Use of umbrella sampling in the calculation of the potential of the mean force for silicon surface oxidation

In order to establish the growth model of silicon oxide films within the thin regime, the potential energy surface was calculated for the reactions that may take place in the initial oxidation of the hydrogen-terminated silicon surface. Particularly, in order to take into account the effect of temperature, which is one of the important process parameters, the umbrella sampling technique was employed. The activation free energy for the oxidation of complete hydrogen-terminated Si surface and that for the desorption of hydrogen from the Si surface are both calculated to be 50 kcal mol^-1 at 700 K. The following oxidation at the hydrogen-defect site created by the desorption, which may be regarded as the oxidation of the clean surface, also requires 50 kcal mol^-1 of activation free energy. However, the insertion of oxygen to form a precursor is the rate determining step in the oxidation of hydrogen-terminated surface, while the oxygen migration from the precursor to form a stable oxide is the one in the oxidation of hydrogen-defect site. The activation free energy for the oxidation of partially oxidized site is 40 kcal mol^-1, hence the preoxidation by the activated oxygen species may accomplish the selective oxidation prior to the hydrogen desorption.