Modeling the photoacoustic signal during the porous silicon formation

TL;DR

This paper develops a modified photoacoustic model to analyze the growth kinetics of porous silicon during etching, enabling determination of growth velocity and layer thickness from experimental data.

Contribution

It extends the Rosencwaig and Gersho model to include dynamic changes in reflectance and sample thickness during porous silicon formation.

Findings

The model accurately predicts photoacoustic signals during PS growth.

It allows extraction of etching velocity and layer thickness from experimental data.

The theoretical results match experimental measurements.

Abstract

Within this work, the kinetics of the growing stage of porous silicon (PS) during the etching process was studied using the photoacoustic technique. A p-type Si with low resistivity was used as a substrate. An extension of Rosencwaig and Gersho model is proposed in order to analyze the temporary changes that take place in the amplitude of the photoacoustic signal during the PS growth. The solution of the heat equation takes into account the modulated laser beam, the changes in the reflectance of the PS-backing heterostructure, the electrochemical reaction, and the Joule effect as thermal sources. The model includes the time-dependence of the sample thickness during the electrochemical etching of PS. The changes in the reflectance are identified as the laser reflections in the internal layers of the system. The reflectance is modeled by an additional sinusoidal-monochromatic light source and its modulated frequency is related to the velocity of the PS growth. The chemical reaction and the DC components of the heat sources are taken as an average value from the experimental data. The theoretical results are in agreement with the experimental data and hence provided a method to determine variables of the PS growth, such as the etching velocity and the thickness of the porous layer during the growing process.