A mathematical model for void evolution in silicon by helium implantation and subsequent annealing process
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abstract
We propose a physically based model that describes the diameter and the density of voids in silicon introduced via high dose helium ion implantation and subsequent annealing. The model takes into account interactions between vacancies, interstitials, small vacancy clusters, and voids. Void evolution in silicon occurs mainly by a migration and coalescence process. Various factors such as implantation energy and dose, anneal temperature, atmospheric pressure, and impurity level in silicon can influence the migration and coalescence mechanism and thus play a role in the void evolution process. Values for model parameters are consistent with known values for point defect parameters and assumed diffusion limited reaction rates. A single “fitting parameter” represents the rate of cavity migration and coalescence and is, therefore, related to surface diffusion of adatoms. Results obtained from simulations based upon the model were compared to our experimental results and to previously reported experimental results obtained over a wide range of conditions. Data from the literature included experiments with helium ion implantation energies in the range 30–300 keV, doses of 1 × 1016−1 × 1017 cm−2, subsequent annealing temperatures in the range 700–1200 °C, and annealing duration in the range 15 min–2 h. Excellent agreement is found between the simulated results and those from reported experiments. The extracted migration and coalescence rate parameter show an activation energy consistent with surface diffusivity of silicon. It shows a linear dependence on helium dose, and increases with decreased implantation energy, decreased ambient pressure, decreased substrate impurities, increased temperature ramp rate, or increased Ge fraction in cavity layer, all consistent with the proposed physical mechanism.
