# Key signal contributions in photothermal deflection spectroscopy

## TL;DR

This paper develops a comprehensive computational framework for photothermal deflection spectroscopy (PDS) in semiconductors, accounting for linear and nonlinear effects, thermal expansion, and spatial gradients to accurately extract absorption properties.

## Contribution

It introduces a rigorous semi-analytic raytracing method that models key physical effects influencing PDS signals, enabling precise interpretation of measurement data.

## Key findings

- Nonlinear absorption significantly affects PDS signals at high pump intensities.
- Thermal expansion and spatial gradients can amplify surface signals by up to two orders of magnitude.
- Guidelines are provided for accurately extracting attenuation coefficients from PDS measurements.

## Abstract

We report on key signal contributions in photothermal deflection spectroscopy (PDS) of semiconductors at photon energies below the bandgap energy and show how to extract the actual absorption properties from the measurement data. To this end, we establish a rigorous computation scheme for the deflection signal including semi-analytic raytracing to analyze the underlying physical effects. The computation takes into account linear and nonlinear absorption processes affecting the refractive index and thus leading to a deflection of the probe beam. We find that beside the linear mirage effect, nonlinear absorption mechanisms make a substantial contribution to the signal for strongly focussed pump beams and sample materials with high two-photon absorption coefficients. For example, the measured quadratic absorption contribution exceeds 5% at a pump beam intensity of about ${1.3}\times{10^{5}}\;{W}/{cm^{2}}$ in Si and at ${5}\times{10^{4}}\;{W}/{cm^{2}}$ in GaAs. In addition, our method also includes thermal expansion effects as well as spatial gradients of the attenuation properties. We demonstrate that these effects result in an additional deflection contribution which substantially depends on the distance of the photodetector from the readout point. This distance dependent contribution enhances the surface related PDS signal up to two orders of magnitude and may be misinterpreted as surface absorption if not corrected in the analysis of the measurement data. We verify these findings by PDS measurements on crystalline silicon at a wavelength of 1550 nm and provide guidelines how to extract the actual attenuation coefficient from the PDS signal.

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Source: https://tomesphere.com/paper/1905.06135