Theoretical Research on Optical Properties of Porous Silicon

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(1)Diffusion-limited modelThe morphology of porous silicon has been generated through the diffusion limited aggregation process of pores. We have shown that this model exhibits the stretched exponential decay of photoluminescence(PL) intensities, whose decay constant is larger for larger PL energies. This result is consistent with some experiments while it is inconsistent with that of the quantum sponge model (our previous model), which is consistent with other experiments. Therefore, the temperature-dependence of the decay constant depends on the detail of the models.(2)Porous silicon as quantum percolation systemThe problem of porous silicon is closely related to that of the quantum percolation. In order to understand properties of porous silicon, we have investigated the character of wavefunctions of the quantum percolation system. First We have shown that sponge structures in both of two-dimensional square lattice and three-dimensional cubic lattice have fractal wavefunclions. Then we have shown that the quantum sponge model for porous silicon have also fractal wavefunctions, which decayaccording to an inverse power law.(3)Ac conductivityIt is known in experiments that ac conductivity of porous silicon is proportional to the power of the frequency : The power is unity in the high frequency region while it is 1/2 in the low frequency region. We have started the calculations of the acconductivity to explain this character as a consequence of the fractal wavefunctions.However, we have not got enough results yet and this work is still on progress.