Dielectric relaxation and transport in porous silicon

Results of dielectric spectroscopy study of porous silicon samples in the frequency range 20 Hz-1 MHz and in the temperature range 173-493 K, are presented. We found three relaxation processes that dominate at low, moderate and high temperatures, respectively. At low temperatures the dielectric dispersion is composed of two Cole-Cole relaxation processes with two activation energies of 0.2 and 0.3 eV, respectively. At moderate temperatures the complex dielectric function exhibits two frequency-dependent power laws that are well described by Jonscher empirical terms. At temperatures above 400 K we found a large dc conductivity, with activation energy of 0.46 eV, and an additional Havriliak-Negami relaxation process with typical relaxation times of the order of (formula presented) Following our findings, we propose a comprehensive model, which assigns these processes to the fractal geometry of porous silicon and to thermally activated relaxation processes from localized and delocalized electronic states of the silicon nanocrystallites. In addition, we argue that the high-temperature Havriliak-Negami process cannot be explained on the basis of electronic response model, and a mode of cooperative relaxation appears at high temperatures.