1. Thermal Transport in Graphene Nano Ribbons COOPERATORS: WU Gang (IHPC) GAN Cheekwan (IHPC) CHIN Saikong (IHPC) WU Ping (IHPC) JIANG Jinwu (NUS) WANG Jiansheng (NUS) LI Baowen (NUS) LIANG Gengchiau (NUS) 08-07-2010 Institute of High Performance Computing LAN Jinghua (IHPC)

2. Outline Part 1: Edge effect on thermal transport of GNR Part2: Isotopic doping effect on the thermal conductivity of graphene – Molecular dynamics and NEGF calculations Part3: Disappearing anisotropic thermal conductance Part4: Reduction of thermal conductivity by 2 orders with vacancy

3. Part1: Edge effect on thermal transport of GNR (a) GNR (n=2) (b) GNR (n=4)

4. Transport of GNR with different widths Edge effects disappear after =12. L =775nm is the mean free path measured by experiment. Thermal conductivity Experimental results:

5. Part2: Isotopic doping effect on the thermal conductivity of Molecular dynamics calculations NEGF calculations

6. Part3:Disappearing anisotropic thermal conductance

7. Part4:Reduction of Thermal Conductivity by vacancy R 334 times reduction

8. CONCLUSION: 1. Atomic edge distortion is important in nanoscale and can be neglected when the system size is big. 2. Doping will reduce thermal conductance and the reduction is proportional to mass difference between isotopic elements. 3. Anisotropic thermal conductance is purely induced by different edges. 4. Vacancy can reduce thermal conductance by 2 orders.

9. Our Strategies to reduce Thermal Conductivity Done Doing Future Plan 1. Vacancy and void 2. Surface roughness 3. Adsorb on surface 4. Inter-chain interaction 5. Alloy of materials 6. External potential field IHPC CONFIDENTIAL

10. Our Methods: Available Developing Future plan Standard phonon/electron band structure calculations Molecular dynamics with empirical potentials (C, Si) Thermal conductivity First-Principles Molecular dynamics Phonon non-equilibrium Green’s function (C, Si) ZT Combine with first-principles calculations Electron non-equilibrium Green’s function (C, Si) Electrical conductivity Seebeck coefficient Hopping parameters for different systems Non-equilibrium Green’s function with el-ph coupling Quantum molecular dynamics IHPC CONFIDENTIAL

11. Techniques to increase The best thermoelectric materials were succinctly summarized as “phonon-glass electron-crystal”. Nanostructure – electron performance improved or maintained with the reduction of thermal conductivity: 1. Super lattice: , An cheap alternative to super lattice – Nanocomposite Extra small size – large ratio of surface atoms and total atoms significantly reduce thermal conductivity. Our remarks: The key factor in these techniques is inducing interfaces and boundaries to scatter phonons more effectively than electrons.

12. Part2: Thermoelectricity Thermoelectric materials ranked by a figure of merit , --- the thermopower or Seebeck coefficient --- the electrical conductivity --- the thermal conductivity --- the absolute temperature. In order to be competitive with conventional refrigerators and generators, one must develop materials with

13. Thermoelectricity

14. Hamiltonian of a given system- Coupled harmonic oscillators- Coupling matrix- , , Left Region Right Region Central Region

15. Methods used in thermal transport in GNR Landauer formula - The Bose-Einstein distribution for phonons - Transmission coefficient Thermal conductance is defined as the limit

16. Transmission through a junction NEGF: Caroli formula Retarded Green’s function for the central region- Retarded self-energy of the leads- Function- Retarded surface green function for the leads- You must know force constant

17. Tight-binding method to obtain 1. Relax the structure to the minimum energy state 2. Move atoms one by one to get the dynamic matrix of the force constant.

18. Edge effect on quantized thermal transport