Thermodynamic insights into Henry's constant in hyperthermal oxidation of silicon for fabricating optical waveguides

Hyperthermal oxidation of silicon is envisaged to be an alternative to silicon-on-insulator (SOI) waveguide fabrication for photonic integrated circuit (PIC) devices, and thus the local oxidation of silicon (LOCOS) technique has attracted attention. In this article, starting with the thermodynamic insights into the Deal-Grove model for defining the thermal oxidation, we model the Henry's law constant in the silicon oxidation process with the ensemble contributions of thermodynamic and chemical energies, and extract an empirical model with the published statistical data. Then, the simulations show the dramatic temperature/time dependences of Henry's constant, and the different effects of the thermodynamic and chemical energies. Systematic simulations of the temperature/time dependences of both the growth rate and thickness of oxide are carried out where the temperature dependence of the oxidant diffusivity is also considered. Consequently, the simulation results from the two models astonishingly agree with each other. Typically, at 1100 °C, with a 3 h oxidation time, 2.10 and 1.34 μm SiO₂ layers can be grown with the thermodynamic model under two diffusivity models, while with the empirical one, the two extreme cases can grow 2.10 and 1.28 μm SiO₂ layers, respectively.