Sensing depths in frequency domain thermoreflectance

Abstract

A method is developed to calculate the length into a sample to which a Frequency Domain Thermoreflectance (FDTR) measurement is sensitive. Sensing depth and sensing radius are defined as limiting cases for the spherically spreading FDTR measurement. A finite element model for FDTR measurements is developed in COMSOL multiphysics and used to calculate sensing depth and sensing radius for silicon and silicon dioxide samples for a variety of frequencies and laser spot sizes. The model is compared to experimental FDTR measurements. Design recommendations for sample thickness are made for experiments where semi-infinite sample depth is desirable. For measurements using a metal transducer layer, the recommended sample thickness is three thermal penetration depths, as calculated from the lowest measurement frequency.

Thermal Transport and Mechanical Stress Mapping of a Compression Bonded GaN/Diamond Interface for Vertical Power Devices

“…To better understand how the phase response evolves as a function of frequency, we examined the sensing depth of FDTR, determined by the thermal properties and pump frequency. The conversion of pump frequency to sensing depth is detailed in ref and is adapted for the GaN/diamond system (see the Supporting Information for more details), where the sensing depth for each frequency is shown in Table . This sample was previously determined to have a GaN thickness of ≈15 μm, indicating that the 162 kHz phase map does not reach the Au/Au interface, while frequencies less than 81 kHz penetrate through the interface and into the diamond.…”

“…FDTR hyperspectral imaging is leveraged to investigate the thermal performance of the GaN/diamond interface resulting from the room-temperature Ar-activated Au compression bond. FDTR is a pump–probe laser technique sensitive to the depth-dependent thermal properties of a sample. − The pump laser (λ pu = 488 nm), whose intensity is periodically modulated from f = 1 kHz up to 60 MHz, provides a periodic surface heat flux, while the continuous wave probe laser (λ pr = 532 nm) monitors the resulting temperature fluctuations via the thermoreflectance effect. Both the pump and probe beams are focused through a 5× objective to 1/ e 2 spot sizes of 7.03 and 5.38 μm, respectively, measured via knife edge, as shown in Figure S3 .…”

Inversion for Thermal Properties with Frequency Domain Thermoreflectance

“…Recent work has combined these techniques to better ascertain depth sensitivity of FDTR. 23 However, more complicated geometries, such as those in HI systems, remain elusive for several reasons. First, with the high frequencies involved (often up to 60 MHz), the finite element method (FEM) requires a highly refined mesh, resulting in many degrees of freedom and an extreme computational burden.…”

“…Pump–probe thermoreflectance techniques have a previously demonstrated ability to map thermal properties of materials, including rich literature on using time-domain thermoreflectance (TDTR) for thermal conductivity mapping near the surface of a sample, − as well as mapping TBC between thin films . In particular, frequency-domain thermoreflectance (FDTR) − has been shown to be sensitive to subsurface interfaces located up to hundreds of microns below the surface of semiconductor materials, opening the door to damage detection on scales not possible with TDTR.…”

“…To process FDTR data, analytical solutions for time-harmonic temperatures based on Hankel transforms, as well as numerical simulations for cylindrically symmetric geometries, have been successful at determining thermophysical properties. Recent work has combined these techniques to better ascertain depth sensitivity of FDTR . However, more complicated geometries, such as those in HI systems, remain elusive for several reasons.…”