Depth-Resolved Thermal Conductivity of HFCVD Diamond Films via Square-Pulsed Thermometry

Ershuai Yin; Junjun Wei; Kexin Zhang; Puqing Jiang; Xiaosong Han; Xin Qian

arxiv: 2604.12522 · v1 · submitted 2026-04-14 · ❄️ cond-mat.mtrl-sci · physics.app-ph

Depth-Resolved Thermal Conductivity of HFCVD Diamond Films via Square-Pulsed Thermometry

Kexin Zhang , Xiaosong Han , Ershuai Yin , Xin Qian , Junjun Wei , Puqing Jiang This is my paper

Pith reviewed 2026-05-10 15:55 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-ph

keywords diamond filmsthermal conductivityHFCVDdepth profilesquare-pulsed thermometrygrain coarseningSiC substratethermal management

0 comments

The pith

Diamond films on SiC show thermal conductivity rising from 60 to 200 W m^{-1} K^{-1} with depth as grains coarsen away from the nucleation layer.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that hot-filament chemical vapor deposition produces diamond films whose ability to carry heat improves markedly from the substrate interface toward the outer surface. Microscopy indicates that grains grow larger with distance from the nucleation zone, and the authors link this structural change directly to the measured rise in conductivity. They obtain the depth profile by varying the frequency of a pulsed heat source so that the thermal wave reaches different layers, then fit the data to a model that allows conductivity to change with depth. A reader would care because diamond layers are used to pull heat away from high-power electronics, and knowing the internal variation helps predict how well the whole stack will perform.

Core claim

By applying square-pulsed source thermometry at multiple frequencies and inverting the signals with a one-dimensional depth-resolved heat-transport model, the authors obtain a quantitative conductivity profile through a five-micrometer HFCVD diamond film on SiC. The profile rises sharply from approximately 60 W m^{-1} K^{-1} near the nucleation interface to approximately 200 W m^{-1} K^{-1} at the free surface, matching the observed progression from fine to coarse grains seen in electron backscatter diffraction and transmission electron microscopy.

What carries the argument

Square-pulsed source thermometry, which extracts depth-dependent conductivity by varying the frequency of the heat pulse and thereby changing the thermal penetration depth inside a layered transport model.

If this is right

Device thermal models for diamond-on-SiC stacks must incorporate the conductivity gradient rather than a single average value.
The nucleation layer contributes the largest thermal resistance, so growth recipes that reduce its thickness or improve its grain structure would lower overall resistance.
Thicker films with more room for grain coarsening will deliver higher average heat-spreading performance.
The same frequency-scanning approach can be used to monitor how changes in deposition parameters alter the conductivity profile.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could be extended to map conductivity in other polycrystalline films where grain size varies through the thickness.
If the gradient is general, then the effective conductivity of a diamond thermal layer depends on both total thickness and the depth at which heat is injected.
Engineering the early nucleation stage may be more important for heat extraction than further optimization of the high-quality surface grains.

Load-bearing premise

The frequency-dependent temperature signals can be inverted uniquely by a one-dimensional depth-resolved model without significant errors from lateral heat flow, unknown interface resistances, or other unaccounted effects.

What would settle it

A cross-sectional measurement that directly probes local thermal conductivity at several depths, for example by a micro-probe or transient grating technique on a polished edge, and finds no systematic increase from interface to surface would falsify the reconstructed profile.

read the original abstract

The integration of high-thermal-conductivity diamond films onto silicon carbide (SiC) substrates offers a promising pathway for thermal management in high-power electronic devices. Here, we investigate the depth-dependent thermal conductivity of a ~5 {\mu}m-thick diamond film grown on SiC by hot-filament chemical vapor deposition (HFCVD) using square-pulsed source (SPS) thermometry. Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) reveal pronounced grain coarsening from the nucleation interface to the film surface. By combining frequency-dependent thermal penetration with a depth-resolved thermal transport model, we quantitatively reconstruct the thermal conductivity profile. The thermal conductivity increases sharply from ~60 W m^(-1) K^(-1) near the nucleation region to ~200 W m^(-1) K^(-1) at the surface, directly reflecting the underlying microstructural evolution. These results provide a physically grounded understanding of graded heat transport in HFCVD diamond and offer practical guidance for engineering diamond-based thermal management layers for next-generation power devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper measures a conductivity rise from ~60 to ~200 W/mK through a 5 µm HFCVD diamond film that tracks grain coarsening, but the 1D model inversion is presented without enough checks to rule out artifacts.

read the letter

The main takeaway is that they grew a thin diamond film on SiC by hot-filament CVD, mapped the grain size increase from interface to surface with EBSD and TEM, and used square-pulsed thermometry to pull out a depth-dependent conductivity profile that rises sharply over that same distance. The numbers are specific and the microstructure link is direct, which gives engineers working on power-device heat spreading something concrete to use when they worry about the nucleation layer killing performance. That combination of frequency-dependent penetration depth with a layered transport model is the actual new measurement here, and it sits on top of established thermometry rather than inventing a new technique. The experimental side looks solid enough on the surface: they have the film, the microscopy, and the reported values that match the expected trend from grain boundary scattering. The soft spot is the inversion itself. The abstract says they reconstruct the profile from frequency-dependent signals through a depth-resolved model, yet it supplies no equations, no fitting details, no error bars, and no discussion of whether diamond-SiC interface resistance or radial heat flow could produce the same signatures. In a 5 µm film those effects are plausible and can mimic a smooth gradient, so the quantitative claim rests on an assumption that the 1D forward model is complete and the inverse problem is well-posed. Without sensitivity tests or cross-checks against a uniform film, it is hard to know how much the reported 60-to-200 range is robust. This is useful incremental data for the thin-film thermal characterization community and for anyone integrating diamond with SiC. A reader who needs real numbers on graded conductivity in these layers will find it worth their time. It is coherent enough and grounded enough in experiment to deserve a full referee process, even if the modeling section will draw questions.

Referee Report

3 major / 2 minor

Summary. The manuscript reports the application of square-pulsed source (SPS) thermometry to reconstruct the depth-dependent thermal conductivity profile in a ~5 μm HFCVD diamond film grown on SiC. Frequency-dependent thermal signals are inverted using a depth-resolved 1D thermal transport model, yielding a conductivity that increases from ~60 W m^{-1} K^{-1} near the nucleation interface to ~200 W m^{-1} K^{-1} at the surface. This gradient is directly linked to grain coarsening observed via EBSD and TEM microstructural characterization.

Significance. If the model inversion is shown to be robust, the work supplies quantitative, non-destructive mapping of graded thermal transport in polycrystalline diamond films and its connection to processing-induced microstructure. This is relevant for thermal management layers in high-power electronics. The combination of frequency-dependent penetration data with direct microstructural correlation provides a concrete experimental demonstration that strengthens the physical basis for engineering such graded films.

major comments (3)

[Methods / data analysis] The specific form of the depth-resolved 1D thermal transport model, the forward calculation of frequency-dependent phase/amplitude, and the inversion procedure used to obtain k(z) are not presented with sufficient detail (see the section on data analysis and modeling). Without the governing equations and fitting protocol, it is impossible to evaluate the well-posedness of the inverse problem or its sensitivity to assumptions.
[Results (conductivity profile reconstruction)] No quantitative checks are reported for the possible contributions of diamond/SiC thermal boundary resistance or lateral heat spreading to the observed frequency dependence. In a ~5 μm film these effects can produce signatures degenerate with a smooth conductivity gradient, directly affecting the central claim that the reconstructed profile (~60 to ~200 W m^{-1} K^{-1}) reflects only microstructural evolution.
[Discussion / experimental validation] The manuscript provides no validation that the heater spot diameter satisfies the 1D approximation (i.e., spot size ≫ film thickness and thermal penetration depth) nor any sensitivity analysis to unmodeled interface resistance; both are load-bearing for the uniqueness of the reported k(z) values.

minor comments (2)

[Abstract and figures] Ensure consistent use of SI units and notation for thermal conductivity throughout the text and figures.
[Figure captions] The EBSD and TEM figures would benefit from explicit labeling of the nucleation interface versus surface regions to aid direct visual correlation with the reported k(z) profile.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We have revised the paper to provide more detail on the thermal model, to include quantitative checks for boundary resistance and lateral spreading, and to add validation of the 1D approximation along with sensitivity analysis. Our responses to each major comment are provided below.

read point-by-point responses

Referee: [Methods / data analysis] The specific form of the depth-resolved 1D thermal transport model, the forward calculation of frequency-dependent phase/amplitude, and the inversion procedure used to obtain k(z) are not presented with sufficient detail (see the section on data analysis and modeling). Without the governing equations and fitting protocol, it is impossible to evaluate the well-posedness of the inverse problem or its sensitivity to assumptions.

Authors: We agree with the referee that additional detail on the model is necessary for a full evaluation of the inverse problem. In the revised manuscript, we have substantially expanded the data analysis and modeling section to include the governing 1D heat diffusion equation with position-dependent thermal conductivity k(z), the Fourier decomposition of the square pulse for frequency-domain analysis, the analytical or numerical forward solution for the temperature phase and amplitude, and the specific inversion method (e.g., iterative fitting with Tikhonov regularization). We have also added a discussion of the well-posedness and sensitivity to assumptions such as the form of k(z). revision: yes
Referee: [Results (conductivity profile reconstruction)] No quantitative checks are reported for the possible contributions of diamond/SiC thermal boundary resistance or lateral heat spreading to the observed frequency dependence. In a ~5 μm film these effects can produce signatures degenerate with a smooth conductivity gradient, directly affecting the central claim that the reconstructed profile (~60 to ~200 W m^{-1} K^{-1}) reflects only microstructural evolution.

Authors: We acknowledge that explicit checks for these effects were missing from the original submission. We have added quantitative analyses in the revised Results section. For the diamond/SiC thermal boundary resistance, we incorporated literature values and modeled its contribution, demonstrating that it does not reproduce the observed gradual frequency dependence. For lateral heat spreading, we verified that the heater spot size significantly exceeds the film thickness and relevant thermal penetration depths, with calculations showing negligible impact on the measured signals. These additions confirm that the conductivity gradient is attributable to the grain coarsening observed in EBSD and TEM. revision: yes
Referee: [Discussion / experimental validation] The manuscript provides no validation that the heater spot diameter satisfies the 1D approximation (i.e., spot size ≫ film thickness and thermal penetration depth) nor any sensitivity analysis to unmodeled interface resistance; both are load-bearing for the uniqueness of the reported k(z) values.

Authors: We have addressed this by adding explicit validation in the revised Discussion. The heater spot diameter used in the experiments is provided and shown to be much larger than the 5 μm film thickness and the frequency-dependent penetration depths (which range from sub-micron to several microns). We have also included a sensitivity analysis varying the interface resistance within plausible bounds and showing that the reconstructed k(z) profile changes only marginally, within the experimental uncertainty. This supports the uniqueness of the reported values under the 1D model assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity: profile reconstructed from experimental data via independent forward model

full rationale

The paper's central result is an experimental reconstruction of k(z) obtained by inverting measured frequency-dependent SPS thermometry signals through a depth-resolved 1D heat-transport forward model. The reported values (∼60 W m^{-1} K^{-1} near the interface rising to ∼200 W m^{-1} K^{-1} at the surface) are outputs of that data-driven fit, not quantities defined by or algebraically identical to any fitted parameter, prior self-citation, or ansatz smuggled in via reference. No step in the derivation chain reduces the claimed profile to the input data by construction; the model supplies an independent mapping whose validity can be checked against the raw phase/amplitude spectra. Self-citations, if present, are not load-bearing for the uniqueness or numerical values of the reported profile.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, invented entities, or non-standard axioms are stated. The reconstruction implicitly relies on standard thermal-transport assumptions.

axioms (2)

domain assumption Frequency-dependent thermal penetration depth can be combined with a depth-resolved model to reconstruct a unique conductivity profile.
Invoked when the abstract states that frequency-dependent penetration plus the model yields the quantitative profile.
domain assumption Heat flow is adequately described by one-dimensional depth-dependent conductivity with no significant lateral or interface effects.
Required for the depth-resolved thermal transport model to map signals directly to the conductivity profile.

pith-pipeline@v0.9.0 · 5506 in / 1423 out tokens · 46992 ms · 2026-05-10T15:55:22.826501+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

[1]

K!" near the nucleation region to ~200 W m!

*Corresponding Authors: (J.W.) weijj@ustb.edu.cn; (P.J.) jpq2021@hust.edu.cn Depth-Resolved Thermal Conductivity of HFCVD Diamond Films via Square-Pulsed Thermometry Kexin Zhang1, Xiaosong Han2,3, Ershuai Yin4, Xin Qian1, Junjun Wei2,*, Puqing Jiang1,* 1School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430...

work page 2000
[2]

M. Li, S. Li, Z. Zhang, C. Su, B. Wong and Y. Hu, Acc Mater Res 6 (5), 563-576 (2025)

work page 2025
[3]

X. Qian, P. Jiang and R. Yang, Materials Today Physics 3, 70-75 (2017)

work page 2017
[4]

Cheng, J

Z. Cheng, J. Liang, K. Kawamura, H. Zhou, H. Asamura, H. Uratani, J. Tiwari, S. Graham, Y. Ohno, Y. Nagai, T. Feng, N. Shigekawa and D. G. Cahill, Nat Commun 13 (1), 7201 (2022)

work page 2022
[5]

Malakoutian, D

M. Malakoutian, D. E. Field, N. J. Hines, S. Pasayat, S. Graham, M. Kuball and S. Chowdhury, ACS Applied Materials & Interfaces 13 (50), 60553-60560 (2021)

work page 2021
[6]

S. Khan, F. Angeles, J. Wright, S. Vishwakarma, V. H. Ortiz, E. Guzman, F. Kargar, A. A. Balandin, D. J. Smith, D. Jena, H. G. Xing and R. Wilson, ACS Appl Mater Interfaces 14 (31), 36178-36188 (2022)

work page 2022
[7]

T. Feng, H. Zhou, Z. Cheng, L. S. Larkin and M. R. Neupane, ACS Appl Mater Interfaces 15 (25), 29655-29673 (2023)

work page 2023
[8]

Z. Guo, B. Guo, J. Zhang, G. Wu, H. Zhao, J. Jia, Q. Meng and Q. Zhao, J Adv Res 74, 333-358 (2025)

work page 2025
[9]

Lu, Functional Diamond 2 (1), 119-141 (2022)

F. Lu, Functional Diamond 2 (1), 119-141 (2022)

work page 2022
[10]

Zhang, R

C. Zhang, R. D. Vispute, K. Fu and C. Ni, Journal of Materials Science 58 (8), 3485-3507 (2023)

work page 2023
[11]

Varshney, J

D. Varshney, J. Palomino, J. Gil, O. Resto, B. R. Weiner and G. Morell, Journal of Applied Physics 115 (5) (2014)

work page 2014
[12]

M. Mohr, L. Daccache, S. Horvat, K. Brühne, T. Jacob and H.-J. Fecht, Acta Materialia 122, 92-98 (2017)

work page 2017
[13]

Anaya, T

J. Anaya, T. Bai, Y. Wang, C. Li, M. Goorsky, T. Bougher, L. Yates, Z. Cheng, S. Graham and K. Hobart, Acta Materialia 139, 215-225 (2017)

work page 2017
[14]

H. Dong, B. Wen and R. Melnik, Sci Rep 4 (1), 7037 (2014)

work page 2014
[15]

T. Chen, S. Song, Y. Shen, K. Zhang and P. Jiang, International Communications in Heat and Mass Transfer 158, 107849 (2024)

work page 2024
[16]

Chen and P

T. Chen and P. Jiang, Physical Review Applied 23 (4), 044004 (2025)

work page 2025
[17]

T. Chen, S. Song, R. Hu and P. Jiang, International Journal of Thermal Sciences 207, 109347 (2025)

work page 2025
[18]

Y. Bao, T. Chen, Z. Miao, W. Zheng, P. Jiang, K. Chen, R. Guo and D. Xue, Advanced Electronic Materials 11 (11), 2400944 (2025)

work page 2025
[19]

Chen and P

T. Chen and P. Jiang, Measurement 249, 117001 (2025)

work page 2025
[20]

Chen and P

T. Chen and P. Jiang, Langmuir 41 (38), 26496-26504 (2025)

work page 2025
[21]

Chen and P

T. Chen and P. Jiang, Applied Physics Letters 127 (19) (2025)

work page 2025
[22]

S. Song, T. Chen and P. Jiang, Journal of Applied Physics 137 (5) (2025)

work page 2025
[23]

Zhang, T

K. Zhang, T. Chen, J. Ma and P. Jiang, Journal of Physics D: Applied Physics 58 (32), 325302 (2025)

work page 2025
[24]

Zhang, D

B. Zhang, D. Wang, T. Chen, H. Ban and P. Jiang, International Journal of Heat and Mass Transfer 255, 127764 (2026). 16

work page 2026
[25]

Bender and S

C. Bender and S. Orszag, Advanced mathematical methods for scientists and engineers. (McGraw-Hill Book Company, 1978)

work page 1978
[26]

Katcho, J

N. Katcho, J. Carrete, W. Li and N. Mingo, Physical Review B 90 (9), 094117 (2014)

work page 2014
[27]

A. Sood, R. Cheaito, T. Bai, H. Kwon, Y. Wang, C. Li, L. Yates, T. Bougher, S. Graham, M. Asheghi, M. Goorsky and K. E. Goodson, Nano Lett. 18 (6), 3466-3472 (2018)

work page 2018
[28]

Zhang, J

Z. Zhang, J. Luo, H. Wu, H. Ma and Y. Zhu, Science Advances 11 (23), eadx5007 (2025)

work page 2025
[29]

Y. Zhou, R. Ramaneti, J. Anaya, S. Korneychuk, J. Derluyn, H. Sun, J. Pomeroy, J. Verbeeck, K. Haenen and M. Kuball, Applied Physics Letters 111 (4) (2017)

work page 2017
[30]

Zhang, G

C. Zhang, G. Chandler, Y. Liu, C. Han, Y. Tang, J. P. Feser and C. Ni, Thin Solid Films 826, 140768 (2025)

work page 2025
[31]

Yates, J

L. Yates, J. Anderson, X. Gu, C. Lee, T. Bai, M. Mecklenburg, T. Aoki, M. S. Goorsky, M. Kuball, E. L. Piner and S. Graham, ACS Appl Mater Interfaces 10 (28), 24302-24309 (2018)

work page 2018
[32]

X. Ji, Z. Huang, Y. Ohno, K. Inoue, Y. Nagai, Y. Sakaida, H. Uratani, J. Sun, N. Shigekawa and J. Liang, Advanced Electronic Materials 11 (4), 2400387 (2025)

work page 2025
[33]

J. Sun, Z. Cheng, J. Liang, N. Shigekawa, K. Kawamura, H. Uratani, Y. Sakaida and D. G. Cahill, Applied Physics Letters 124 (4) (2024)

work page 2024
[34]

Moriyama, Z

C. Moriyama, Z. Cheng, Z. Huang, Y. Ohno, K. Inoue, Y. Nagai, N. Shigekawa and J. Liang, Advanced Materials Technologies 10 (21), e00437 (2025)

work page 2025

[1] [1]

K!" near the nucleation region to ~200 W m!

*Corresponding Authors: (J.W.) weijj@ustb.edu.cn; (P.J.) jpq2021@hust.edu.cn Depth-Resolved Thermal Conductivity of HFCVD Diamond Films via Square-Pulsed Thermometry Kexin Zhang1, Xiaosong Han2,3, Ershuai Yin4, Xin Qian1, Junjun Wei2,*, Puqing Jiang1,* 1School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430...

work page 2000

[2] [2]

M. Li, S. Li, Z. Zhang, C. Su, B. Wong and Y. Hu, Acc Mater Res 6 (5), 563-576 (2025)

work page 2025

[3] [3]

X. Qian, P. Jiang and R. Yang, Materials Today Physics 3, 70-75 (2017)

work page 2017

[4] [4]

Cheng, J

Z. Cheng, J. Liang, K. Kawamura, H. Zhou, H. Asamura, H. Uratani, J. Tiwari, S. Graham, Y. Ohno, Y. Nagai, T. Feng, N. Shigekawa and D. G. Cahill, Nat Commun 13 (1), 7201 (2022)

work page 2022

[5] [5]

Malakoutian, D

M. Malakoutian, D. E. Field, N. J. Hines, S. Pasayat, S. Graham, M. Kuball and S. Chowdhury, ACS Applied Materials & Interfaces 13 (50), 60553-60560 (2021)

work page 2021

[6] [6]

S. Khan, F. Angeles, J. Wright, S. Vishwakarma, V. H. Ortiz, E. Guzman, F. Kargar, A. A. Balandin, D. J. Smith, D. Jena, H. G. Xing and R. Wilson, ACS Appl Mater Interfaces 14 (31), 36178-36188 (2022)

work page 2022

[7] [7]

T. Feng, H. Zhou, Z. Cheng, L. S. Larkin and M. R. Neupane, ACS Appl Mater Interfaces 15 (25), 29655-29673 (2023)

work page 2023

[8] [8]

Z. Guo, B. Guo, J. Zhang, G. Wu, H. Zhao, J. Jia, Q. Meng and Q. Zhao, J Adv Res 74, 333-358 (2025)

work page 2025

[9] [9]

Lu, Functional Diamond 2 (1), 119-141 (2022)

F. Lu, Functional Diamond 2 (1), 119-141 (2022)

work page 2022

[10] [10]

Zhang, R

C. Zhang, R. D. Vispute, K. Fu and C. Ni, Journal of Materials Science 58 (8), 3485-3507 (2023)

work page 2023

[11] [11]

Varshney, J

D. Varshney, J. Palomino, J. Gil, O. Resto, B. R. Weiner and G. Morell, Journal of Applied Physics 115 (5) (2014)

work page 2014

[12] [12]

M. Mohr, L. Daccache, S. Horvat, K. Brühne, T. Jacob and H.-J. Fecht, Acta Materialia 122, 92-98 (2017)

work page 2017

[13] [13]

Anaya, T

J. Anaya, T. Bai, Y. Wang, C. Li, M. Goorsky, T. Bougher, L. Yates, Z. Cheng, S. Graham and K. Hobart, Acta Materialia 139, 215-225 (2017)

work page 2017

[14] [14]

H. Dong, B. Wen and R. Melnik, Sci Rep 4 (1), 7037 (2014)

work page 2014

[15] [15]

T. Chen, S. Song, Y. Shen, K. Zhang and P. Jiang, International Communications in Heat and Mass Transfer 158, 107849 (2024)

work page 2024

[16] [16]

Chen and P

T. Chen and P. Jiang, Physical Review Applied 23 (4), 044004 (2025)

work page 2025

[17] [17]

T. Chen, S. Song, R. Hu and P. Jiang, International Journal of Thermal Sciences 207, 109347 (2025)

work page 2025

[18] [18]

Y. Bao, T. Chen, Z. Miao, W. Zheng, P. Jiang, K. Chen, R. Guo and D. Xue, Advanced Electronic Materials 11 (11), 2400944 (2025)

work page 2025

[19] [19]

Chen and P

T. Chen and P. Jiang, Measurement 249, 117001 (2025)

work page 2025

[20] [20]

Chen and P

T. Chen and P. Jiang, Langmuir 41 (38), 26496-26504 (2025)

work page 2025

[21] [21]

Chen and P

T. Chen and P. Jiang, Applied Physics Letters 127 (19) (2025)

work page 2025

[22] [22]

S. Song, T. Chen and P. Jiang, Journal of Applied Physics 137 (5) (2025)

work page 2025

[23] [23]

Zhang, T

K. Zhang, T. Chen, J. Ma and P. Jiang, Journal of Physics D: Applied Physics 58 (32), 325302 (2025)

work page 2025

[24] [24]

Zhang, D

B. Zhang, D. Wang, T. Chen, H. Ban and P. Jiang, International Journal of Heat and Mass Transfer 255, 127764 (2026). 16

work page 2026

[25] [25]

Bender and S

C. Bender and S. Orszag, Advanced mathematical methods for scientists and engineers. (McGraw-Hill Book Company, 1978)

work page 1978

[26] [26]

Katcho, J

N. Katcho, J. Carrete, W. Li and N. Mingo, Physical Review B 90 (9), 094117 (2014)

work page 2014

[27] [27]

A. Sood, R. Cheaito, T. Bai, H. Kwon, Y. Wang, C. Li, L. Yates, T. Bougher, S. Graham, M. Asheghi, M. Goorsky and K. E. Goodson, Nano Lett. 18 (6), 3466-3472 (2018)

work page 2018

[28] [28]

Zhang, J

Z. Zhang, J. Luo, H. Wu, H. Ma and Y. Zhu, Science Advances 11 (23), eadx5007 (2025)

work page 2025

[29] [29]

Y. Zhou, R. Ramaneti, J. Anaya, S. Korneychuk, J. Derluyn, H. Sun, J. Pomeroy, J. Verbeeck, K. Haenen and M. Kuball, Applied Physics Letters 111 (4) (2017)

work page 2017

[30] [30]

Zhang, G

C. Zhang, G. Chandler, Y. Liu, C. Han, Y. Tang, J. P. Feser and C. Ni, Thin Solid Films 826, 140768 (2025)

work page 2025

[31] [31]

Yates, J

L. Yates, J. Anderson, X. Gu, C. Lee, T. Bai, M. Mecklenburg, T. Aoki, M. S. Goorsky, M. Kuball, E. L. Piner and S. Graham, ACS Appl Mater Interfaces 10 (28), 24302-24309 (2018)

work page 2018

[32] [32]

X. Ji, Z. Huang, Y. Ohno, K. Inoue, Y. Nagai, Y. Sakaida, H. Uratani, J. Sun, N. Shigekawa and J. Liang, Advanced Electronic Materials 11 (4), 2400387 (2025)

work page 2025

[33] [33]

J. Sun, Z. Cheng, J. Liang, N. Shigekawa, K. Kawamura, H. Uratani, Y. Sakaida and D. G. Cahill, Applied Physics Letters 124 (4) (2024)

work page 2024

[34] [34]

Moriyama, Z

C. Moriyama, Z. Cheng, Z. Huang, Y. Ohno, K. Inoue, Y. Nagai, N. Shigekawa and J. Liang, Advanced Materials Technologies 10 (21), e00437 (2025)

work page 2025