2026
- IEEE T-ED
Effect of Non-Fourier Heat Transport on Temperature Distribution in High Bandwidth MemoryZhihao Zhou, Yu He, Shixian Liu, Lina Yang*, and Nuo Yang*IEEE Transactions on Electron Devices, 2026High Bandwidth Memory, as a key development trend in future memory chip technology, significantly enhances computer performance. At the same time, the thermal challenges arising from its stacked architecture have drawn considerable attention. Most existing studies on thermal management of high bandwidth memory are based on Fourier’s law, neglecting the non-Fourier effects introduced by the micro/nanoscale structures. In this study, the Monte Carlo method is employed to solve the phonon Boltzmann transport equation and investigate the impact of non-Fourier heat transport on the thermal behavior of high bandwidth memory structures. The results reveal that non-Fourier heat transport leads to a junction temperature that is 59.8 K higher than that predicted by Fourier’s law. Furthermore, it is found that the phonon transmittance at the chip interlayers has a severe impact on heat dissipation, with the temperature variation reaching up to 56.6 K. These findings provide more accurate thermal insights, which are critical for the optimized design of high bandwidth memory systems.
@article{zhihao2025hbm, title = {Effect of Non-Fourier Heat Transport on Temperature Distribution in High Bandwidth Memory}, author = {Zhou, Zhihao and He, Yu and Liu, Shixian and Yang, Lina and Yang, Nuo}, journal = {IEEE Transactions on Electron Devices}, volume = {73}, pages = {561-568}, year = {2026}, doi = {10.1109/TED.2025.3628342}, }
2025
- J. Appl. Phys.
Temperature Dependence of Specific Heat Capacity of Nanostructures via Neuroevolution Machine-learned PotentialShixian Liu, Ge Zhang, Fei Yin, A.A. Barinov, V.I. Khvesyuk*, and Nuo Yang*Journal of Applied Physics, 2025In this study, lattice dynamics calculations based on the Neuroevolution Machine-learned Potential (NEP) were performed for three types of silicon nanostructures: thin films, nanowires, and quantum dots. The temperature and size dependence of the specific heat capacity was systematically examined. The results reveal a significant enhancement in the specific heat capacity of nanostructures at low temperatures compared to bulk silicon, primarily due to phonon confinement, discrete energy spectra, and the emergence of low-frequency surface vibrational modes. These findings underscore the dominant role of nonlinear acoustic phonons at low temperatures, with increasing contributions from optical modes as the temperature rises. Notably, this work reports the temperature-dependent evolution of local fitting exponents in the specific heat scaling relation C_v ∼T^n(T) for nanostructured systems. The high accuracy and computational efficiency of the NEP model allow for detailed characterization of the complex phonon behaviors that govern thermal properties at the nanoscale.
@article{shixian2025jap, title = {Temperature Dependence of Specific Heat Capacity of Nanostructures via Neuroevolution Machine-learned Potential}, author = {Liu, Shixian and Zhang, Ge and Yin, Fei and Barinov, A.A. and Khvesyuk, V.I. and Yang, Nuo}, journal = {Journal of Applied Physics}, volume = {138}, pages = {104301}, year = {2025}, doi = {10.1063/5.0284002}, } - Physica B
An Enhanced Framework for Wave Reflection from a Periodically Rough BoundaryFei Yin, Shixian Liu, A.A. Barinov, and V.I. Khvesyuk*Physica B: Condensed Matter, 2025This paper presents an updated comprehensive model for specular reflection from a periodically rough boundary. The model accounts for both phase loss and angular deviations of the reflected wave, enabling a statistical evaluation of the specular reflection probability as a function of wavelength, roughness amplitude, roughness period, and incident angle. Notably, the model reveals oscillatory behavior in the specular reflection probability within the high-frequency regime. The proposed formulation is further incorporated into the Ziman model and applied in Monte Carlo simulations to evaluate thermal conductivity.
@article{yin2025pb, title = {An Enhanced Framework for Wave Reflection from a Periodically Rough Boundary}, author = {Yin, Fei and Liu, Shixian and Barinov, A.A. and Khvesyuk, V.I.}, journal = {Physica B: Condensed Matter}, volume = {716}, pages = {417743}, year = {2025}, doi = {10.1016/j.physb.2025.417743}, } - Int. J. Therm. Sci.
Quantifying Particle and Wave Effects in Phonon Transport of Pillared Graphene NanoribbonsShixian Liu†, Zhicheng Zong†, Fei Yin, V.I. Khvesyuk*, and Nuo Yang*International Journal of Thermal Sciences, 2025This study investigates the dual nature of phonons—encompassing both particle-like and wave-like behaviors—and their roles in thermal transport within pillared graphene nanoribbons (PGNRs). Monte Carlo simulations are employed to evaluate how the presence of pillars affects the thermal conductivity of graphene nanoribbons (GNRs), revealing that pillars significantly reduce thermal conductivity by enhancing phonon-boundary scattering, thereby emphasizing particle effects. A comparison with molecular dynamics simulations enables quantitative assessment of the respective contributions of particle and wave phenomena to the observed reduction in thermal conductivity. Notably, as the width of PGNRs decreases, the influence of wave effects initially increases and then diminishes, suggesting a saturation behavior. Furthermore, this study introduces and evaluates the concept of phonon resonance hybridization depth in PGNRs.
@article{shixian2025wave, title = {Quantifying Particle and Wave Effects in Phonon Transport of Pillared Graphene Nanoribbons}, author = {Liu, Shixian and Zong, Zhicheng and Yin, Fei and Khvesyuk, V.I. and Yang, Nuo}, journal = {International Journal of Thermal Sciences}, volume = {217}, pages = {110067}, year = {2025}, doi = {10.1016/j.ijthermalsci.2025.110067}, } - Phys. Lett. A
Temperature Fluctuations in Quantum Dots: Insights from a \(T^{3/2}\)Heat Capacity ModelShixian Liu and V.I. Khvesyuk*Physics Letters A, 2025In this study, the temperature fluctuations in three-dimensional confined nanostructures (quantum dots) of germanium, silicon, and diamond were calculated using the \(T^{3/2}\)model based on the particle-in-a-box (PIAB) approach and compared with the Debye \(T^3\)model. The analysis focused on quantum dots with sizes ranging from 1 to 100 nm. According to the PIAB \(T^{3/2}\)model, temperature fluctuations decrease as the temperature decreases, consistent with the principles of statistical physics. In contrast, the Debye \(T^3\)model predicts an increase in temperature fluctuations with decreasing temperature, contradicting the principles of statistical physics. These results emphasize the significant impact of quantum confinement and highlight the limitations of the Debye \(T^3\)model in describing nanoscale systems. Furthermore, distribution diagrams illustrating temperature fluctuations as functions of size and temperature were established for the first time. Based on these diagrams, clear boundaries were defined for the temperature and thermophysical property ranges where reliable predictions can be made.
@article{shixian2025fluctuation, title = {Temperature Fluctuations in Quantum Dots: Insights from a \(T^\{3/2\}\) Heat Capacity Model}, author = {Liu, Shixian and Khvesyuk, V.I.}, journal = {Physics Letters A}, volume = {534}, pages = {130261}, year = {2025}, doi = {10.1016/j.physleta.2025.130261}, } - Int. J. Thermophys.
Investigating Anisotropic Three-Phonon Interactions in Graphene’s Thermal Conductivity Using Monte Carlo MethodShixian Liu, Fei Yin, and V.I. Khvesyuk*International Journal of Thermophysics, 2025This study introduces a novel method for calculating the thermal conductivity of graphene using a Monte Carlo approach to evaluate anisotropic three-phonon interactions. The phonon dispersion relation is derived using a force constant model that incorporates up to fifth-order nearest-neighbor interactions, while the phonon density of states (DOS) is computed via a generalized Gilat-Raubenheimer method. A quantitative relationship for the scaling exponent of the specific heat capacity at low temperatures is established, emphasizing the unique two-dimensional characteristics of graphene. To address anisotropic effects, the Monte Carlo approach efficiently identifies three-phonon combinations that adhere to the conservation laws of energy and momentum. The findings highlight the pivotal role of anisotropic phonon interactions in graphene’s thermal conductivity. The thermal conductivity values obtained through the iterative method exhibit strong agreement with previous three-phonon calculations, thereby validating the model. Nevertheless, discrepancies with experimental data suggest that incorporating higher-order phonon processes, such as four-phonon scattering, may further improve predictive accuracy.
@article{shixian2025graphene, title = {Investigating Anisotropic Three-Phonon Interactions in Graphene's Thermal Conductivity Using Monte Carlo Method}, author = {Liu, Shixian and Yin, Fei and Khvesyuk, V.I.}, journal = {International Journal of Thermophysics}, volume = {46}, number = {2}, pages = {22}, year = {2025}, doi = {10.1007/s10765-024-03498-x}, }
2024
- Chin. Phys. Lett.
Determination of Thermal Properties of Unsmooth Si NanowiresShixian Liu, A.A. Barinov*, Fei Yin, and V.I. KhvesyukChinese Physics Letters, 2024We estimate the thermal properties of unsmooth Si nanowires, considering key factors such as size (diameter), surface texture (roughness) and quantum size effects (phonon states) at different temperatures. For nanowires with a diameter of less than 20 nm, we highlight the importance of quantum size effects in heat capacity calculations, using dispersion relations derived from the modified frequency equation for the elasticity of a rod. The thermal conductivities of nanowires with diameters of 37, 56, and 115nm are predicted using the Fuchs– Sondheimer model and Soffer’s specular parameter. Notably, the roughness parameters are chosen to reflect the technological characteristics of the real surfaces. Our findings reveal that surface texture plays a significant role in thermal conductivity, particularly in the realm of ballistic heat transfer within nanowires. This study provides practical recommendations for developing new thermal management materials.
@article{shixian2024determination, title = {Determination of Thermal Properties of Unsmooth Si Nanowires}, author = {Liu, Shixian and Barinov, A.A. and Yin, Fei and Khvesyuk, V.I.}, journal = {Chinese Physics Letters}, volume = {41}, number = {1}, pages = {016301}, year = {2024}, doi = {10.1088/0256-307X/41/1/016301}, }
2022
- Nucl. Eng. Des.
Validation of the STEG code using experiments on two-phase flow across horizontal tube bundlesShixian Liu, Fei Yin, V.I. Melikhov*, and O.I. MelikhovNuclear Engineering and Design, 2022The results of the validation of the STEG code using the experiments on two-phase flow across horizontal tube bundles are presented. The experiments are carried out on two water–air SG models, consisting of a transparent vessels, inside of which there is a tube bundle, a perforated sheet and a bead separating the upstream section of the circulation circuit of the model from the downstream one. The void fractions and water velocities are measured in different locations of the models. The brief description of the STEG code based on the 3D two-fluid model is presented. A set of interfacial drag correlations, which was recently developed by the authors, are used in the validation calculations. The peculiarities of the spatial two-phase flows have been established, and a quantitative comparison with experimental data has been performed. Good agreement between the calculated and experimental data is obtained.
@article{liu2022validation, title = {Validation of the STEG code using experiments on two-phase flow across horizontal tube bundles}, author = {Liu, Shixian and Yin, Fei and Melikhov, V.I. and Melikhov, O.I.}, journal = {Nuclear Engineering and Design}, volume = {399}, pages = {112048}, year = {2022}, doi = {10.1016/j.nucengdes.2022.112048}, }
2026
- IEEE T-ED Effect of Non-Fourier Heat Transport on Temperature Distribution in High Bandwidth MemoryZhihao Zhou, Yu He, Shixian Liu, Lina Yang*, and Nuo Yang*IEEE Transactions on Electron Devices, 2026
High Bandwidth Memory, as a key development trend in future memory chip technology, significantly enhances computer performance. At the same time, the thermal challenges arising from its stacked architecture have drawn considerable attention. Most existing studies on thermal management of high bandwidth memory are based on Fourier’s law, neglecting the non-Fourier effects introduced by the micro/nanoscale structures. In this study, the Monte Carlo method is employed to solve the phonon Boltzmann transport equation and investigate the impact of non-Fourier heat transport on the thermal behavior of high bandwidth memory structures. The results reveal that non-Fourier heat transport leads to a junction temperature that is 59.8 K higher than that predicted by Fourier’s law. Furthermore, it is found that the phonon transmittance at the chip interlayers has a severe impact on heat dissipation, with the temperature variation reaching up to 56.6 K. These findings provide more accurate thermal insights, which are critical for the optimized design of high bandwidth memory systems.
@article{zhihao2025hbm, title = {Effect of Non-Fourier Heat Transport on Temperature Distribution in High Bandwidth Memory}, author = {Zhou, Zhihao and He, Yu and Liu, Shixian and Yang, Lina and Yang, Nuo}, journal = {IEEE Transactions on Electron Devices}, volume = {73}, pages = {561-568}, year = {2026}, doi = {10.1109/TED.2025.3628342}, }
2025
- J. Appl. Phys. Temperature Dependence of Specific Heat Capacity of Nanostructures via Neuroevolution Machine-learned PotentialShixian Liu, Ge Zhang, Fei Yin, A.A. Barinov, V.I. Khvesyuk*, and Nuo Yang*Journal of Applied Physics, 2025
In this study, lattice dynamics calculations based on the Neuroevolution Machine-learned Potential (NEP) were performed for three types of silicon nanostructures: thin films, nanowires, and quantum dots. The temperature and size dependence of the specific heat capacity was systematically examined. The results reveal a significant enhancement in the specific heat capacity of nanostructures at low temperatures compared to bulk silicon, primarily due to phonon confinement, discrete energy spectra, and the emergence of low-frequency surface vibrational modes. These findings underscore the dominant role of nonlinear acoustic phonons at low temperatures, with increasing contributions from optical modes as the temperature rises. Notably, this work reports the temperature-dependent evolution of local fitting exponents in the specific heat scaling relation C_v ∼T^n(T) for nanostructured systems. The high accuracy and computational efficiency of the NEP model allow for detailed characterization of the complex phonon behaviors that govern thermal properties at the nanoscale.
@article{shixian2025jap, title = {Temperature Dependence of Specific Heat Capacity of Nanostructures via Neuroevolution Machine-learned Potential}, author = {Liu, Shixian and Zhang, Ge and Yin, Fei and Barinov, A.A. and Khvesyuk, V.I. and Yang, Nuo}, journal = {Journal of Applied Physics}, volume = {138}, pages = {104301}, year = {2025}, doi = {10.1063/5.0284002}, } - Physica B An Enhanced Framework for Wave Reflection from a Periodically Rough BoundaryFei Yin, Shixian Liu, A.A. Barinov, and V.I. Khvesyuk*Physica B: Condensed Matter, 2025
This paper presents an updated comprehensive model for specular reflection from a periodically rough boundary. The model accounts for both phase loss and angular deviations of the reflected wave, enabling a statistical evaluation of the specular reflection probability as a function of wavelength, roughness amplitude, roughness period, and incident angle. Notably, the model reveals oscillatory behavior in the specular reflection probability within the high-frequency regime. The proposed formulation is further incorporated into the Ziman model and applied in Monte Carlo simulations to evaluate thermal conductivity.
@article{yin2025pb, title = {An Enhanced Framework for Wave Reflection from a Periodically Rough Boundary}, author = {Yin, Fei and Liu, Shixian and Barinov, A.A. and Khvesyuk, V.I.}, journal = {Physica B: Condensed Matter}, volume = {716}, pages = {417743}, year = {2025}, doi = {10.1016/j.physb.2025.417743}, } - Int. J. Therm. Sci. Quantifying Particle and Wave Effects in Phonon Transport of Pillared Graphene NanoribbonsShixian Liu†, Zhicheng Zong†, Fei Yin, V.I. Khvesyuk*, and Nuo Yang*International Journal of Thermal Sciences, 2025
This study investigates the dual nature of phonons—encompassing both particle-like and wave-like behaviors—and their roles in thermal transport within pillared graphene nanoribbons (PGNRs). Monte Carlo simulations are employed to evaluate how the presence of pillars affects the thermal conductivity of graphene nanoribbons (GNRs), revealing that pillars significantly reduce thermal conductivity by enhancing phonon-boundary scattering, thereby emphasizing particle effects. A comparison with molecular dynamics simulations enables quantitative assessment of the respective contributions of particle and wave phenomena to the observed reduction in thermal conductivity. Notably, as the width of PGNRs decreases, the influence of wave effects initially increases and then diminishes, suggesting a saturation behavior. Furthermore, this study introduces and evaluates the concept of phonon resonance hybridization depth in PGNRs.
@article{shixian2025wave, title = {Quantifying Particle and Wave Effects in Phonon Transport of Pillared Graphene Nanoribbons}, author = {Liu, Shixian and Zong, Zhicheng and Yin, Fei and Khvesyuk, V.I. and Yang, Nuo}, journal = {International Journal of Thermal Sciences}, volume = {217}, pages = {110067}, year = {2025}, doi = {10.1016/j.ijthermalsci.2025.110067}, } - Phys. Lett. A Temperature Fluctuations in Quantum Dots: Insights from a \(T^{3/2}\)Heat Capacity ModelShixian Liu and V.I. Khvesyuk*Physics Letters A, 2025
In this study, the temperature fluctuations in three-dimensional confined nanostructures (quantum dots) of germanium, silicon, and diamond were calculated using the \(T^{3/2}\)model based on the particle-in-a-box (PIAB) approach and compared with the Debye \(T^3\)model. The analysis focused on quantum dots with sizes ranging from 1 to 100 nm. According to the PIAB \(T^{3/2}\)model, temperature fluctuations decrease as the temperature decreases, consistent with the principles of statistical physics. In contrast, the Debye \(T^3\)model predicts an increase in temperature fluctuations with decreasing temperature, contradicting the principles of statistical physics. These results emphasize the significant impact of quantum confinement and highlight the limitations of the Debye \(T^3\)model in describing nanoscale systems. Furthermore, distribution diagrams illustrating temperature fluctuations as functions of size and temperature were established for the first time. Based on these diagrams, clear boundaries were defined for the temperature and thermophysical property ranges where reliable predictions can be made.
@article{shixian2025fluctuation, title = {Temperature Fluctuations in Quantum Dots: Insights from a \(T^\{3/2\}\) Heat Capacity Model}, author = {Liu, Shixian and Khvesyuk, V.I.}, journal = {Physics Letters A}, volume = {534}, pages = {130261}, year = {2025}, doi = {10.1016/j.physleta.2025.130261}, } - Int. J. Thermophys. Investigating Anisotropic Three-Phonon Interactions in Graphene’s Thermal Conductivity Using Monte Carlo MethodShixian Liu, Fei Yin, and V.I. Khvesyuk*International Journal of Thermophysics, 2025
This study introduces a novel method for calculating the thermal conductivity of graphene using a Monte Carlo approach to evaluate anisotropic three-phonon interactions. The phonon dispersion relation is derived using a force constant model that incorporates up to fifth-order nearest-neighbor interactions, while the phonon density of states (DOS) is computed via a generalized Gilat-Raubenheimer method. A quantitative relationship for the scaling exponent of the specific heat capacity at low temperatures is established, emphasizing the unique two-dimensional characteristics of graphene. To address anisotropic effects, the Monte Carlo approach efficiently identifies three-phonon combinations that adhere to the conservation laws of energy and momentum. The findings highlight the pivotal role of anisotropic phonon interactions in graphene’s thermal conductivity. The thermal conductivity values obtained through the iterative method exhibit strong agreement with previous three-phonon calculations, thereby validating the model. Nevertheless, discrepancies with experimental data suggest that incorporating higher-order phonon processes, such as four-phonon scattering, may further improve predictive accuracy.
@article{shixian2025graphene, title = {Investigating Anisotropic Three-Phonon Interactions in Graphene's Thermal Conductivity Using Monte Carlo Method}, author = {Liu, Shixian and Yin, Fei and Khvesyuk, V.I.}, journal = {International Journal of Thermophysics}, volume = {46}, number = {2}, pages = {22}, year = {2025}, doi = {10.1007/s10765-024-03498-x}, }
2024
- Chin. Phys. Lett. Determination of Thermal Properties of Unsmooth Si NanowiresShixian Liu, A.A. Barinov*, Fei Yin, and V.I. KhvesyukChinese Physics Letters, 2024
We estimate the thermal properties of unsmooth Si nanowires, considering key factors such as size (diameter), surface texture (roughness) and quantum size effects (phonon states) at different temperatures. For nanowires with a diameter of less than 20 nm, we highlight the importance of quantum size effects in heat capacity calculations, using dispersion relations derived from the modified frequency equation for the elasticity of a rod. The thermal conductivities of nanowires with diameters of 37, 56, and 115nm are predicted using the Fuchs– Sondheimer model and Soffer’s specular parameter. Notably, the roughness parameters are chosen to reflect the technological characteristics of the real surfaces. Our findings reveal that surface texture plays a significant role in thermal conductivity, particularly in the realm of ballistic heat transfer within nanowires. This study provides practical recommendations for developing new thermal management materials.
@article{shixian2024determination, title = {Determination of Thermal Properties of Unsmooth Si Nanowires}, author = {Liu, Shixian and Barinov, A.A. and Yin, Fei and Khvesyuk, V.I.}, journal = {Chinese Physics Letters}, volume = {41}, number = {1}, pages = {016301}, year = {2024}, doi = {10.1088/0256-307X/41/1/016301}, }
2022
- Nucl. Eng. Des. Validation of the STEG code using experiments on two-phase flow across horizontal tube bundlesShixian Liu, Fei Yin, V.I. Melikhov*, and O.I. MelikhovNuclear Engineering and Design, 2022
The results of the validation of the STEG code using the experiments on two-phase flow across horizontal tube bundles are presented. The experiments are carried out on two water–air SG models, consisting of a transparent vessels, inside of which there is a tube bundle, a perforated sheet and a bead separating the upstream section of the circulation circuit of the model from the downstream one. The void fractions and water velocities are measured in different locations of the models. The brief description of the STEG code based on the 3D two-fluid model is presented. A set of interfacial drag correlations, which was recently developed by the authors, are used in the validation calculations. The peculiarities of the spatial two-phase flows have been established, and a quantitative comparison with experimental data has been performed. Good agreement between the calculated and experimental data is obtained.
@article{liu2022validation, title = {Validation of the STEG code using experiments on two-phase flow across horizontal tube bundles}, author = {Liu, Shixian and Yin, Fei and Melikhov, V.I. and Melikhov, O.I.}, journal = {Nuclear Engineering and Design}, volume = {399}, pages = {112048}, year = {2022}, doi = {10.1016/j.nucengdes.2022.112048}, }