Effective conductivity of porous silicon: A theoretical approach

From a theoretical point of view, linear transport in homogeneous systems is well understood. However, transport phenomena through porous materials are far more complicated. In fact, there are some materials like porous silicon with a very promising technological impact, where mainly experimental evidence is available and theoretical models have scarcely been developed. In a previous work, we obtained an analytical expression for the axial effective electrical conductivity of a model simulating porous silicon (PS). We used the averaging volume method that has proven to be successful in treating fluid transport in porous media. The PS model was based on experimental information about the structure of this new material and experimental data for crystalline Si and hydrogenated a-Si thin films. With this method we can calculate the bulk and the surface contribution to the tensorial effective conductivity. Here we present the transverse effective conductivity results where percolation effects can be observed, using the same method and model. However, in the XY plane the calculation is more complicated and it can only be performed numerically. The understanding of the effective electrical conductivity behavior as a whole may be important for electronic applications of PS.