Theoretical Research on Optical Properties of Porous Silicon

（1）扩散限制模型多孔硅的形貌是通过孔的扩散限制聚集过程产生的。我们已经表明，该模型表现出光致发光（PL）强度的拉伸指数衰减，其衰减常数是较大的PL能量。这一结果与某些实验一致，但与量子海绵模型（我们以前的模型）的结果不一致，而量子海绵模型与其他实验一致。因此，衰减常数的温度依赖性取决于模型的细节。（2）多孔硅作为量子逾渗系统多孔硅问题与量子逾渗问题密切相关。为了了解多孔硅的性质，我们研究了量子逾渗系统波函数的性质。首先，我们证明了二维正方晶格和三维立方晶格中的海绵结构都具有分形波函数。然后，我们证明了多孔硅的量子海绵模型也具有分形波函数，它按逆幂律衰减。(3)Ac电导率在实验中已知，多孔硅的交流电导率与频率的功率成正比：功率在高频区为1，而在低频区为1/2。我们已经开始计算电导率来解释分形波函数的这种性质，但是我们还没有得到足够的结果，这项工作还在进行中。

(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.