Analytical models for the thermal properties of n-type porous silicon layers: Dependence of porosity

Several reports in the literature concern the thermal properties of porous silicon samples considering the porous layer plus the silicon substrate, but not so of the porous layer in particular. This work uses the frequency domain photoacoustic technique in a heat transmission configuration together with an analysis based on a composite two-layer model of thermal resistances on n-type porous silicon and the porosity concept to develop a non-separative (and hence non-destructive) methodology for determining the thermal properties of the porous layer of n-type porous silicon and provide analytical models to obtain such properties as a function of its porosity. The porous silicon samples were elaborated by anodization, with anodization times from 10 to 100 min on (100)-oriented n-type crystalline silicon wafers and using a 48% hydrofluoric acid water solution. These wafers were non-degenerated, phosphorous doped, 500 μm roughly thick, and had 1.72 Ω cm electrical resistivity. In each sample, gravimetry determined porosity ranging from 0.279 to 0.702, and the porous layer's thickness was determined by electron microscopy. An analytical expression was obtained for the effective thermal diffusivity of the n-type porous silicon as a whole. After fitting it to the data obtained by the photoacoustic measurements, a value around 0.076 cm2/s, independent of porosity, was obtained for the thermal diffusivity of the porous layer. In addition, analytical expressions were obtained for the porous layer's thermal conductivity, volumetric heat capacity, and thermal effusivity, all showed a decreasing linear dependence on the porosity.