Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials

In the paper

“Over the past two decades, ultrafast laser-based time-domain thermoreflectance (TDTR) has emerged and evolved as a reliable, powerful, and versatile technique to measure the thermal properties of a wide range of bulk and thin film materials and their interfaces.”

• Also stated in: § I. INTRODUCTION · plain

  “Over the past two decades, ultrafast laser-based transient thermoreflectance (TTR) methods have emerged and evolved into a powerful and versatile technique 22-25 for characterizing thermal properties of a large variety of samples including both thin films 26-31 with a thickness down to ~20 nm, 26, 27 and bulk materials 32-35 .”

What the sources say

• ?Not checked — no full text of the sourcecites [22] 2004, Rev. Sci. Instrum. source
• ?Not checked — no full text of the sourcecites [23] 2008, Rev. Sci. Instrum. source
• ?Not checked — no full text of the sourcecites [24] 2008, Rev. Sci. Instrum. source
• ?Not checked — no full text of the sourcecites [25] 2010, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [26] 2007, Science source
• ?Not checked — no full text of the sourcecites [27] 2012, Science source
• ?Not checked — no full text of the sourcecites [28] 2010, Appl. Phys. Lett. source
• ?Not checked — no full text of the sourcecites [29] 2012, Phys. Rev. Lett. source
• ?Not checked — no full text of the sourcecites [30] 2016, Adv. Mater. Interfaces source
• Partly supported

  The paper calls TDTR a standard thermal-characterization method and uses it to measure thermal conductivity in graphite films (p. 3). It also fits interface thermal conductance in a multilayer sample (p. 4). It does not establish the claimed two-decade evolution or use across a wide range of bulk and thin-film materials. (LLM, conf=0.85)

  cites [31] 2016, Nano Lett. sourceExperimental — accuracy not yet measured

In the paper

“This approach has the merit of simple configuration and works well for optically smooth samples with surface roughness <15 nm. 12”

What the sources say

• Partly supported

  The Implementation section identifies spatial separation with an aperture as a way to suppress the reflected pump beam. The Limitations section gives <15 nm rms roughness as an approximate rule of thumb for TDTR measurements generally, not a performance threshold specifically established for spatial separation. The source also does not describe that approach as having a simple configuration. Page numbers were not provided for these passages. (LLM, conf=0.84)

  cites [12] 2014, Appl. Phys. Rev. sourceExperimental — accuracy not yet measured

In the paper

“Similarly, while TDTR can be used to study non-equilibrium phenomena such as quasi-ballistic phonon transport 90, 91, 109-111 and electronphonon coupling 55 due to its ability to detect temperature evolutions at micrometer-scale and picosecond-scale resolutions, the majority of the experimental work in the literature deduced thermal properties based on Fourier's”

What the sources say

• ?Not checked — no full text of the sourcecites [90] 2007, Phys. Rev. B source
• Partly supported

  The paper’s main text (page not specified in our copy) says that transient thermoreflectance extracts thermal properties by fitting temperature-decay data to a thermal model, and it reports fitted thermal conductivities that differ with heater size. It does not establish that a majority of experimental work in the literature used Fourier’s law with an effective thermal conductivity. (LLM, conf=0.82)

  cites [91] 2011, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Supported

  The passage labeled Abstract says experimental characterization is usually carried out by fitting measured thermal responses to a conventional Fourier diffusion model. The Figure 1 caption adds that conventional approaches extract effective thermal parameters, including conductivity. Together, these support the paraphrase about the majority of experimental work. (LLM, conf=0.90)

  cites [109] 2014, Phys. Rev. B source
• Partly supported

  The Implications for transient laser thermoreflectometry section (p. 7) says many observations of quasi-ballistic heat flow are interpreted with modified Fourier theory using a reduced effective thermal conductivity. The Introduction (p. 1) calls such models conventional for experimental analysis, but the paper does not establish that a majority of experimental work in the literature uses them. (LLM, conf=0.82)

  cites [110] 2015, Phys. Rev. B sourceExperimental — accuracy not yet measured
• Supported

  The Introduction (p. 1) says that most experiments showing nondiffusive thermal transport are interpreted with modified Fourier theory—a regular diffusion model with adjusted thermal parameters. The opening summary (p. 1) states this more specifically as Fourier theory with modified thermal conductivity for nearly all experimental observations of quasi-ballistic heat flow. (LLM, conf=0.94)

  cites [111] 2015, Phys. Rev. B source
• ?Not checked — no full text of the sourcecites [55] 2015, J. Appl. Phys. source

In the paper

“Therefore, TDTR is often used to measure the through-plane thermal conductivity Kz of the sample and the transducer/sample interface conductance G without much elaboration.”

What the sources say

• Supported

  The Advances section describes TDTR as a general-purpose method for measuring thermal conductivity and interface conductance. The Limitations section says it is primarily sensitive to through-thickness conductivity, while Signal analysis and sensitivities discusses its sensitivity to interface conductance G. Page numbers are unavailable in our copy; “without much elaboration” reads as the citing authors’ presentation, not a separate measurement claim. (LLM, conf=0.91)

  cites [12] 2014, Appl. Phys. Rev. source
• ?Not checked — no full text of the sourcecites [40] 2005, Phys. Rev. B source
• ?Not checked — no full text of the sourcecites [120] 2002, J. Heat Transfer source
• ?Not checked — no full text of the sourcecites [121] 2005, Phys. Rev. B source
• ?Not checked — no full text of the sourcecites [122] 2007, Acta Mater. source
• ?Not checked — no full text of the sourcecites [123] 2009, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [124] 2011, Adv. Mater. source
• ?Not checked — no full text of the sourcecites [125] 2013, Phys. Rev. B source

In the paper

“Meanwhile, the small thermal mass of the transducer layer also enables an enhanced sensitivity to the interface thermal conductance 150 when the thermal conductivity of the substrate is small.”

What the sources say

• Supported

  The Conclusion states that reduced-transducer-mass TR-MOKE increases sensitivity to the conductance of interfaces with low-thermal-conductivity materials. Section D explains that reducing transducer thickness increases sensitivity because the smaller thermal mass produces a larger temperature and signal change for heat crossing the interface. (LLM, conf=0.94)

  cites [150] 2017, Phys. Rev. B source

In the paper

“TDTR can also incorporate a novel temperature sensing technique utilizing time-resolved magneto-optic Kerr effect (TR-MOKE). 34, 149, 150”

What the sources say

• Supported

  The Introduction describes MOKE as an alternative way to probe surface temperature. Section B, Experimental setup, says the TR-MOKE setup is the same as their two-tint TDTR setup except for the detection scheme, supporting the claim that TDTR can incorporate TR-MOKE temperature sensing. (LLM, conf=0.94)

  cites [34] 2014, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [149] 2016, J. Phys. Chem. Lett. source
• Supported

  The Setup section describes a shared pump–probe apparatus with detection schemes for both TDTR and TR-MOKE, and explains how the TR-MOKE signal is isolated for thermometry. This supports the claim that TR-MOKE can serve as a temperature-sensing technique in a TDTR-style setup, although the paper names the two detection schemes separately. No page number is available in our copy. (LLM, conf=0.88)

  cites [150] 2017, Phys. Rev. B source

In the paper

“A thinner transducer with a lower thermal conductivity cam minimize lateral heat flow in the transducer layer and thus enhancing the measurement sensitivity to the in-plane thermal conductivity. 34, 87”

What the sources say

• Supported

  In II. Experimental Details A. Analysis (page not provided), the authors find that a thinner transducer lowers sensitivity to uncertainties in the transducer’s thermal conductivity and recommend a thinner, lower-conductivity transducer to reduce error in measuring the sample’s in-plane conductivity. This supports the citing sentence’s practical point; reduced lateral heat flow is its physical explanation rather than wording used in the passage. (LLM, conf=0.85)

  cites [34] 2014, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [87] 2014, Rev. Sci. Instrum. source

In the paper

“To overcome this challenge, a dual-frequency TDTR approach has been developed 184 that takes the advantage of the different frequency dependence in the sensitivities of the different parameters.”

What the sources say

• Supported

  Section B (pp. 7–8) reports that TDTR sensitivity to cross-plane thermal conductivity changes substantially with modulation frequency, while sensitivity to Al-film thickness changes only weakly. The authors explicitly say they take advantage of this difference to propose an additional measurement at a lower frequency. (LLM, conf=0.94)

  cites [184] 2016, Rev. Sci. Instrum. source

In the paper

“Dilhaire and co-workers 172, 173 proposed a high-throughput time-domain thermoreflectance (HT-TDTR) technique that combines ASOPS with high-frequency modulation of the pump beam, enabling fast and accurate measurements of thermal properties.”

What the sources say

• ?Not checked — no full text of the sourcecites [172] 2011, J. Appl. Phys. source
• Supported

  The Introduction (p. 2) says HT-TDTR improves an ASOPS-based setup. The setup description (p. 3) specifies pump-beam amplitude modulation at 9.76 MHz, and the performance discussion (p. 5) reports faster measurements and improved accuracy. (LLM, conf=0.93)

  cites [173] 2017, Rev. Sci. Instrum. source

In the paper

“The Brillouin scattering arises from the interaction between the reflected probe beam and the acoustic waves inside the black phosphorus sample caused by the birefringence originated from the inplane anisotropy in black phosphorus. 152, 153”

What the sources say

• ?Not checked — no full text of the sourcecites [152] 2001, J. Appl. Phys. source
• Partly supported

  The Abstract (page not provided) supports the general point that Brillouin scattering arises from interaction between light and an acoustic wave. It does not support the claim about a reflected probe beam in black phosphorus or birefringence caused by that material’s in-plane anisotropy; the paper instead studies silica nanowires, as stated in the Discussion (page not provided). (LLM, conf=0.88)

  cites [153] 2016, Nat. Commun. sourceExperimental — accuracy not yet measured

In the paper

“This method has then been successfully applied in several studies of anisotropic materials including both layered two-dimensional materials (such as transition metal dichalcogenides 35 and their alloys 192 and boron nitride nanosheets 193 ) and bulk crystals (such as silicon carbide 33 ).”

What the sources say

• ?Not checked — no full text of the sourcecites [35] 2017, Adv. Mater. source
• Supported

  The citation to this paper is attached to the example of transition-metal dichalcogenide alloys, not to bulk crystals. In the supplied passage labeled Abstract, the authors describe using different TDTR laser spot sizes to measure cross-plane and in-plane thermal conductivity in layered WSe₂(1−x)Te₂x alloys. The bulk-crystal example has a separate citation. (LLM, conf=0.94)

  cites [192] 2018, Appl. Phys. Lett. source
• ?Not checked — no full text of the sourcecites [193] 2018, Nanoscale source

In the paper

“This dual-frequency approach has been shown to be able to improve the accuracy in determining Kz of thin films by ൎ 3 times”

What the sources say

• Supported

  The Summary (p. 15) states that dual-frequency TDTR can improve the accuracy of cross-plane thermal-conductivity measurements by up to approximately three times. It specifies that this improvement applies to suitable high-thermal-conductivity thin films on low-thermal-conductivity substrates. (LLM, conf=0.92)

  cites [184] 2016, Rev. Sci. Instrum. source

In the paper

“By changing the relative size of laser spot as compared to the thermal penetration depth, as illustrated in Figure 18(a), TDTR can measure both the in-plane and the through-plane thermal conductivities.”

What the sources say

• Supported

  The variable-spot-size TDTR section (p. 6) explains that a spot much larger than the thermal penetration depth makes the signal predominantly sensitive to through-plane conductivity, while a smaller spot makes it sensitive to both directions. It states that two measurements with different spot sizes can therefore determine both conductivities. (LLM, conf=0.94)

  cites [37] 2017, Rev. Sci. Instrum. source

In the paper

“both with their intrinsic limitations that impair the accuracy of their measurements. 221, 222”

What the sources say

• Supported

  Section 2.2, “Problems in the existing experimental setups,” describes substantial measurement uncertainty in confocal micro-Raman spectroscopy and uncertainty from contact resistance in the thermal bridge method. These are limitations affecting measurements of thermal conductivity in low-dimensional and 2D materials. (LLM, conf=0.93)

  cites [221] 2016, J. Phys. Condens. Matter. source
• ?Not checked — no full text of the sourcecites [222] 2016, Phys. Rev. B source

In the paper

“Reconstructing the phonon MFP spectrum [ i.e . ߶ ሺΛሻ or ߙ ሺΛሻ ] from the measured ܭ ஺ ሺ ܮ ௖ ሻ and the derived ܵ ቀ ஃ ௅೎ ቁ is thus an inverse problem of Eq.(4.14) that involves complex optimization. 203-205”

What the sources say

• Supported

  The paper’s inverse-problem formulation (passage 2) relates measured thermal conductivities and the suppression function to the MFP distribution and explicitly calls reconstruction an inverse problem. Its numerical-solution discussion (passages 5 and 7) describes the problem as ill-posed and solves it through constrained convex optimization. The supplied passages have no page labels. (LLM, conf=0.91)

  cites [203] 2012, Phys. Rev. Lett. source
• ?Not checked — no full text of the sourcecites [204] 2014, Phys. Rev. B source
• Partly supported

  The discussion on p. 2 says a phonon MFP distribution can be obtained from experimentally measured thermal conductivity using a suppression function. The optimization described on p. 7 concerns a trial function for solving the BTE, not optimization of the inverse MFP reconstruction. The paper therefore supports the reconstruction premise but not the claim that this inverse problem involves complex optimization. (LLM, conf=0.86)

  cites [205] 2016, Phys. Rev. B sourceExperimental — accuracy not yet measured

In the paper

“So far, the thermal conductivities of monolayer or few-layer 2D materials have been dominantly measured by micro-Raman spectroscopy and thermal bridge method”

What the sources say

• Supported

  Section 2.1.1 calls confocal micro-Raman one of the most commonly used techniques for measuring thermal conductivity in 2D materials. Section 3.2 reports thermal-bridge measurements of few-layer h-BN, while Section 2.1.3 explains why several other techniques have not been used to measure in-plane thermal conductivity in 2D materials. Together, these passages support the broad statement about the dominant methods; the copy provides no numerical breakdown. (LLM, conf=0.88)

  cites [221] 2016, J. Phys. Condens. Matter. source
• ?Not checked — no full text of the sourcecites [222] 2016, Phys. Rev. B source

In the paper

“A higher interface density generally reduces the Kz of superlattices (see Figure 6(c)) due to the interface thermal resistance introduced by the periodic boundaries. 79, 137”

What the sources say

• ?Not checked — no full text of the sourcecites [79] 2004, Science source
• ?Not checked — no full text of the sourcecites [137] 2018, Phys. Rev. B source

In the paper

“The reliability of the TDTR technique for thermal conductivity characterization has been verified on a series of standard bulk material samples over a wide range of thermal conductivity values.”

In the paper

“The through-plane thermal conductivity of superlattices has been found to depend on several factors including the interface density (=2/ dSL , where dSL is the period thickness), the total film thickness, and the thickness ratio between the two materials.”

In the paper

“The lowest thermal conductance was reported for the interface between Bi and hydrogen-terminated diamond, with a value of ~8 MW m -2 K -1 at room temperature, 41”

What the sources say

• ?Not checked — no full text of the sourcecites [41] 2006, Phys. Rev. B source

In the paper

“It shows that TDTR has been applied across a broad range of thermal conductivity and interface thermal conductance.”

In the paper

“The through-plane thermal conductivity Kz of the sample and the transducer/sample interface conductance G affect the ratio signal R =-V in / V out in different manners over the 0.1-8 ns delay time range.”

In the paper

“However, in practice, the modulation frequency is limited to be &lt; 20 MHz due to the poor SNR at higher modulation frequencies.”

In the paper

“These oscillations are also cancelled out by the corrective subtraction (note that the corrected signals in Figure 13(a) are smooth without oscillations).”

In the paper

“Figure 23(c) shows that the apparent thermal conductivity of SiGe determined from TDTR experiments with the hybrid nano-patterned transducers depends on the nano-heater size D .”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Hu et al. 206

In the paper

“From the elliptical-beam experiments, the thermal conductivities along the in-plane directions perpendicular to and parallel to the c -axis of ZnO are determined to be Ka = 46 W m -1 K -1 and Kc = 56 W m -1 K 1 , respectively.”

In the paper

“When the size of the nano-lines decreased from 1000 to 50 nm, the measured apparent boundary thermal resistance between the nickel lines and the sapphire substrate increased by as much as three times.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Siemens et al. 88

In the paper

“However, most of the conventional thermal conductivity measurement techniques lack the spatial resolution to measure the temperature gradient/difference or the heat flux across a length scale below tens of microns.”

What the sources say

• Not checked yetcites [16] 2004
• ?Not checked — no full text of the sourcecites [17] 1962, Ind. Eng. Chem. Fundam. source
• ?Not checked — no full text of the sourcecites [18] 1971, Phys. Rev. B source
• ?Not checked — no full text of the sourcecites [19] 1969, Int. J. Heat Mass Transfer source
• ?Not checked — no full text of the sourcecites [20] 1986, AIAA J. source
• ?Not checked — no full text of the sourcecites [21] 2006, Proc. IEEE source

In the paper

“The decay rate of V in, which represents the cooling process of sample surface due to heat dissipation, directly relates to the thermal diffusivity of the sample.”

In the paper

“For example, it requires minimal sample preparation and no delicate design of electrical heaters or temperature sensors, and it works equally well in regular ambient conditions or through the window of a vacuum chamber. 48”

What the sources say

• ?Not checked — no full text of the sourcecites [48] 2014, Annu. Rev. Heat Transfer source

In the paper

“The out-of-phase V out, on the other hand, is mainly due to the modulated continuous heating of the sample at the modulation frequency ω 0.”

In the paper

“Using the phase signal for data reduction has the advantage over the amplitude signal as it does not require normalization. 22”

What the sources say

• ?Not checked — no full text of the sourcecites [22] 2004, Rev. Sci. Instrum. source

In the paper

“The metal transducer thickness h m can be determined by picosecond acoustics 72 .”

What the sources say

• ?Not checked — no full text of the sourcecites [72] 2012, Rev. Sci. Instrum. source

In the paper

“Schmidt 24 further extended the model for anisotropic heat conduction where thin films are very likely anisotropic due to the size effect of energy carriers.”

What the sources say

• ?Not checked — no full text of the sourcecites [24] 2008, Rev. Sci. Instrum. source

In the paper

“Both the two-tint and the two-color approach can effectively filter the reflected pump beam but at a significant sacrifice of the laser power.”

What the sources say

• ?Not checked — no full text of the sourcecites [23] 2008, Rev. Sci. Instrum. source
• ?Not checked — no full text of the sourcecites [25] 2010, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [103] 2008, Rev. Sci. Instrum. source

In the paper

“Such a laser power loss is a critical issue for measurements of highly conductive materials such as diamond, where a sufficiently high laser power intensity is desired to generate a high enough signal-to-noise ratio (SNR).”

In the paper

“However, due to the small value of thermoreflectance coefficient d R /d T (~ 10 -4 K -1 ), a tiny amount of reflected pump beam even with an intensity less than 0.01% of the reflected probe beam is significant enough to distort the TDTR measurements. 95”

What the sources say

• ?Not checked — no full text of the sourcecites [95] 2016, Rev. Sci. Instrum. source

In the paper

“In this case, the TDTR signals are most sensitive to the thermal properties in the through-plane direction ( Kz and G ).”

In the paper

“For optically rough samples, the pump and the probe beams need to be spectrally separated so that the reflected pump beam can be eliminated using highly efficient optical filters.”

In the paper

“In addition, the normalized amplitude signal loses sensitivity to the thermal properties of the sample especially when the V out signal is small.”

In the paper

“The complexity of the thermal model described above potentially also enables TDTR for determining many thermal properties involved in the model, including the heat capacity C , inplane thermal conductivity Kr , cross-plane thermal conductivity Kz , and interface conductance G .”

In the paper

“whose surface reflectance changes linearly with temperature when the temperature rise is small (typically <10% of the absolute temperature or <10 K, whichever is smaller).”

In the paper

“The in-phase signal V in represents the surface temperature change because of the pulse heating.”

In the paper

“This double lock-in scheme removes coherent pick-up contributions to the signal at the radio frequency. 39”

What the sources say

• ?Not checked — no full text of the sourcecites [39] 2013, Rev. Sci. Instrum. source

In the paper

“To make the lock-in detection effective, the reflected pump beam must be blocked from the photodiode detector.”

In the paper

“Another benefit is that the frequency difference f 1 -f 2 can also be chosen to be close to the upper limit of the frequency range of the lock-in amplifier so that the higher harmonic components are naturally excluded from the lock-in detection. 147”

What the sources say

• ?Not checked — no full text of the sourcecites [147] 2013, Rev. Sci. Instrum. source

In the paper

“In ultrafast-laser-based TDTR and FDTR, this instrumentation phase can be conveniently corrected by the fact that the ܸ ௢௨௧ signal should be constant across the zero delay time.”

In the paper

“By holding the delay stage at a fixed location, an ultrafast-laser-based TDTR can also be implemented as FDTR. 93”

What the sources say

• ?Not checked — no full text of the sourcecites [93] 2009, Rev. Sci. Instrum. source

In the paper

“An advanced dual-frequency TDTR configuration can be employed to improve the accuracy in determining Kz of thermally thin films, see Section IV(B) for more details.”

In the paper

“Extending modulation frequency range greatly expands the capability of FDTR.”

In the paper

“The thermal transport model for TDTR (shown in Section II(B)) still applies to FDTR, with only one difference that the signals are computed as a function of the modulation frequency instead of the delay time.”

In the paper

“The uncertainties of multiple fitting parameters can be estimated using a multivariate errorpropagation formula based on Jacobian matrices derived by Yang et al . 127”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Yang et al. 127

In the paper

“A heterodyne technique called broadband frequencydomain thermoreflectance (BB-FDTR) 147 has thus been implemented to extend the modulation frequency up to 200 MHz .”

What the sources say

• ?Not checked — no full text of the sourcecites [147] 2013, Rev. Sci. Instrum. source

In the paper

“For thermally thin films with ݄ ୤୧୪୫ ൏ ݀ ௣,௭ , the measurements of Kz of the film would be challenging due to the low sensitivity to Kz .”

In the paper

“Both Kz and G can thus be simultaneously determined from one single set of TDTR measurements.”

In the paper

“One major challenge of CW-laser-based FDTR is the accurate determination of the phase signal in FDTR experiments.”

In the paper

“The only difference is that the resonant circuit used to eliminate the higher harmonic signals in TDTR cannot be used in FDTR experiments since the data are acquired as a continuous function of modulation frequency while the resonant circuits are usually at fixed cutoff frequencies.”

In the paper

“The thermal conductivity of superlattices and nanolaminates 27, 59, 78, 79, 123, 132-138 (see Figure 6(b) for an example) has been extensively characterized using TDTR over the last 15 years.”

What the sources say

• ?Not checked — no full text of the sourcecites [27] 2012, Science source
• ?Not checked — no full text of the sourcecites [59] 2014, Nat. Mater. source
• ?Not checked — no full text of the sourcecites [78] 1999, Phys. Rev. B source
• ?Not checked — no full text of the sourcecites [79] 2004, Science source
• ?Not checked — no full text of the sourcecites [123] 2009, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [132] 2001, J. Appl. Phys. source
• ?Not checked — no full text of the sourcecites [133] 2005, Appl. Phys. Lett. source
• ?Not checked — no full text of the sourcecites [134] 2009, Adv. Funct. Mater. source
• ?Not checked — no full text of the sourcecites [135] 2013, Nano Lett. source
• ?Not checked — no full text of the sourcecites [136] 2014, Appl. Phys. Lett. source

In the paper

“Thermometry based on the thermo-magneto-optic Kerr effect allows the use of much thinner magnetic transducer films that are not necessarily optically opaque as required in conventional TDTR method.”

In the paper

“However, the Kz of superlattices was also found to depend on the total film thickness, as shown in Figure 6(d), indicating that a significant fraction of phonons can coherently transport across the interfaces and are only scattered by the film boundary. 27, 137”

What the sources say

• ?Not checked — no full text of the sourcecites [27] 2012, Science source
• ?Not checked — no full text of the sourcecites [137] 2018, Phys. Rev. B source

In the paper

“Instead of thermoreflectance, TR-MOKE relies on the temperature-dependent transient polar Kerr rotation to detect the temperature response of a magnetic transducer under pump laser heating, from which the thermal properties of the material underneath the transducer film can be derived, following the same data reduction scheme of TDTR.”

In the paper

“However, through the detailed sensitivity analysis, Jiang et al . 119 found that the FWHM of V out had the highest sensitivity to Kr of the sample when dp,r ≈ w 0.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Jiang et al. 119

In the paper

“The ultralow thermal conductivities are due to the alternating layered structures with very different atomic configurations between the ALD atomic layers and the MLD molecular layers that strongly scatter the phonons.”

What the sources say

• ?Not checked — no full text of the sourcecites [181] 2013, Nano Lett. source

In the paper

“ASOPS-TDTR and conventional TDTR should produce exactly the same signals as a function of the delay time, only in different manners of data acquisition.”

In the paper

“Jiang et al . 119 also pointed out that the NbV transducer as a replacement of the conventional Al transducer is effective in reducing the measurement uncertainty in beam-offset experiments only when the substrate has a Kr in the range 6-30 W m -1 K -1 .”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Jiang et al. 119

In the paper

“For this reason, TR-MOKE is more suitable to perform beam-offset experiments because much thinner transducer films (as thin as ~5 nm) can be used for the measurements.”

In the paper

“Besides the bulk samples, this frequency-dependent TDTR approach also applies to thin film materials.”

In the paper

“The detected signals in ASOPS-TDTR are not pure sinusoidal as those in conventional TDTR but are centered at the modulation frequency with sidebands of Δ f in the frequency domain. 172”

What the sources say

• ?Not checked — no full text of the sourcecites [172] 2011, J. Appl. Phys. source

In the paper

“The variable spot size TDTR approach described above is limited to materials that are transversely isotropic because the thermal model assumes a cylindrical symmetry.”

In the paper

“Much faster data acquisition is possible with asynchronous optical sampling (ASOPS), using two different modelocked lasers with slightly different pulse repetition rates.”

• Also stated in: § C. Asynchronous optical sampling (ASOPS) · boosted

  “ASOPS enables much faster data acquisition.”

In the paper

“This fast data acquisition allows ASOPS to average many repeated measurements, significantly reducing the detection noise to a very low level.”

• Also stated in: § C. Asynchronous optical sampling (ASOPS) · plain

  “The noise level can thus be significantly reduced by averaging over a large amount of data acquired within a short period of time.”

In the paper

“While TDTR signals are most sensitive to thermal conductivity in the through-plane direction, TDTR can also be configured to measure anisotropic thermal transport properties.”

In the paper

“TDTR can measure the through-plane thermal conductivity Kz of thin films using a high modulation frequency and a large laser spot size, in which configuration the heat flow is mainly one-dimensional in the through-plane direction.”

In the paper

“In this approach, the pump beam is swept across the probe beam and the full-width half-maximum (FWHM) of the out-of-phase signal at a negative delay time ( e.g. , -100 ps) is used to derive the inplane thermal conductivity along the scanning direction. 194”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [194]

In the paper

“Very low thermal conductivities of 0.15-0.35 W m -1 K -1 were measured for these thin films.”

What the sources say

• ?Not checked — no full text of the sourcecites [181] 2013, Nano Lett. source

In the paper

“TDTR has been demonstrated to determine thermal conductivity K and heat capacity C simultaneously for both bulk and thin film materials by performing multiple measurements using different modulation frequencies, 38, 39”

What the sources say

• ?Not checked — no full text of the sourcecites [38] 2013, Rev. Sci. Instrum. source
• ?Not checked — no full text of the sourcecites [39] 2013, Rev. Sci. Instrum. source

In the paper

“Phonon transport becomes quasi-ballistic when ݀ ௣ is comparable to the phonon MFPs.”

In the paper

“Despite the initial apparent success of Minnich et al. 91 , their interpretations, however, are subject to many assumptions.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Minnich et al. 91

In the paper

“For samples with Kr &lt; 6 W m -1 K -1 , neither NbV nor Al transducer is likely to work, as the measurement uncertainty becomes very high for both transducers.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Jiang et al. 119

In the paper

“A later publication by Regner et al . 210 confirmed the nonnegligible effect of the transducer type on TDTR/FDTR experiments.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Regner et al. 210

In the paper

“Understanding that the spot size-dependent TDTR approach has a limit on the smallest laser spot size achievable due to the diffraction limit, Hu et al. 206 returned to nanostructured samples similar to Siemens et al . 88 to reconstruct the MFP spectrum by performing TDTR measurements of samples using nano-patterned heaters with size D varying from 30 nm to 60 μ m.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Hu et al. 206
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Siemens et al. 88

In the paper

“By using a highly elliptical pump beam for TDTR experiments, a quasi-one-dimensional temperature profile that has a fast decay along the short axis of the pump beam is induced on the sample surface.”

In the paper

“The detected TDTR signal is thus exclusively sensitive to the in-plane thermal conductivity along the short axis of the elliptical beam.”

In the paper

“The very first experimental observation of quasi-ballistic phonon transport induced by nanosized heaters was realized by Siemens et al . 88 using pump-probe measurements based on an ultrafast soft X-ray detection scheme.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Siemens et al. 88

In the paper

“The beam-offset TDTR approach is subject to measurement uncertainty from the FWHM signals and from the input parameters, especially the laser spot size.”

In the paper

“Alternatively, based on the physical picture that the sensitivity of TDTR signals to the in-plane thermal conductivity depends on how the spot size ݓ ଴ is compared to ݀ ௣,௥ , an elliptical-beam TDTR approach was recently developed to measure the in-plane thermal conductivity of transversely anisotropic samples. 119”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Jiang et al. 119

In the paper

“Yang and Dames 202 later introduced a suppression function with a more realistic model for the apparent thermal conductivity ܭ ஺ as:”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Yang and Dames 202

In the paper

“Current TDTR cannot be used to measure the thermal conductivity of monolayer or fewlayer two-dimensional (2D) materials.”

In the paper

“TDTR measurements at low temperatures &lt; 30 K are usually challenging due to the small heat capacities of both the metal transducer and the experimental sample that do not allow a high enough laser power for the measurements without inducing too much temperature excursion.”

In the paper

“On the other hand, TDTR measurements at high temperatures are mainly limited by the chemical and physical stabilities of the metal transducer layer.”

In the paper

“TDTR combined with x-ray diffraction 244 also provides insight into the nature of heat transfer in the quasiballistic regime.”

What the sources say

• ?Not checked — no full text of the sourcecites [244] 2007, Phys. Rev. B source

In the paper

“suggesting that the heat diffusion equation cannot accurately describe the experiment.”

In the paper

“These assumptions are not rigorously justified unless the couplings between different heat carriers are sufficiently strong, and the mean-free-paths of all of the significant heat carriers are small compared to the characteristic lengths (e.g., thermal penetration depth, laser spot size, etc.).”

In the paper

“TDTR measurements using Al transducer is usually limited to be at &lt; 600 K due to the low melting point of Al.”

In the paper

“which, despite some recent progress, 110, 111, 215, 228 inevitably complicates the data reduction process.”