Modeling stress retarded self-limiting oxidation of suspended silicon nanowires for the development of silicon nanowire-based nanodevices

In this paper, we present a model for the oxidation of silicon nanowires (NWs) based on a modification of the cylindrical Deal and Grove equation and taking into account stress effects associated with non-uniform deformation of the oxide by viscous flow. The validity of this model has been tested on a set of experimental results describing the thermal oxidation of suspended silicon NWs. The NWs oxidation is examined upon different atmospheres (pure O2 and H2O) and at different thermal budgets by scanning electron microscopy and transmission electron microscopy measurements. The good agreement between the experimental results and the simulations confirm the validity of the key model assumptions: the SiO2 flow can be approximated as purely viscous and the non-linear effects of shear stress on oxide viscosity [S. M. Hu, J. Appl. Phys. 64, 323 (1988)] can be neglected. In addition, the model gives some interesting insight about the physics of the oxidation process. In particular, we demonstrate that the compressive stress at the Si/SiO2 interfaces is the main parameter controlling the experimentally observed self-limitation of the oxidation rate for long oxidation times. Finally, it will be shown that thermal oxidation can be used to not only to decrease the core diameter and round off the nanostructures but also to reduce the size dispersion of a nanowire assembly and that our predictive model can be employed to optimize this process.