Experimental Validation of Formula for Calculation Thermal Diffusivity in Superlattices Performed Using a Combination of Two Frequency-Domain Methods: Photothermal Infrared Radiometry and Thermoreflectance

Michał Pawlak,Arne Ludwig,Nikolai Spitzer,Timo Kruck,Dariusz Dziczek,Andreas D Wieck

doi:10.3390/app11136125

Abstract

In this paper, we validate two theoretical formula used to characterize thermal transport of superlattices at different temperatures. These formulas are used to measure cross-plane thermal conductivity and thermal boundary resistance, when it is not possible to obtain heat capacity or thermal diffusivity and in-plane thermal conductivity. We find that the most common formula for calculating thermal diffusivity and heat capacity (and density) can be used in a temperature range of −50 °C to 50 °C. This confirms that the heat capacity in the very thin silicon membranes is the same as in bulk silicon, as was preliminary investigated using an elastic continuum model. Based on the obtained thermal parameters, we can fully characterize the sample using a new procedure for characterization of the in-plane and cross-plane thermal transport properties of thin-layer and superlattice semiconductor samples.

Highlights

In order to measure the thermal conductivity in the time-domain thermoreflectance (TDTR), method, researchers need to use the heat capacity of the bulk material
We study thin-layer and superlattice samples using both frequency domain methods, propagation for the one-dimensional (PTR) and thermoreflectance (FDTR), at different temperatures
We present the combination of two methods, FD-PTR and frequency-domain thermoreflectance (FD-TR), which can completely characterize the thermal properties of thin films as well as a superlattices, and experimentally verified formulas used in other studies on the thermal properties of superlattices

Summary

Introduction

A preliminary theoretical investigation, used an elastic continuum model, suggested that the heat capacity in the very thin silicon membranes is the same as in bulk silicon [15] The benefit of using frequency domain methods over time-resolved methods is their unique profilometry capability This relies on the observation that one can relate the origin of a signal at a given frequency to the depth or penetration length of the thermal wave (i.e., thermal diffusion length). This allows the thermal conductivity as a function of depth to be probed by varying the frequency. There are many frequency-domain methods, such as photoacoustic [16,17], photothermal beam reflection [18,19], thermoreflectance [20,21]

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