Phonon Boltzmann Transport Equation Research Articles

Machine learning assisted understanding of the layer-thickness dependent thermal conductivity in fluorinated graphene

Manipulating thermal conductivity (κ) plays vital role in high-performance thermoelectric conversion, thermal insulation and thermal management devices. In this work, we using the machine learning-based interatomic potential and the phonon Boltzmann transport equation to systematically investigate layer thickness dependent κ of fluorinated graphene (FG). We show that the lattice κ of FG can be significantly decreased with Bernal bilayer stacking. Surprisingly, the further increasing of stacking layer can no longer affect the κ, however, the κ is increased in the bulk configuration. The variation of κ can be attributed to the crystal symmetry change from P-3m1 (164) at single layer to P3m1 (156) at multilayer. The decreasing crystal symmetry from single layer to bilayer resulting stronger phonon scattering and thus leading a lower κ. Moreover, we also show that the contribution of acoustic mode to κ decreases with the increase of layers, while the contribution of optical mode to κ is increased with increasing layers. These results provide a further understanding for the phonon scattering mechanism of layer thickness dependent κ.

Thermal Spreading Resistance of Near Surface Localized Heating-Induced Size Effects in Semiconductors

Abstract Localized heating is encountered in various scenarios, including the operation of transistors, light-emitting diodes, and some thermal spectroscopy techniques. When localized heating occurs on a scale comparable to the mean free path of the dominant energy carriers, additional thermal resistance is observed due to ballistic effects. The main objective of this study is to find a relation between this resistance, problem geometry, and material thermal properties in situations involving localized heating. Models based on the solution of the Fourier heat diffusion equation and the gray phonon Boltzmann Transport Equation are solved simultaneously to calculate the additional thermal resistances that arise from localized heating. Subsequently, the results are analyzed to derive the desired relationship. It is noted that in the context of localized heating resistance, the effects of geometrical variables are non-linear and substantial, particularly when the Knudsen numbers for the boundary and heat source exceed certain thresholds. Specifically, when the Knudsen number for the heat source becomes comparable to 1 localized heating resistance is observed. However, when the Knudsen number based on heat source height and width surpasses 8 and 20, respectively the heat source behaves akin to a point source, no longer significantly affecting the localized heating resistance. At this juncture, the maximum resistance limit is reached.

Comparison of the excellent thermoelectric properties of the half-Heusler compounds RbMgSb with a host-guest structure and LiMgSb

In this work, we systematically studied the thermoelectric (TE) transport properties of the half-Heusler compounds AMgSb (A = Li, Rb) based on an incorporation of first-principles calculations with self-consistent phonon theory and Boltzmann transport equations. We noted significant changes in the vibrational behavior of alkali metal atoms with a substantial increase in atomic mass. This alteration led to the formation of a host-guest structure in RbMgSb. In contrast, the stronger harmonic vibrations in LiMgSb results in it maintaining a Half-Heusler structure, without the pronounced anharmonicity found in RbMgSb. The calculation results reveal that RbMgSb has ultra-low lattice thermal conductivity κL, which is ten times lower than LiMgSb. We show that rattlers cause tenfold reductions in the thermal conductivity by increasing the phonon–phonon scattering probability, occurred in a wide frequency range. In addition, after careful consideration of multiple scattering mechanisms, the multiple valleys, high dispersion, flat band edges and band asymmetry near the Fermi level give both materials excellent electron transport properties. At the same time, LiMgSb itself already has a very low electron thermal conductivity κe, but the κe of RbMgSb is ten times smaller than that. As a consequence, remarkable ZT values of 2.51 and 3.45 at 900 K are captured in n-type LiMgSb and p-type RbMgSb, respectively. These findings reveal the promising potential of AMgSb in TE applications.

Evidence of Higher Order Phonon Anharmonicity in Gray Arsenic Crystal.

Phonons play a key role in the heat transport process of quantum materials. The understanding of thermal behaviors of phonons will be beneficial for designing modern electronic devices. In this study, we utilize specific heat, Raman spectroscopy, and first-principles calculations combined with the phonon Boltzmann transport equation to explore the thermal transport of gray arsenic. Our specific heat data indicate the presence of the phonon anharmonicity at high temperature. This is further supported by temperature-dependent Raman data showing evident phonon softening and line width broadening. More interestingly, from the analysis of temperature-dependent Raman modes, we found that the four-phonon scattering process is indispensable for interpreting the line width broadening at high temperatures. Moreover, we evaluate the importance of the four-phonon scattering process in the heat transport of gray arsenic using the moment tensor potential method. Our work sheds light on the importance of a higher order phonon scattering process in heat transport of the materials with moderate thermal conductivity.

Anisotropic Fourier Heat Conduction and phonon Boltzmann transport equation based simulation of time domain thermo-reflectance experiments

The anisotropic Fourier Heat Conduction Equation (FHCE) and the multidimensional phonon Boltzmann Transport Equation (BTE) were solved numerically in cylindrical coordinates and in time domain to simulate a Time Domain Thermo-Reflectance (TDTR) experimental silicon/aluminum substrate/transducer setup. The out-of-phase response of the probe laser was predicted at various beam offset distances for a pump laser pulse frequency of 80 MHz and modulation frequency of 10 MHz and compared against experimental measurements for a silicon substrate. The isotropic FHCE was also solved for comparison. Results show that the isotropic FHCE with bulk thermal conductivity of 145 W/m/K significantly underpredicts the out-of-phase temperature difference, particularly at smaller beam offsets. With an isotropic thermal conductivity of 105 W/m/K, the computed results match experimental data at smaller beam offsets well, but overpredicts the experimental data at larger beam offsets. An almost-perfect match is obtained by using an anisotropic thermal conductivity wherein the radial (in-plane) thermal conductivity is set to 85 W/m/K and the axial (through-plane) conductivity is set to 130 W/m/K. The multidimensional frequency and polarization dependent phonon BTE is next solved. The BTE results for the out-of-phase temperature difference match experimental observations well at small and intermediate beam offsets, but overpredicts the experimental data at larger beam offsets. FHCE results are fitted to the BTE predictions, and the extracted (best fit) thermal conductivity is found to be 110 W/m/K.

Loose bonding induced ultralow lattice thermal conductivity of a metallic crystal KNaRb

In the domain of metallic systems, electronic thermal conductivity typically governs heat transfer, while lattice (phononic) thermal conductivity (LTC) remains non-negligible magnitude. This study introduces the exceptional metallic material, cubic half-Heusler-type KNaRb, via phonon Boltzmann transport equation (BTE) resolution and first-principles calculations. KNaRb exhibits an ultralow LTC of 0.114 W/mK at room temperature, comparable to the lowest reported for metallic materials, contributing merely 0.66 % to overall thermal transport. Analysis attributes KNaRb's low LTC to low group velocity and strong anharmonicity, originating from its loosely bonded electronic structure. Acoustic modes, primarily from Rb atoms, dominate thermal transport. Examination of mean square displacement and potential energy profiles reveals significant movement of loosely bonded Rb atoms within KNaRb, acting as intrinsic "rattlers," inducing pronounced phonon anharmonicity and ultrashort lifetimes. This study advances understanding of heat conduction in metals, offering insights into materials with extremely low lattice thermal conductivity for potential future applications.

Unleashing the power of artificial intelligence in phonon thermal transport: Current challenges and prospects

The discovery of advanced thermal materials with exceptional phonon properties drives technological advancements, impacting innovations from electronics to superconductors. Understanding the intricate relationship between composition, structure, and phonon thermal transport properties is crucial for speeding up such discovery. Exploring innovative materials involves navigating vast design spaces and considering chemical and structural factors on multiple scales and modalities. Artificial intelligence (AI) is transforming science and engineering and poised to transform discovery and innovation. This era offers a unique opportunity to establish a new paradigm for the discovery of advanced materials by leveraging databases, simulations, and accumulated knowledge, venturing into experimental frontiers, and incorporating cutting-edge AI technologies. In this perspective, first, the general approach of density functional theory (DFT) coupled with phonon Boltzmann transport equation (BTE) for predicting comprehensive phonon properties will be reviewed. Then, to circumvent the extremely computationally demanding DFT + BTE approach, some early studies and progress of deploying AI/machine learning (ML) models to phonon thermal transport in the context of structure–phonon property relationship prediction will be presented, and their limitations will also be discussed. Finally, a summary of current challenges and an outlook of future trends will be given. Further development of incorporating AI/ML algorithms for phonon thermal transport could range from phonon database construction to universal machine learning potential training, to inverse design of materials with target phonon properties and to extend ML models beyond traditional phonons.

Non-equilibrium thermal transport study in steady state GaN MISHEMT channel layer based on electron Monte Carlo and phonon BTE

An electro-thermal coupling simulator for GaN devices based on electron Monte Carlo (e-MC) simulations is established. Taking GaN Metal Insulator Semiconductor High Electron Mobility Transistor (MISHEMT) as example, the non-equilibrium thermal transport processes of self-heating effect in the channel layer are studied. This simulator is mainly coupled by e-MC and the phonon Boltzmann transport equation (pBTE), physical property parameters and electric field parameters are provided by first-principles and Technology Computer Aided Design (TCAD), respectively. We first verify the e-MC program by calculating the electron transport properties of GaN materials, verify the feasibility of the established GaN MISHEMT model by using TCAD and obtained its operating characteristics. Further, the simulator is used to evaluate the non-equilibrium processes inside the channel layer in detail, the results show that there is significant consistency in the peak positions of electric field strength, heat generation and diffusion temperature, the diffusion temperature peak occurs at the secondary peak of heat generation. The frequency distribution of phonon emission under different drain-source bias voltages is revealed by phonon emission spectrum analysis. The strength of the non-equilibrium effect is measured by effective temperature. Increasing the drain-source bias voltage will significantly increase the peak temperature of hotspot and further enhance the non-equilibrium effect. Our study reports an efficient scheme for electro-thermal simulations of GaN MISHEMT, which provides insights for thermal management of GaN-based transistor devices.

The origin of anomalous mass-dependence of thermal conductivity in Janus XBAlY (X = Se, S, Te; Y = S, Se, O; X ≠ Y) monolayers

Owing to the unique asymmetric geometry, Janus monolayer compounds exhibit various exotic thermal properties and have promising applications in thermal management. In this study, we combine machine learning potentials and the phonon Boltzmann transport equation to perform a comparative study of the thermal transport properties in Janus XBAlY (X = Se, S, Te; Y = S, Se, O; X ≠ Y) monolayers. Our findings unveil a thermal conductivity (κp) ranking as SeBAlS > TeBAlO > SBAlSe, contradicting the conventional expectation that a higher κp is typically observed when the average atomic mass is smaller. At room temperature, the κp of SeBAlS is 174 Wm−1 K−1, which is 4.8 times that of SBAlSe when considering three-phonon scattering processes. Moreover, the consideration of four-phonon scatterings does not alter such ranking. The anomalous κp phenomenon was explained through a detailed analysis of the phonon–phonon scattering mechanism, phonon bandgap, phonon anharmonicity, and chemical bond strength. This study highlights the intricate relationship between atomic mass, bonding characteristics, and thermal properties, offering insights for designing Janus materials with tailored thermal conductivity.

Effect of van der Waals homogeneous interface on lattice thermal conductivity of Janus WSSe bilayer

Vertically stacked 2D materials have provided an unprecedented platform to identify various physical properties and discover novel interfacial emergent phenomena. In this study, the lattice thermal conductivity of Janus WSSe bilayer, involving diverse interfacial stacking configurations, has been clarified by solving the phonon Boltzmann transport equation based on first-principles calculations. The effect of homogeneously stacking on thermal conductivity and potential modulation approaches has also been revealed for Janus WSSe. Our results indicate that the thermal transport in Janus WSSe bilayer can be suppressed by van der Waals interface, and depends on both the stacking patterns and interfacial compositions (S-S, Se-Se and Se-S interfaces). Moreover, the interface effect can be further modulated by an applied vertical pressure. A further reduction in thermal conductivity can be achieved for Janus WSSe bilayer under vertical pressure, implying great potential for efficient thermal management and sensing applications.

Thermal transport in Yb-based 1-2-20 materials

Lattice thermal-transport properties of heavy-fermion YbT2Zn20-based (T = Co, Rh, and Ir) 1-2-20 compounds are calculated with the single-mode relaxation-time approximation and the full solution of the linearized phonon Boltzmann transport equation from first-principles anharmonic phonon calculations. We predict low lattice thermal conductivity κ L with a maximum value of ∼24.16 ·K at 85.14 K, 137.29 ·K at 9.67 K, and 23.55 ·K at 67.50 K and ∼12.02, 40.04, and 10.30 ·K at room temperature for YbCo2Zn20, YbRh2Zn20, and YbIr2Zn20, respectively. Based on the analysis of the cumulative κ L as a function of the phonon mean free path and the frequency-dependent joint density of states at various temperatures, we attribute the low κ L to a rattling mode with an average characteristic rattling frequency that enhanced phonon scattering processes, which reduced the phonon mean free paths, suppressed the phonon lifetime, and enhanced the probability of three-phonon scattering events. The predicted low κ L , especially in YbCo2Zn20 and YbIr2Zn20, makes them promising candidate materials for thermoelectric applications and thermal management.

Thermal transport of defective β-Ga2O3 and B(In)GaO3 alloys from atomistic simulations

β-Ga2O3 is a new generation of semiconductor material with a wide bandgap of 4.9 eV. However, the β-Ga2O3 devices inevitably produce defects within them after irradiation, leading to changes in their thermal conductivities. At present, the effect of radiation-damage-induced defects on thermal conductivity of β-Ga2O3 has not been carried out. Herein, we have employed molecular dynamics simulations to investigate the impact of defects on the thermal transport of β-Ga2O3, and the obtained thermal conductivity of non-defect β-Ga2O3 is in good agreement with recent reports. Our findings indicate that the thermal conductivity of β-Ga2O3 at room temperature exhibits a consistent decrease with an increase in the concentration of Ga vacancies, but shows a decreasing and then increasing trend as the number of O vacancies increases. In addition, doping/alloying is found to improve the irradiation resistance of β-Ga2O3 based on reported defect formation energy calculations, so the mechanism of alloying effect on the thermal conductivity is deeply analyzed through first-principles calculations. Moreover, the lattice thermal conductivities of ordered InGaO3 and BGaO3 alloys are predicted by solving the phonon Boltzmann transport equation. The obtained results that κ(Ga2O3) = κ(BGaO3) > κ(InGaO3) are attributed to the combined effect of volume, specific heat capacity, group velocity, and phonon lifetime of the three materials. This work can help to disclose the radiation damage influence on thermal properties of β-Ga2O3 semiconductors.

Importance of hydrogen bond configuration on lattice thermal conductivity of hydrogenated borophene

Due to the electron deficiency of boron, two-dimensional boron systems and its derivatives have a great diversity of configurations, such as the hydrogenated borophene, providing a promising platform to realize different electronic and thermal functions. In this work, using first-principles calculations combined with phonon Boltzmann transport equation, we study the lattice thermal conductivity (κL) of two hydrogenated borophene structures with different B–H bond configurations. We find that the κL of hydrogenated borophene can be doubled, when the B–H bond is replaced by the bridged B–H–B bond. Benefit from the electron deficiency of boron, the bridged B–H–B bond can provide electrons to the borophene layer, generating stronger B–B covalent bonds. This configuration further results in the blue-shift of phonon modes as well as the bunching effect for acoustic branches, which simultaneously increase the phonon group velocity and suppress the phonon–phonon scatterings, consequently enhancing the thermal conductivity. Our work offers an effective approach to optimize lattice thermal conductivity of two-dimensional materials via structure engineering, without varying the material content.

Self-consistent phonon calculations and quartic anharmonic lattice thermal conductivity in 2D InS monolayer

Low lattice thermal conductivity (κl) is a crucial factor for higher figure-of merit and hence the efficiency of thermoelectric generators. There are several reports on intrinsically low κl values in two-dimensional (2D) van der Waals materials using density functional theory and molecular dynamics simulations. In general, phonon dispersions are studied at absolute zero temperature using the finite-displacement approach within harmonic approximations. In addition, the κlis calculated using the third-order cubic interatomic force constants (IFCs) by solving the Boltzmann transport equation for phonons. In these calculations, we use quartic IFCs to solve self-consistent phonon equations to obtain dynamical dispersion relations at a finite temperature of 300 K using finite-temperature Green’s function for Bosonic systems in 2D indium sulfide (InS) monolayer. The cubic and quartic IFCs are calculated using machine learning algorithms, namely, the ordinary least square fitting and the least absolute shrinkage and selection operator. It was found that there is a lowering of the renormalized anharmonic phonon frequencies in the dispersion relations at 300 K upon the inclusion of quartic IFCs and anharmonic terms in the case of the InS monolayer. Thus, the κlvalue is reduced to 0.6 W/mK as compared to 0.9 W/mK obtained using cubic IFCs.

Prediction of novel ground-state structures and analysis of phonon transport in two-dimensional GexSy compounds.

We conducted this study to explore the ground-state structures of two-dimensional (2D) variable-composition GexSy compounds, driven by the polymorphic characteristics of bulk germanium sulfides and the promising thermoelectric performance of 2D GeS (Pmn21). To accomplish this, we utilized the highly successful evolutionary-algorithm-based code USPEX in conjunction with VASP for total energy calculations, leading to the discovery of three previously unexplored structures of Ge2S (P2/c), GeS (P3̄m1), and GeS2 (P21/c). These 2D materials exhibit significantly lower formation energies compared to their reported counterparts. We thoroughly scrutinized the structural stability and subsequently analyzed their electronic structures. Our analysis reveals a nearly direct band gap of 0.12/0.84 eV with the PBE/HSE06 functional for 2D Ge2S and an indirect band gap for 2D GeS and GeS2. Their semiconducting nature highlights the crucial importance of lattice thermal conductivity (κl), which we determined by solving the Boltzmann transport equation for phonons. Importantly, we predict a room temperature κl value of 6.82 W m-1 K-1 for GeS, lower than its 2D orthorhombic counterpart. In the case of GeS2, we observed an anisotropic κl value of 16.95/10.68 W m-1 K-1 along the zigzag/armchair directions at 300 K, with an in-plane anisotropy ratio of 1.59, surpassing that of 2D IV-VI compounds. We delve into detailed discussions regarding the role of lattice anharmonicity, group velocities, phonon lifetimes, and three-phonon weighted phase space in the overall thermal conductivity analysis.

First-principles prediction of the thermal conductivity of two configurations of difluorinated graphene monolayer.

Lattice thermal conductivity (κL) plays a crucial role in the thermal management of electronic devices. In this study, we systematically investigate the thermal transport properties of monolayer fluorinated graphene using a combination of machine learning-based interatomic potentials and the phonon Boltzmann transport equation. At a temperature of 300 K, we find that the κL values for chair-configured fluorinated graphene monolayers are 184.24 W m-1 K-1 in the zigzag direction and 205.57 W m-1 K-1 in the armchair direction. For the boat configuration, the κL values are 120.45 W m-1 K-1 and 64.26 W m-1 K-1 in the respective directions. The disparities in κL between these two configurations predominantly stem from differences in phonon relaxation times, which can be elucidated by examining the Grüneisen parameters representing the degree of anharmonicity. A more in-depth analysis of bond strengths, as assessed by the crystal orbital Hamiltonian population, reveals that the stronger in-plane CC bonds in chair-configured fluorinated graphene monolayers are the primary contributors to the observed variations in anharmonicity.

Giant manipulation of thermal conductivity anisotropy in black phosphorene under external electric fields.

The thermal anisotropy of materials holds significant theoretical and practical implications in the domains of thermal transport and thermoelectricity. Black phosphorene, a novel two-dimensional (2D) semiconductor, is notable for its exceptional chemical and physical properties, attracting substantial attention for its thermal transport characteristics. Similar to other 2D materials, black phosphorene exhibits pronounced in-plane thermal anisotropy. Given its expanding applications in nanoelectronics, optoelectronics, and thermoelectrics, there is a growing need to manipulate its anisotropic thermal transport. Current methods for adjusting anisotropy or isotropy typically involve structural engineering or materials processing, which are often costly, time-consuming, and irreversible. In contrast, little progress has been made with methods that are intact, robust, and reversible. Driven by the intrinsic relationship between interatomic interaction-mediated phonon transport and electronic charges, we conduct a comprehensive investigation into the impact of an external electric field on the thermal transport properties of 2D black phosphorene using first-principles calculations and the phonon Boltzmann transport equation. Our findings reveal that applying an electric field in the Zigzag direction reduces the lattice thermal conductivity of black phosphorene, with the Zigzag direction being more responsive to the electric field than the Armchair direction. By adjusting the electric field to a maximum of E(f_xx) = 0.2 V Å-1, the anisotropic thermal conductivity of black phosphorene decreases by more than 28%, demonstrating effective manipulation of anisotropy. This significant transition in anisotropic thermal transport arises from the substantial reduction in thermal conductivity along the Zigzag direction at moderate electric field strengths. The underlying cause of this variation in anisotropy can be attributed to changes in group velocity, with the phonon lifetime serving as a scaling factor for reducing anisotropy. Analysis of the electronic structures shows that stronger electric fields induce more charges, enhancing the screening effect. The electric field significantly alters thermal conductivity by affecting bond ionicity and anharmonicity. Our study introduces a robust approach for tuning the anisotropy of phonon transport in materials using an external electric field, without altering the atomic structure, thus offering considerable advantages for applications in nanoelectronics and thermoelectric energy conversion.

Giant thermal conductivity and strain thermal response of nitrogen substituted diamane: a machine-learning-based prediction.

With the ongoing trend of seeking miniaturization and enhanced performance for electronic devices, effective thermal management has emerged as a critical concern. The discovery and investigation of high thermal conductivity (κ) materials have proved to be pivotal in addressing this challenge. This study aims to explore the distinctive properties and potential applications of nitrogen substituted diamane (NCCN), a two-dimensional material with a diamond-like structure composed of carbon and nitrogen atoms. This work systematically delves into NCCN's thermal, mechanical, and electrical properties. It is predicted that NCCN exhibits an exceptional κ, ∼2288 W m-1 K-1, at room temperature (300 K) by combining the machine-learning interatomic potential method and the phonon Boltzmann transport equation, surpassing that of H-diamane and rivaling that of diamond, and an impressive electronic band gap of ∼4.47 eV (PBE). For mechanical properties, the stress-strain relationship reveals that NCCN exhibits isotropic elastic properties and anisotropic tensile strengths. Additionally, the variations in NCCN's κ and electronic energy band structure under different strains underscore its substantial potential in the field of thermoelectric applications.

Intrinsic ultralow lattice thermal conductivity in lead-free halide perovskites Cs3Bi2X9 (X = Br, I).

Lead-free halide perovskites have recently garnered significant attention due to their rich structural diversity and exceptionally ultralow lattice thermal conductivity (κL). Here, we employ first-principles calculations in conjunction with self-consistent phonon theory and Boltzmann transport equations to investigate the crystal structure, electronic structure, mechanical properties, and κLs of two typical vacancy-ordered halide perovskites, denoted with the general formula Cs3Bi2X9 (X = Br, I). Ultralow κLs of 0.401 and 0.262 W mK-1 at 300 K are predicted for Cs3Bi2Br9 and Cs3Bi2I9, respectively. Our findings reveal that the ultralow κLs are mainly associated with the Cs rattling-like motion, vibrations of halide polyhedral frameworks, and strong scattering in the acoustic and low-frequency optical phonon branches. The structural analysis indicates that these phonon dynamic properties are closely relevant to the bonding hierarchy. The presence of the extended Bi-X antibonding states at the valence band maximum contributes to the soft elastic lattice and low phonon group velocities. Compared to Cs3Bi2Br9, the face-sharing feature and weaker bond strength in Cs3Bi2I9 lead to a softer elasticity modulus and stronger anharmonicity. Additionally, we demonstrate the presence of wave-like κC in Cs3Bi2X9 by evaluating the coherent contribution. Our work provides the physical microscopic mechanisms of the wave-like κC in two typical lead-free halide perovskites, which are beneficial to designing intrinsic materials with the feature of ultralow κL.

Thermal rectification induced by phonon hydrodynamics in asymmetric 2D microstructures

A thermal diode/rectifier, where the thermal resistance is direction dependent, has always been highly sought after and may find applications in potential thermal logic devices and thermal management systems. By using a more accurate local spatial linear approximation (LSLA) when numerically solving the phonon Boltzmann transport equation (BTE) under Callaway's dual model, it is shown here for the first time that phonon hydrodynamics combined with geometric asymmetry can lead to thermal rectification (TR). Interestingly, in a T-shaped graphene microribbon heat preferentially flows from the narrow end to the wide end, which is opposite to what is observed in T-shaped graphene nanoribbons. Flexural acoustic (ZA) phonons play the dominant role in the TR effect, due to their prominent hydrodynamic behavior. By analysis of the temperature spatial distribution and the phonon mean free paths (MFP), the reasons for TR are explained. By adjusting geometric parameters, the 16 % TR ratio is reached. Furthermore, the impact of edge roughness, temperature difference and strength of phonon hydrodynamics on the TR effect are investigated. This work points to a new mechanism for enabling thermal rectification and may provide insight into the unique interplay between phonon hydrodynamics and engineered microstructures.