Introduction to frequency-domain thermoreflectance (FDTR)



What is frequency-domain thermoreflectance (FDTR)?


Time-domain thermoreflectance (TDTR) is an effective tool for characterizing the thermal properties of bulk and thin films. However, imperfections of the mechanical moving stage can introduce measurement errors, and ultrafast pulsed lasers are expensive.


Frequency-domain thermoreflectance (FDTR) is a variation of TDTR where the thermoreflectance signals are measured by varying the modulation frequency of the pump beam instead of the delay time between the pump beam and the probe beam. FDTR is used to characterize the various thermal properties of bulk and thin films without a moving stage and ultrafast pulsed laser; thus, the disadvantages of TDTR are eliminated.


In both TDTR and FDTR, the sensitivity of the measurement signal to the thermal properties is affected by the modulation frequency. For a highly accurate TDTR measurement, the modulation frequency must be properly selected according to the purpose of the analysis, which is not a problem for FDTR.




Overview of FDTR measurement


There are two possible experimental setups for FDTR: a pulsed-laser system and a continuous-wave (CW) laser system.


Pulsed-laser FDTR uses almost the same setup as TDTR; hence, both FDTR and TDTR can be conducted. The frequency of the pump beam is modulated in the range of 0.1 - 20 MHz, while the position of the mechanical moving stage is fixed at a certain delay time, avoiding all the artifacts involved in the stage movements of TDTR.


(Click "Basic principles of time-domain thermoreflectance (TDTR)" for further information.)


In CW-laser FDTR, two CW lasers are used for the pump and probe beams. The frequency of the pump beam is modulated by the EOM and generates heat flux on the sample surface. The probe beam is focused by the same objective lens as the pump beam to detect the thermoreflectance signals. Because it is not necessary to use an ultrafast pulsed laser, the CW FDTR can be configured at a low cost.


The evaluation process for the thermal properties is identical between TDTR and FDTR.


Theoretically, in contrast to pulsed TDTR/FDTR, a pump beam of CW FDTR can be modulated at an infinite frequency. However, in practice, the modulation frequency is limited to < 20 MHz because of the decreasing signal intensity and the presence of noise at high frequencies.


Broadband frequency-domain thermoreflectance (BB-FDTR) has been implemented to eliminate this frequency limitation and extend it to 200 MHz using heterodyne detection.



Advantages of FDTR


  • In addition to bulk samples, thin films having thicknesses ranging from tens of nanometers to a few micrometers can be measured.
  • By utilizing different laser spot sizes and modulation frequencies, various thermal properties, such as the cross-plane thermal conductivity Kz, in-plane thermal conductivity Kr, interface thermal conductance G, and heat capacity C, can be evaluated.
  • Non-contact measurements work either under regular ambient conditions or through the window of a vacuum chamber.
  • In contrast to TDTR, FDTR avoids the complexity of a long mechanical time delay. Additionally, an expensive pulsed laser is not necessary.
  • Frequency selection, which is closely related to the unknowns and consequently difficult to perform before TDTR measurement, can be avoided in FDTR measurements.

    • Jan. 2022