A quantitative stress-related model for the evolution of the pore size in porous silicon during high temperature annealing

An original two dimensional model for the simulation of structural pore evolution post-high temperature annealing of porous silicon is proposed. The model treats the pore as a group of vacancies and deals with their diffusion in crystalline materials under mechanical stress. A coupled solution of the mechanical and diffusion field equations is carried out numerically using finite element method. It is found that the pore shape evolution upon annealing at high temperature is essentially dependent on the initial strain created by the pore. The proposed model provides a theoretical basis for the determination of the critical initial pore radius that determines whether the pore will increase or decrease in size upon annealing. Such a critical radius is found to be dependent on the annealing temperature and is calculated for the range 700–1300 °C.