Determination of thermal diffusivity of thin films by applying Fourier expansion analysis to thermo-reflectance signal after periodic pulse heating

Takahiro Baba,Kazuko Ishikawa,Tetsuya Baba,Takao Mori

doi:10.1063/5.0069375

Abstract

The flash methods, which are the most popular transient methods for measuring the thermal diffusivity of solid materials, have evolved into ultrafast laser flash methods by using picosecond or nanosecond pulse lasers as a heating source and a thermo-reflectance technique such as high-speed thermometry. In conventional ultrafast laser flash methods, thermal diffusivity is determined by fitting an analytical equation after single pulse heating to observe thermo-reflectance signals, although actual thermo-reflectance signals are observed after periodic pulse heating. This paper presents an exact analytical solution of the temperature response expressed by Fourier series for one-dimensional heat diffusion after periodic pulse heating. These Fourier coefficients are directly related to the Laplace transformation of the temperature response after single pulse heating. The signal observed for a 100 nm thick platinum thin film on a fused quartz substrate was analyzed by this Fourier expansion analysis and fitted by analytical equations with three parameters: heat diffusion time across thin film, the ratio of heat effusion of the substrate to thin film, and the amplitude of the signal over the entire range of pulse interval in the time domain. Robustness in determining the thermal diffusivity of the thin film by the ultrafast laser flash method can be improved by this new analysis approach.

Highlights

In order to measure the thermal diffusivity of dense solid materials, such as metals, alloys, ceramics, semiconductors, etc., the flash method has been established as the standard method.[1,2,3,4] It is popularly used and commercial instruments are widely available
In conventional ultrafast laser flash methods, thermal diffusivity is determined by fitting an analytical equation after single pulse heating to observe thermo-reflectance signals, actual thermo-reflectance signals are observed after periodic pulse heating
This paper presents an exact analytical solution of the temperature response expressed by Fourier series for one-dimensional heat diffusion after periodic pulse heating

Summary

Introduction

In order to measure the thermal diffusivity of dense solid materials, such as metals, alloys, ceramics, semiconductors, etc., the flash method has been established as the standard method.[1,2,3,4] It is popularly used and commercial instruments are widely available. The metrological standard of thermal diffusivity has been established in the metric convention by the Task group of thermophysical quantities of the Consultative Committee of Thermometry (CCT), International Bureau of Weight and Measures (BIPM).[5] Document standards are established internationally by ISO, ASTM, etc.[4]. Since the importance of thin films is rapidly growing in modern material science and industry, there are urgent needs to develop technology for measuring the thermophysical property of thin films,[6–8] and various experimental and theoretical studies have been made.[9–11]. In order to measure the cross-plane thermophysical properties of thin films from 10 nm to several micrometers thick by thermo-reflectance methods under the configuration of front heat– Since the importance of thin films is rapidly growing in modern material science and industry, there are urgent needs to develop technology for measuring the thermophysical property of thin films,[6–8] and various experimental and theoretical studies have been made.[9–11] In order to measure the cross-plane thermophysical properties of thin films from 10 nm to several micrometers thick by thermo-reflectance methods under the configuration of front heat–

Methods

Results

Discussion

Conclusion