The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements

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.