Conductivity and relaxation time of porous silicon using the Kramers-Kronig relation

Abstract

To review the dielectric characteristics of porous silicon samples with various porosities, an equivalent circuit including a capacitor and parallel resistance was used. By applying AC voltage with a constant amplitude of 200mV to the circuit and using impedance measurements of the samples between 10–100KHz, the variations in the capacitance, dielectric function, refractive index, and resistance for the samples at room temperature and up to 350°C were studied. The dielectric characteristics of the samples decreased with increasing frequency. In addition, with increasing temperature, the pore diameters increased, and the dielectric characteristics varied. In this paper, we demonstrate that the relaxation time and DC conductivity could be obtained using the Kramers-Kronig function and Hilbert transformation. Our results indicate that the relaxation time and DC conductivity increase with increasing porosity, and with increasing temperature, the relaxation time decreases and the DC conductivity increases.