood that when a negatively charged AFM tip is brought near a grounded silicon surface, as is shown in Figure 3.10, an electric field is generated in the formed water meniscus. The presence of the strong field breaks up the water into ions (O$^-$, OH$^-$, and H$^+$) and causes the downward acceleration of the negatively charged ions towards the surface. The combination of these ions with holes (h$^+$) present at the surface results in the localized growth of SiO$_2$, which grows into the silicon wafer as well as into the water meniscus. In the case of a silicon surface, the oxidation at the anode end (Si) follows the chemical reaction

$$Si+2h^{+}+2\left(OH^{-}\right)\longrightarrow Si\left(OH\right)_{2}\longrightarrow SiO_{2}+2H^{+}+2e^{-},$$ (103)

where h$^+$ is a free hole in the Si sample and e$^-$ is a free electron [62], [213]. Similarly, the chemical reaction taking place at the AFM needle tip (cathode) follows

$$2H^{+}\left(aq\right)+2e^{-}\longrightarrow H_{2},$$ (104)

where e$^-$ is a free electron.

The goal of LON models is to give a predictable shape for a nanodot or nanowire under various ambient conditions, while it is within the scope of this work to incorporate these models into the LS simulator described in Section 1.4.1.