Truncated Levy model for TDTR

By Amr Mohammed1, Ali Shakouri1

1. Purdue University

Simulate the transient thermal response of materials probed using optical pump probe experiment (TDTR)

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Version 1.0 - published on 20 Feb 2017

doi:10.4231/D3542J93X cite this

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Time domain thermoreflectance is an optical pump-probe method used to measure the thermal properties of materials specially thin films.  A fs laser pulse is splitted into modulared pump beam at frequency (fmod) to heat the surface of the metal transducer deposited on  sample and probe beam which is used to record the thermal decay through lock-in detection of the reflected signal. A mechanical delay line is used to vary the arrival times between the pump and the probe beams at the sample surface with picosecond resolution [1].

Standard mathematical manipulations of the single pulse response provide theoretical model expressions for the in-phase Vin(tpp) and out-of-phase Vout(tpp) lock-in signal components at a given modulation frequency as a function of pump-probe delay (tpp). These are then fitted to the measured counterparts to identify the thermal properties of the sample. The actual identification process is typically performed on the ratio −Vin/Vout. This acts as signal normalization and increases the signal to noise ratio.

Conventional Fourier analysis first extracts the thermal resistivity rms of the metal-semiconductor interface from data at high modulation frequency, where the sensitivity to rms is highest, and then identifies effective thermal conductivities keff(fmod).  

Developing models that account accurately for ballistic heat transport becomes essential to enable innovative device designs for thermoelectrics as well as ultrafast thermal management of high power electronics and optoelectronics. This can also be used for advanced phonon spectroscopy.  A new model based on Truncated Lévy (TL) flight is introduced to describe the phonon random walk[2]. We can extract the fractal diffusion exponent  for several alloys as evidence for anomalous diffusion (superdiffusion) at early times. This approach captures the ballistic heat transport at early time/ short length scales. The truncation at a characteristic length (uBD) e to converge to normal diffusion is necessary to extract the bulk thermal conductivity.


[1] D. G. Cahill, Rev. Sci. Instrum. 75, 5119 (2004).

[2] B. Vermeersch, A. M. S. Mohammed, G. Pernot, Y. R. Koh, and A. Shakouri,  Phys. Rev. B 91, 085203 (2015).

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Researchers should cite this work as follows:

  • Amr Mohammed; Ali Shakouri (2017), "Truncated Levy model for TDTR," (DOI: 10.4231/D3542J93X).

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