Thermal transport in 2d and 3d nanoscale phononic crystals

THERMAL TRANSPORT IN 2D AND 3D NANOSCALE PHONONIC CRYSTALS YANG LINA NATIONAL UNIVERSITY OF SINGAPORE 2014 THERMAL TRANSPORT IN 2D AND 3D NANOSCALE PHONONIC CRYSTALS YANG LINA A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE 2014 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirely. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Yang Lina Acknowledgements First and foremost, I would like to express my sincere gratitude to my supervisor at National University of Singapore, Prof. Li Baowen. During the course of my candidature, Prof. Li gives wise guidance, kind encouragement and his immense knowledge. There would be no this research work without his far-insight and guidance. Meanwhile, I am extremely grateful to Prof. Yang Nuo at Huazhong University of Science and Technology for his patient guidance and numerous discussions. I would like to thank Prof. Wang Jian-Sheng and Prof. Gong Jiangbin at National University of Singapore for their lectures. I also would like to thank Prof. Zhang Chun for his help on first principle calculation and Prof. Qiu Chengwei for collaboration and discussion. I am grateful to Dr. Wu Gang, Dr. Chen Jie, and Dr. Liu Sha, Dr. Zhu Liyan, Dr. Zhang Gang for their kind help, valuable suggestions and comments. I am also grateful to many group members and friends in Singapore for their help: Dr. Feng Ling, Dr. Zhu Guimei, Dr. Ren Jie, Dr. Zhang Lifa, Liu Dan, Dr. Wang Jiayi, Bai Xue, Xuwen, Zhang Cheng, Qin Chu, Zhou Hangbo, Tao Lin, Dr. Hou Ruizheng, Dr. Wang Hailong, Dr. Tang Qinglin, Dr. Wang Chen, Zhou Longwen, Zhao Qifang to name a few. Finally, I would like to express my deepest gratitude to my family for their supports. i Table of Contents Acknowledgements . i Table of Contents .ii Abstract . v List of Publications vii List of Tables viii List of Figures ix Introduction . 1.1 Phononic Crystal . 1.1.1 Background 1.1.2 Nanoscale Phononic Crystals . 1.2 Thermoelectrics . 16 1.2.1 Thermoelectric Application and Basis . 16 1.2.2 Thermoelectric Efficiency and Challenges 18 1.2.3 Advantages of Phononic Crystals 21 1.3 Thesis Outline . 27 Methodology 29 2.1 Brief Introduction to Molecular Dynamics Simulation 29 2.2 Stillinger-Weber Potential and Optimized Tersoff Potential 33 2.3 Velocity Verlet Algorithm 36 2.4 Non-Equilibrium Molecular Dynamics 37 2.5 Equilibrium Molecular Dynamics . 42 ii 2.6 Brief Introduction to Lattice Dynamics 44 2.7 Phonon Relaxation Time and Phonon Participation Ratio 49 Thermal Transport in 3D Nanoscale Phononic Crystals 53 3.1 Motivation . 53 3.2 Thermal Conductivity of the 3D Isotopic PnCs of Si . 55 3.3 Phonon Modes Analysis 62 3.4 Discussion . 66 Thermal Transport in 3D Nanoscale Phononic Crystal with Spherical Pores 68 4.1 Motivation . 68 4.2 Extreme Low Thermal Conductivity of 3D Si PnCs 71 4.3 Phonon Modes Analysis 80 4.3 Discussion . 84 Thermal Transport in Graphene Phononic Crystal 86 5.1 Motivation . 86 5.2 Manipulate Graphene Thermal Conductivity by Phononic Crystal Structure 89 5.3 Phonon Modes Analysis 97 5.4 Discussion . 99 Thermoelectric Properties of 3D Si Phononic Crystal 101 6.1 Motivation . 101 6.2 Electronic Properties of 3D Si PnCs with Spherical Pores . 103 6.3 Discussion . 114 Conclusions 115 7.1 Contribution 115 iii 7.2 Future Work and Outlook . 118 iv Abstract The demand for energy in the world is increasing, but the nonrenewable fossil fuel becomes less and less in the earth. Thermoelectric materials could supply sustainable and clean electricity from waste heat. However, it is challenging to improve the efficiency of thermoelectric materials. The recent advances achieved in this field are mainly due to the significant reduction of the thermal conductivity by nanostructures. Nanoscale phononic crystals (PnCs) could have very low thermal conductivity, in addition, they have advantages in preserving the electronic properties. This thesis is devoted to investigating the thermal conductivity of two-dimensional (2D) and three-dimensional (3D) nanoscale PnCs and understanding the underlying physical mechanism. Moreover, the electronic properties of nanoscale 3D PnCs with spherical pores are studied. Molecular dynamics simulation method is applied to investigate the thermal conductivity of PnCs. We found that 3D isotopic Si PnCs could have very low thermal conductivity and phononic band gaps exist at high frequencies in the PnCs. The thermal conductivity of Si PnCs with spherical pores has extreme low thermal conductivity, and the low frequency phonons mainly contribute to the thermal conductivity. In addition to Si based PnCs, graphene PnCs are also studied, and their thermal conductivity could be tuned by varying the porosity. Phonon dispersion analyses show that phonon dispersions of PnCs are greatly suppressed and flattened, which will cause the v reduction of phonon group velocities. Phonon eigenmodes analyses find that phonon modes are strongly localized in PnCs, which could cause the reduction of thermal conductivity. Finally, the electronic properties of 3D nanoscale Si PnCs with spherical pores are calculated by density functional theory and Boltzmann transport equation under the relaxation time approximation. The electronic properties are little degraded, but the degradation is much less significant than the reduction of lattice thermal conductivity. Therefore, the value of ZT could be greatly enhanced in Si PnCs with spherical pores. vi List of Publications [1] L. Yang, N. Yang, and B. Li, Thermoelectric Properties of 3D Si Phononic Crystal, in preparation (2014). (Chapter 6) [2] L. Yang, J. Chen, N. Yang, and B. Li, Significant Reduction of Graphene Thermal Conductivity by Phononic Crystal Structure, submitted (2014). (Chapter 5) [3] L. Yang, N. Yang and B. Li, Extreme Low Thermal Conductivity in Nanoscale 3D Si Phononic Crystal with Spherical Pores, Nano Lett. 14, 1734 (2014). (Chapter 4) [4] L. Yang, N. Yang and B. Li, Reduction of Thermal Conductivity by Nanoscale 3D Phononic Crystal, Sci. Rep. 3, 1143 (2013). (Chapter 3) vii Chapter Conclusions of bulk Si decreases as temperature increases proportional to 1/T. Importantly, we found that the thermal conductivity is mainly contributed by phonon modes with frequencies smaller than 0.1 THz. The thermal conductivity could be reduced by a factor up to 104 times at room temperature. Therefore, implementing PnC structure in Si is a useful method to reduce the thermal conductivity. Besides Si based PnCs, PnCs based on graphene were also designed and studied by molecular dynamics method. Graphene has super high thermal conductivity (3000 ~ 5000 W/m-K), while the graphene PnCs could greatly reduce the thermal conductivity. The thermal conductivity of graphene increases as the length increases from several nanometers to micrometers. However, the thermal conductivity of graphene PnCs with period length of 25 nm and porosity of 28% is 142 W/m-K when the length is 250 nm, and the thermal conductivity increase slowly when the length is larger than 250 nm. The simulation results show that porosity and period length are two important factors that could significantly impact the thermal conductivity. After investigating the thermal properties of PnCs, we also studied the electronic properties of Si PnCs with spherical pores by first principle calculation and Boltzmann transport equation under the relaxation time approximation. We found that the electrical conductivity and electronic thermal conductivity is decreased very little. Similar as lattice thermal conductivity, the electrical conductivity and the electronic thermal conductivity decrease as the porosity increases but the reduction is much less 117 Chapter Conclusions significant than that of lattice thermal conductivity. The value of ZT of Si PnCs could be greatly enhanced due to the significant reduction of lattice thermal conductivity and the preservation of electronic properties. From our results of PnCs, we could conclude that PnCs could have very low thermal conductivity; meanwhile the electronic properties of bulk materials will be preserved. The thermal conductivity could be sufficiently controlled by varying period length, isotopes and porosity. These findings will encourage the fabrication of such PnCs and the practical applications of PnCs as thermoelectric materials. 7.2 Future Work and Outlook In this thesis, we have investigated the thermal conductivity of PnCs. The thermal conductivity of PnCs could be greatly impacted by the period length, isotopes and porosity. It is interesting to know how the combination of these factors could further reduce the thermal conductivity, because reduction of the lattice thermal conductivity is critical to improve the efficiency of thermoelectric materials. We found that the 3D Si PnCs with spherical pores have extreme low thermal conductivity (Chapter 4). The surfaces of the spherical pores are smooth in the PnCs. Because rough surface is more realistic in practical fabrication, it is meaningful to investigate how the rough surface could affect 118 Chapter Conclusions the thermal conductivity of PnCs. Additionally, the electronic properties of Si PnCs with rough surface is worthy of being studied. The phonon band gaps exist at high frequencies in the 3D Si isotopic PnCs (Chapter 3), however, the criteria for the formation of the band gaps in THz in PnC is still unclear. Engineering the band gaps in PnCs is very important to control the thermal transport. Thus, theoretical work is needed to study the phonon band gaps of PnCs. Other geometry such as hexagonal, triangle pores in PnCs also should be investigated and compared with the results of PnCs with spherical pores. The pattern of the pores is another factor that could affect the thermal conductivity. Only simple cubic pattern are studied in this thesis, other pattern like hexagonal should be further investigated. 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B 45, 13244 (1992). 132 [...]... minimum value of thermal conductivity as the change of period length.[70] The thermal conductivity of SiNTs by introducing a hollow in the center of SiNWs is studied and compared with that of SiNWs.[71] SiNTs could have much lower thermal conductivity than SiNWs, because phonon modes are more localized in SiNTs Further, the phonon modes are likely localized at the internal and external boundaries in. .. wave characteristic of phonons should be considered It is meaningful to investigate the heat transport in nanoscale PnCs, which will encourage and lay foundation for designing new devices such as heat waveguides, thermal imaging, thermooptics, thermal diodes, thermal cloaking and thermoelectric materials.[40] 1.1.2 Nanoscale Phononic Crystals Nanoscale PnCs could control THz lattice vibrations, i.e phonons,... elastic composites in 1993,[18] and later experimentally observed in the frequency range between 1000 and 1120 kHz by Montero de Espinosa using periodic arrangement of cylindrical holes in 1998.[19] In 2000, a three-dimensional (3D) PnC was constructed by arranging balls in three spatial directions, which could be used as local resonant sonic materials.[20] In Fig 1 1, a shows 1D, 2D and 3D PnCs which are... scale and materials The transient thermal grating technique for non-contact, non-destructive measurements of thermal transport has been invented by Nelson group.[46] The frequency domain thermoreflectance method is used to detect broadband phonon mean free path contribution to thermal conductivity.[47] First principle method is applied to investigate the intrinsic phonon relaxation time in bulk Si and. .. three phonon scattering, impurity scattering, isotopic scattering, defect scattering, interface scattering, etc Each of these scattering process could be characterized by its relaxation time, and the combined relaxation time follows the Matthiessen rule[52] With the developments of synthesizing and processing of nanoscale materials, many works have been done on nanostructures including onedimensional... 30.5%, and Si PnC with porosity 38%, respectively 113 xx Chapter 1 Introduction Chapter 1 Introduction This chapter firstly introduces the properties of phononic crystals (PnCs), the development from macroscale sonic crystals to nanoscale PnCs, and the applications of PnCs Theoretically, nanoscale PnCs could be used to control waves in THz which is phonons in crystal, and thus PnCs are promising candidate... negligible Phonon scatterings are characterized by two parameters, relaxation time and phonon mean free path (MFP) The relaxation time is the average time between two scattering events, and MFP is the average length that a phonon travels between two scattering events.[41,42] MFPs is important for understanding and engineering the thermal transport in materials, many theoretical and experimental works... studied by Volz and Chen[60] and experimentally found by Li et al.[61] The reduction of thermal conductivity is caused by the surfaces disorder and the reduction of phonon relaxation time in SiNWs.[62] 7 Chapter 1 Introduction Thermal conductivity could also depend on the length in nanoscale materials The length dependence of thermal conductivity and the anomalous heat diffusion in SiNWs were demonstrated... materials Because nanoscale PnCs have the common feature of nanostructures, we will first review the general properties of thermal transport in nanostructure Later, the recent developments of thermal transport in nanoscale PnCs are reviewed The mechanism of phonon transport in nanostructure has been widely studied In semiconductors and dielectric materials, the main contribution to thermal conductivity... al using non-equilibrium molecular dynamics method.[63] They found that the thermal conductivity increases as the length of SiNWs increases Besides length effect, the isotopic doping effect on the thermal conductivity is also studied SiNWs doped with isotopic atoms were investigated by Yang et al in 2008.[64] They found that the thermal conductivity of SiNWs could be exponentially reduced by random . THERMAL TRANSPORT IN 2D AND 3D NANOSCALE PHONONIC CRYSTALS YANG LINA NATIONAL UNIVERSITY OF SINGAPORE 2014 THERMAL TRANSPORT IN 2D AND 3D NANOSCALE PHONONIC. This thesis is devoted to investigating the thermal conductivity of two-dimensional (2D) and three-dimensional (3D) nanoscale PnCs and understanding the underlying physical mechanism. Moreover,. Phonon Relaxation Time and Phonon Participation Ratio 49 3 Thermal Transport in 3D Nanoscale Phononic Crystals 53 3.1 Motivation 53 3.2 Thermal Conductivity of the 3D Isotopic PnCs of Si 55