Name: The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements (Video) | JoVE Journal
Uploaded: 2025-12-05T13:25:00.000+00:00
Duration: 9 min 10 s
Description: Learn the Frequency Domain Thermoreflectance technique for thermal property measurements using laser-based methods. This approach enables nondestructive microscale characterization of grain boundaries and thermal connectivity.

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Some of the authors were supported by partial funding from the Northwestern University Center for Engineering Sustainability and Resilience through a seed-funded project entitled &#34;Toward Engineering Metamaterials for Sustainable Energy Solutions: Local Thermal Properties of Grain Boundaries in Polycrystalline Materials&#34;.

The authors disclose no conflicts of interest.

The FDTR technique presented here is used to characterize the local substrate &#954; of a single-crystal silicon substrate and to map the &#954; distribution around an interface between two plasma-sintered silicon substrates. One critical aspect of the measurement is the use of the modeling fitting to determine the unknown thermal properties of the substrate and the transducer-substrate interface. The accuracy of the measurement depends on the proper selection of the spot size and modulation frequencies of the pump laser...

Thermal metrology and characterization tools are critical to the design and optimization of advanced materials used in, for example, thermoelectric generators and refrigeration applications1,2. Materials with low thermal conductivity and high electrical conductivity are generally preferred in these applications to maintain a large temperature gradient between hot and cold junctions and for efficient thermal-to-electrical energy conversion. Realizing these disparate properties in bulk crystalline materials is challenging. However, microstructure engineering through the introduction of point and interfacial defects (such as grain boundaries) is a promising direction to design high-performance thermoelectric materials1. A majority of the grain boundary (GB)-controlled thermal conductivity studies have mainly focused on the grain size as the fundamental structural property of importance2,3,4,5, as they lack the spatial resolution to probe a GB's local thermal environment.Thermal metrology at the micro- and nano-scale can provide local information on how heat flows near individual GBs. For example, recent microscale thermal imaging measurements by Isotta et al.6,7 revealed that the bulk thermal conductivity (κ) is locally suppressed near individual GBs in polycrystalline tin telluride (SnTe) and silicon. The observed κ suppression was correlated with different GB properties, including misorientation angle, roughness of the GB plane, nanotwinning density, and porosity. These types of measurements can facilitate tuning the bulk κ by providing local information on the microstructure-κ relationship. As interest in the local effects of defects on κ continues to grow, both computational8 and experimental9,10 approaches that provide insight into these contributions will become increasingly relevant.
Optical thermoreflectance methods11,12,13,14,15 are widely used for nondestructive thermal metrology of bulk solids, thin film superlattices, and interfaces. The methods use ultrafast or intensity-modulated lasers to locally heat a sample and probe their thermal response with high frequency or temporal resolution16, making them ideal for characterizing thermophysical properties. Thermoreflectance techniques, including time-domain thermoreflectance (TDTR)13,16 and frequency-domain thermoreflectance (FDTR)17,18, are the most common high-resolution thermal metrology methods. FDTR uses a focused intensity-modulated pump laser to generate a local periodic heat source in the sample. The resulting sample temperature change is transduced into a modulation frequency-dependent thermoreflectance signal that is recorded with a lock-in amplifier. To facilitate the measurement, a thin transducer layer with a large thermoreflectance coefficient19 at the probe laser wavelength is deposited on the sample. The TDTR technique, on the other hand, utilizes ultrafast pump and probe lasers, and the transient thermoreflectance signal of the transducer layer is monitored at different time delays between the pump and probe lasers, with picosecond time resolution.
Thermoreflectance techniques offer microscale lateral spatial resolution for probing thermophysical properties, and the measurements can be configured to characterize both isotropic and anisotropic κ of materials. Recently, Sood et al.10 used the TDTR technique to map local κ inhomogeneities in boron-doped polycrystalline diamond that were correlated with electron-backscatter diffraction imaging. In their measurements, regions in the sample with small grains had a lower κ compared to the bulk value. However, their measurements did not show whether the κ suppression was due to the small grain sizes or resistive GBs. Following this work, Isotta et al. showed that the local κ suppression around individual GBs, observed in microscale FDTR maps of SnTe, a mid-temperature thermoelectric material, is directly correlated to the GB misorientation angle6, so far only predicted theoretically 20,21,22,23 or rarely measured in fabricated GBs 24. Compared to the TDTR approach used by Sood et al., FDTR is less expensive and allows for the measurement of multiple properties, such as the substrate κ and constant-pressure heat capacity (C), and the film-substrate interface thermal conductance, in a single measurement that spans a broad frequency range25. Two-dimensional thermoreflectance phase maps obtained at multiple pump laser modulation frequencies with the highest sensitivity to the sample's thermal properties are converted to a κ image.
The thermoreflectance phase represents the phase shift between the periodic temperature oscillations at the surface of a transducer layer and the modulated heat source produced by the absorbed pump laser. In a standard FDTR approach, the pump and probe lasers are focused to the same point on the sample surface, and the thermoreflectance phase at that point is measured with a lock-in amplifier at different pump laser modulation frequencies. A layered heat conduction model is fitted to the measured data to determine the sample's thermal properties (i.e., κ, C, and the transducer-sample interface conductance)14. Variations of the standard FDTR approach allow for improved sensitivity of the measured thermoreflectance phase to the sample's anisotropic κ. These include the use of (i) spatially offset pump and probe lasers26, (ii) elliptical27 or line28 shaped pump laser-generated heat sources, and (iii) FDTR measurements with variable pump laser spot sizes29. Beyond thermal characterization of bulk properties, the FDTR technique can be used to characterize interface thermal properties30,31,32,33,34,35, since the thermal penetration depth of the heat source, defined as <img alt="Thermal penetration depth formula, \(d = \sqrt{\kappa/\pi fC}\), in heat transfer study." src="/files/ftp_upload/68908/68908eq1.jpg" style="opacity: 0.9; margin: 0px;" data-altupdatedat="1783396841000" data-alt="Equation 1"> depends on the pump laser modulation frequency (f). The interface causes a thermal resistance due to the transmission and reflection of heat carriers (i.e., electrons and phonons)36. The resistance is characterized in FDTR experiments in terms of an interface thermal conductance. FDTR measurements of the interface thermal conductance of self-assembled monolayers33,35, metal-substrate interfaces37,38,and thin interface layers39 have been reported in the literature. Finally, FDTR measurements with thin magnetic transducer films were recently shown to allow for the characterization of anisotropic κ of two-dimensional materials40.
This article provides a detailed description of the procedures involved in a FDTR measurement that utilizes coaxially focused pump and probe lasers on the transducer surface. Representative measurements of local κ of a bulk silicon substrate are provided, and the measurement uncertainties are quantified. Finally, we provide a simple example that illustrates the FDTR imaging of the local κ near a single vertical interface between two (100) single-crystal silicon substrates bonded by surface activated bonding (SAB).

<table><tbody><tr><td>3-Axis NanoMax Stage, Stepper Motor Drives</td><td>Thorlabs</td><td>MAX383</td><td>Sample translation stage</td></tr><tr><td>532 nm Continuous Wave Laser</td><td>SpectraPhysics</td><td>SPFL 532-20</td><td>Probe laser</td></tr><tr><td>Achromatic Doublet, f=150mm, 2&quot;</td><td>Thorlabs</td><td>AC508-150-C-ML</td><td>Relay lenses in the 4-f optical imaging system used to image the center of the Gimbal scanner to the back aperture of the microscope objective</td></tr><tr><td>Beamsplitter Cube</td><td>Thorlabs</td><td>BS019</td><td>Optics</td></tr><tr><td>Broadband Power/Energy Meter</td><td>Melles Griot</td><td>13PEM001</td><td>To measure laser powers</td></tr><tr><td>Closed-Loop Picomotor Controller</td><td>New Focus</td><td>8743-CL</td><td>For scanning the pump beam on the sample surface</td></tr><tr><td>Color CMOS Camera</td><td>Thorlabs</td><td>CS165CU1</td><td>For imaging the sample surface</td></tr><tr><td>Current-Limited Power Supply</td><td>New Focus</td><td>901</td><td>To power the high-speed photodetector</td></tr><tr><td>Fiber Amplifier</td><td>IPG Photonics</td><td>LDR-3U</td><td>Pump laser</td></tr><tr><td>Free-Space Isolator, 1550 nm</td><td>Thorlabs</td><td>IO-5-1550-HP</td><td>For preventing back reflections of the pump laser into the fiber amplifier</td></tr><tr><td>Free-Space Isolator, 532 nm</td><td>Thorlabs</td><td>IO-3-532-LP</td><td>For preventing back reflections of the probe laser into the diode laser</td></tr><tr><td>Function / Arbitrary Waveform Generator</td><td>Agilent</td><td>33220A</td><td>For modulating the pump laser intensity</td></tr><tr><td>Gimbal Optic Mount</td><td>Newport</td><td>605-2</td><td>For scanning the pump beam on the sample surface</td></tr><tr><td>Gold Mirrors, 1&quot;</td><td>Thorlabs</td><td>PF10-03-M01</td><td>High reflectivity mirrors for the pump laser</td></tr><tr><td>Half Waveplate (1550)</td><td>Thorlabs</td><td>WPH05M-1550</td><td>Polarization optics</td></tr><tr><td>Half Waveplate (532 nm)</td><td>Thorlabs</td><td></td><td>Polarization optics</td></tr><tr><td>IR 1 GHz Low Noise Photoreceiver</td><td>New Focus</td><td>1611</td><td>For monitoring the modulated intensity of the pump laser</td></tr><tr><td>Laser Diode Controller</td><td>ILX Lightwave&amp;nbsp;</td><td>LDC-3742B</td><td>For controlling the seed pump laser intensity</td></tr><tr><td>Lock-In Amplifier</td><td>Stanford Research&lt;br/&gt; Systems</td><td>SR844</td><td>For high-frequency measurements</td></tr><tr><td>Lock-In Amplifier</td><td>Stanford Research&lt;br/&gt; Systems</td><td>SR830</td><td>For low-frequency measurements</td></tr><tr><td>Mechanical Chopper Controller</td><td>Stanford Research Systems</td><td>SR540</td><td>For modulating the probe beam intensity</td></tr><tr><td>MgO:PPLN Crystal</td><td>Covesion</td><td></td><td>Second harmonic generation crystal for frequency doubling the 1550 nm pump laser to the 775 nm reference light source</td></tr><tr><td>Polarizing Beamsplitter Cube</td><td>Thorlabs</td><td>PBS254</td><td>Polarization optics</td></tr><tr><td>RF Signal Generator</td><td>Agilent</td><td>N9310A</td><td>For modulating the pump laser intensity</td></tr><tr><td>Stepper Motor Controller</td><td>Thorlabs</td><td>BSC200</td><td>Controller for the sample translation stage</td></tr><tr><td>Temperature Controller</td><td>Covesion</td><td>OC1</td><td>For controlling the MgO:PPLN Crystal temperature</td></tr><tr><td>Visible 1 GHz Low Noise Photoreceiver</td><td>New Focus</td><td>1601</td><td>For monitoring the thermoreflectance signal</td></tr></tbody></table>

the frequency domain thermoreflectance technique for thermal property measurements

The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements

The frequency domain thermoreflectance (FDTR) technique is a nondestructive method for thermal characterization and imaging with microscale spatial resolution. The technique relies on a pump laser to generate a modulated temperature change in a sample and a probe laser to monitor the sample&#39;s local thermal response. The sample&#39;s thermal properties are determined by fitting a thermal model to the sample&#39;s thermoreflectance response. This article presents detailed protocols for implementing the technique and conducting local measurements of a substrate&#39;s local thermal conductivity. Special attention is devoted to discussing how the measurement is influenced by the laser source parameters, error sources in an FDTR measurement, and quantifying the measurement uncertainty. Finally, we discuss a thermal conductivity imaging experiment conducted near a single vertical interface between two surface-activated bonded single-crystal silicon substrates. The thermal conductivity at the interface is suppressed by 3% compared to the bulk value in the adjoining single crystals. The ability to probe interface thermal properties with the FDTR technique may facilitate local studies of heat flow around individual grain boundaries, particularly in thermoelectric materials, where they can be tuned to optimize the performance of thermoelectric devices.

Point measurements
The goal of the point measurement presented here is to determine the room-temperature thermal conductivity (κ) of (100) single-crystal silicon based on the measured thermoreflectance phase of the gold transducer film on the sample. A two-layer heat conduction model is fitted to the measured phase data to determine the best-fit substrate κ and the transducer-silicon interface thermal conductance (G). The measured transducer thickness, thermal conduct...

This article presents the Frequency Domain Thermoreflectance (FDTR) technique for local nondestructive thermal characterization and imaging.

The frequency domain thermoreflectance (FDTR) technique is a nondestructive method for thermal characterization and imaging with microscale spatial ...

We study how microscale defects in materials, such as grain boundaries, affect a material thermal connectivity with micron scale spatial resolution. The continuum scale assumption that thermal properties are size independent breaks down as small length scales. To begin, turn the power switch of the 532 nanometer diode laser to the on position to activate the power supply.Wait until the enable light turns on, indicating that the laser crystal's temperature is stable. Then, turn the laser switch to initiate the emission of the 532 nanometer laser and use a power meter to confirm that the input probe laser power is between 20 and 30 milliwatts before proceeding. Next, turn on the pump laser diode controller.Enable thermoelectric cooling by setting the correct resistance value according to the diode laser specifications. After the temperature stabilizes, switch on the laser current, then turn on the Erbium-Doped Fiber Amplifier, or EDFA and set the output power to the desired value in watts. Press the emission button.Set the radio frequency, or RF, RF amplitude and bias voltage on the signal generator to modulate the pump laser intensity. Now, turn on the lock-in amplifier and photo detector. Ensure the reference port is connected to the RF signal generator output and the signal input port is connected to the photo detector.Turn on the temperature controller for the Periodically Poled Lithium Niobate crystal and enable the Proportional Integral Derivative, or PID control. Mount the sample on the multi-axis precision stage equipped with a micrometer knob for Z position adjustment. Use thin double-sided tape to secure the sample and prevent it from sliding during measurement.Next, mount the cold mirror above the objective to begin focusing the lasers on the sample surface. Observe the sample surface through the CCD camera and adjust the Z knob on the stage until the surface comes into focus on the live camera feed. Continue to fine tune until the laser spot reaches its minimum size.Once in focus, remove the cold mirror. Now, using the lab view virtual instrument, adjust the tilt angles of the gimbal steering mirror to align the pump laser along the optical axis of the probe laser. Monitor the thermo reflectance amplitude and look for the maximum signal to confirm the lasers are coincident on the sample surface.Select the desired pump power level and mount the sample on the multi-axis translation stage. View the sample through the CCD camera and adjust its position to ensure that the probe laser is reflected at a clean, impurity free spot on the surface. Perform the focus and alignment procedures as demonstrated earlier.Decide on the frequency range for the point measurement. Verify that the chosen thermal diffusion model is sensitive and appropriate for the material properties within that range. Select the proper sensitivity level on the lock-in amplifier for the chosen frequency range.Program the point measurement lab view virtual instrument with the lock-in sensitivity level, frequency range, and total number of frequencies to be measured. If required, configure multiple stages with varying sensitivity levels to optimize the signal to noise ratio. Run the point measurement and save the recorded data as a text file.Record the phase data from the lock-in amplifier three times once for the probe laser signal, once for the reference laser signal, and once for the noise. Block the unused beams during each recording and block both beams when collecting noise data. Select the desired pump power level.Mount the sample on the multi-axis translation stage and position the laser spot directly over the intended measurement area. Ensure that the selected region is free of dirt and irregularities in surface roughness. Avoid moving the translation axes of the stepper motor stage to their extremes to prevent coupling with the Z-axis.Now program the measurement area into the image measurement lab view virtual instrument. Run a quick scan over the designated area, for example, three steps in both the X and Y directions, while monitoring the CCD camera live feed. Identify and confirm the precise boundaries of the measurement area.Complete the focus and alignment procedure. Select at least five frequencies at which the sample will be scanned. Verify that the chosen thermal model is appropriately sensitive to the samples measured properties within this frequency range.Lock the probe laser and record the endphase X and quadrature Y readings for the reference laser from the lock and amplifier display. Then, block both the probe and reference lasers to capture the X and Y noise readings. When data collection is complete, unblock the probe laser.Input the number of steps representing the number of point measurements for each scan direction into the lab view six and start the map measurement. Once the map measurement is complete, repeat the procedure for recording x and Y readings for both the reference and noise signals. Finally, calculate the average X and Y values from before and after the measurement for both signals to obtain the final corrected results.The gold transducer layer thickness measured using the picosecond ultrasonic method showed coherent oscillations in the time domain waveform with a corresponding fourier amplitude peak at 29 gigahertz, giving a thickness of around 55.5 nanometers. Knife edge measurements determined the pomp and probe laser spot sizes with average one by E radii of approximately 10 micrometers along both X and Y directions confirming circular symmetry of the laser spots. The thermoreflectance face sensitivity curves demonstrated distinct frequency-dependent behavior for the substrate thermal conductivity and interfacial conductance, confirming uncorrelated properties between 100 kilohertz and 10 megahertz.The measured thermo reflectance phase decreased with increasing modulation frequency and showed a turning point near one megahertz where heat flow transitioned from three dimensional to one dimensional. Monte Carlo simulations of probe spot size uncertainty produced Gaussian distributions for fitted substrate thermal conductivity and interfacial conductance values with corresponding uncertainties of around five and 3.3%Increasing uncertainties in model inputs led to linear increases in uncertainty of fitted thermal properties with pump and probe spot sizes contributing the largest propagation errors. Local thermal conductivity mapping across a vertical silicon interface showed a 3%reduction in conductivity at the interface, while the interfacial conductance map remained nearly uniform.We have measured thermal connectivity suppression across grain boundaries in silicon and thermoelectric and demonstrated that the amount of suppression correlates with the structural features of the boundary, such as misorientation angle. We can measure thermal conductivity on a micron scale rather than relying on bulk measurements provided by, for example, laser flash analysis, which cannot distinguish local heterogeneities on the sample. Grain boundaries are typically assumed to be structureless defects.However, we use FDTR to show that grain boundaries have unique thermal properties, which depend on their structure.

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Learn the Frequency Domain Thermoreflectance technique for thermal property measurements using laser-based methods. This approach enables nondestructive microscale characterization of grain boundaries and thermal connectivity.

The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements

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