Frequency-domain probe beam deflection method for measurement of thermal conductivity of materials on micron length scale

TL;DR

This paper introduces a frequency-domain probe beam deflection method for measuring thermal conductivity at micron scales, overcoming limitations of traditional thermoreflectance techniques by leveraging thermoelastic deformation signals.

Contribution

The authors develop an analytical model for probe beam deflection based on thermoelastic effects, enabling accurate thermal conductivity measurements without strict optical property constraints.

Findings

Achieves thermal conductivity measurements within 6% of accepted values.

Effective for materials from polymers to gold, spanning 0.1-300 W/(m K).

Reduces sensitivity to laser beam radii and coating requirements.

Abstract

Time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance (FDTR) have been widely used for non-contact measurement of anisotropic thermal conductivity of materials with high spatial resolution. However, the requirement of high thermoreflectance coefficient restricts the choice of metal coating and laser wavelength. The accuracy of the measurement is often limited by the high sensitivity to the radii of the laser beams. We describe an alternative frequency-domain pump-probe technique based on probe beam deflection. The beam deflection is primarily caused by thermoelastic deformation of the sample surface with a magnitude determined by the thermal expansion coefficient of the bulk material to measure. We derive an analytical solution to the coupled elasticity and heat diffusion equations for periodic heating of a multilayer sample with anisotropic elastic constants, thermal conductivity, and thermal expansion coefficients. In most cases, a simplified model can reliably describe the frequency dependence of the beam deflection signal without knowledge of the elastic constants and thermal expansion coefficients of the material. The magnitude of the probe beam deflection signal is larger than the maximum magnitude achievable by thermoreflectance detection of surface temperatures if the thermal expansion coefficient is greater than 5x10^(-6) /K. The sensitivity to laser beam radii is suppressed when a larger beam offset is used. We find nearly perfect matching of the measured signal and model prediction, and measure thermal conductivities within 6% of accepted values for materials spanning the range of polymers to gold, 0.1 - 300 W/(m K).