Thermal transport in a silicon/diamond micro-flake with quantum dots inserts

Saad Bin Mansoor; Bekir Sami Yilbas

doi:10.1515/jnet-2025-0025

Article

Thermal transport in a silicon/diamond micro-flake with quantum dots inserts

Saad Bin Mansoor and Bekir Sami Yilbas

Published/Copyright: May 22, 2025

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From the journal Journal of Non-Equilibrium Thermodynamics Volume 50 Issue 3

Abstract

Non-equilibrium thermal energy transfer in small scale films pairs, composing of different film materials, is important for designing semiconductor devices or thermoelectric energy generators. The present study examines thermal energy transfer in low size silicon-diamond film pairs with the quantum dots in placed. Equation for Phonon Radiative Transport (EPRT) is used to predict the distribution of phonon intensities via adopting the discrete ordinate method. Thermal energy transport is quantified in the form phonon energies via using integral form of equilibrium phonon intensities. Because of the mismatch of properties between silicon and diamond films, interface conditions are formulated after considering energy balance across both films. Findings reveal that equivalent equilibrium temperature decays gradually in the film for small size quantum dots. As the quantum dot size increases, equivalent equilibrium temperature decays sharply because films edges behave like heat sink reducing equilibrium phonon intensities in the region of film edges. Temperature jump, due to mismatch properties of the films, signifies at the mid-section of the interface and it increases slightly with increasing quantum dot size. The magnitude of heat flux vector remains higher in diamond than silicon film. The effective thermal conductivity predicted is in agreement with the previous data for silicon film.

Keywords: thin film pairs; nanoscale thermal transport; film interface; phonon intensity distribution

Corresponding author: Saad Bin Mansoor, Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; and IRC for Sustainable Energy Systems (IRC-SES), King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, E-mail: saadbin@kfupm.edu.sa

Acknowledgments

The authors would like to acknowledge the support of King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia. Acknowledgement is also extended to the Interdisciplinary Research Center for Sustainable Energy Systems (IRC-SES), King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia.

Research ethics: Not applicable.
Informed consent: Not applicable.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission. Saad Bin Mansoor: Mathematical formulation, Code development, Performing parametric study, Production of graphs, Paper writing. Bekir S. Yilbas: Formulation of the study idea, Paper writing, Reviewing.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors state no conflict of interest.
Research funding: None declared.
Data availability: Not applicable.

Nomenclature

C: volumetric heat capacity (J m⁻³ K⁻¹)
I: phonon intensity (W m⁻² sr⁻¹)
I ^o: equilibrium phonon intensity (W m⁻² sr⁻¹)
k: thermal conductivity (W m⁻¹ K⁻¹)
l: ratio of quantum-dot edge length to the flake edge length
q′′: heat flux vector (W m⁻²)
RE: phonon reflectance
T: equivalent equilibrium temperature (K)
T _int,Si: equivalent equilibrium temperature at the interface in silicon (K)
T _int,Di: equivalent equilibrium temperature at the interface in diamond (K)
TR: phonon transmittance
v: phonon speed (m s⁻¹)
x: x-coordinate (m)
z: z-coordinate (m)

Greek symbols

Λ: phonon mean-free-path (m)
θ: polar angle (rad)
ϕ: azimuthal angle (rad)

Subscripts

D: diamond
S: silicon

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Received: 2025-03-02

Accepted: 2025-05-06

Published Online: 2025-05-22

Published in Print: 2025-07-28

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Articles in the same Issue

https://doi.org/10.1515/jnet-2025-0025

Keywords for this article

thin film pairs; nanoscale thermal transport; film interface; phonon intensity distribution