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ATK 方法的扩展及其应用

ATK 方法的扩展及其应用. 王雪峰 苏州大学物理系. 2009.11.28 ZJNU-JinHua. Outline. Introduction Inelastic scattering Gate effect: electrostatic potential profile Optimization of tridiagonal matrix inverter Thermoelectric effect Improvement of functionals Summary. 2009.11.28 ZJNU-JinHua.

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ATK 方法的扩展及其应用

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  1. ATK 方法的扩展及其应用 王雪峰 苏州大学物理系 2009.11.28 ZJNU-JinHua

  2. Outline • Introduction • Inelastic scattering • Gate effect: electrostatic potential profile • Optimization of tridiagonal matrix inverter • Thermoelectric effect • Improvement of functionals • Summary 2009.11.28 ZJNU-JinHua

  3. KS Hamiltonian Matrix TranSIESTA SIESTA Nonequilibrium Green’s Function Other transport packages: Smeagol, OpenMX,WanT,PWSCF TranSIESTA-C Jose M. Soler, et al., J. Phys.: CM 14, 2745 (2002); J. Taylor, H. Guo and J. Wang, Phys. Rev. B 63, 245407 (2001); M. Brandbyge, et al., Phys. Rev. B 65, 165401 (2002); www.openmx-square.org www.smeagol.tcd.ie www.icmab.es/siesta/ www.quantumwise.com www.wannier-transport.org www.pwscf.org ATK+VNL 2009.11.28 ZJNU-JinHua

  4. The system T1, m1 T2, m2 vibration http://nanohub.org/ 2009.11.28 ZJNU-JinHua

  5. Band-diagram of the system in equilibrium

  6. Effect of gate voltage Not just a shift in reality!

  7. Effect of source-drain voltage

  8. Escape time, contact coupling

  9. Current Occupation number N E

  10. Broadening N is then obtained 2009.11.28 ZJNU-JinHua

  11. More general expression

  12. Potential profile capacitance

  13. Real system: numbers to matrices Ref. S. Datta, “Quantum Transport: Atom to Transistor”, Cambridge University Press (2005). 2009.11.28 ZJNU-JinHua

  14. Tight-binding model

  15. Inflow and outflow

  16. Coherent transport for one level model

  17. Formalism • Electronic structures of two electrodes and equivalent bulk system: self-consistent Kohn-Sham potentials and Hamiltonian matrices • Kohn-Sham Hamiltonian: • Poisson equation: • Hamiltonian Matrix H: • The Green’s function of open system, G: M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor, and K. Stokbro, PRB 65, 165401 (2002). K. Stokbro, J. Taylor, M. Brandbyge, and P. ordejon, Ann. NY. Acad. Sci. 1006, 212 (2003). 2009.11.28 ZJNU-JinHua

  18. Density matrix: • In equilibrium: • In nonequilibrium: • The electron density: • The current through the contact:

  19. Self-consistent Loop Initially define the system geometry Bulk calculations of Veff for the left and right electrodes Calculate Kohn-Sham Hamiltonian Calculate Current 2009.11.28 ZJNU-JinHua

  20. Phonon effect in the lowest order D G

  21. Inelastic scattering p.287 p.336

  22. Elastic scattering for one level model

  23. Inelastic scattering for one level model D G

  24. A7-atom gold wire with L=29.20 Å is coupled to semi-infinite electrodes. The vibrational region is taken to include the atoms in the pyramidal bases. The device region (describing the e-ph couplings) includes also the outermost surface layers. T. Frederiksen, M. Paulsson, M. Brandbyge, A. P. Jauho, Phys. Rev. B 75, 205413 (2007) 2009.11.28 ZJNU-JinHua

  25. The measured (noisy black curves) are for different strain. The calculated (smooth colored lines) are for different damping. T=4.2K

  26. MOSFETs are the most important building blocks Si nanostructures are still the fundamental units: Si cluster, nanowire, nanoslab, and so on Gate effect: Si MOSFET devices Vg Equivalent capacitive circuit 2009.11.28 ZJNU-JinHua

  27. Top-down technologiesin traditional semiconductor industry -- Microelectronics m 100nm 10nm nm 0.1nm 45 32 0.54 CPU wire Si lattice ITRS Intl. Tech. Roadmap Semi. Bottom-up technologiesMolecular electronics, Spintronics, Quantum computation m 0.1nm 10 nm 100nm nm Quantum dot Si lattice H2O DNA nanotube, nanowire 2009.11.28 ZJNU-JinHua

  28. Atomistic model systems S D (b) (a) Geometrically optimized Si-H bond length and Si-SiO2 interfaces 2009.11.28 ZJNU-JinHua

  29. Calculation Method • ATK Two-Probe method • Multigrid Poisson solver • Norm-conserving pseudopotential of Troullier-Martins scheme • LDA with Perdew-Zunger parameterization • Standard SIESTA SZP basis set • Mesh cutoff 4348 eV or 0.092 Å L. N. Zhao, et al., J. Comp. Electronics 7, 500 (2008); X. F. Wang, et al., Int. J. Nanoscience 8, 113 (2009). 2009.11.28 ZJNU-JinHua

  30. Si-slab based MOSFET capacitor Result: 2009.11.28 ZJNU-JinHua

  31. Charge and electrostatic potential distribution r V X X 2009.11.28 ZJNU-JinHua

  32. Total induced charge and surface potential versus gate voltage Vs Q Q Vs Vg Vg Vg 2009.11.28 ZJNU-JinHua

  33. Transmission spectrum under gate voltage T T e e 2009.11.28 ZJNU-JinHua

  34. Thermoelectric effects

  35. Thermoelectric effects

  36. thermoelectric devices Thermal conductance 2009.11.28 ZJNU-JinHua

  37. 2009.11.28 ZJNU-JinHua

  38. 2009.11.28 ZJNU-JinHua

  39. Charge current and heat current Here we do not include the phonon effect 2009.11.28 ZJNU-JinHua

  40. ZT=S2sT/k silicon nanowires array silicon nanowires A. I. Hochbaum et al., Nature 451, 163 (2008). Akram I. Boukai, ibid. 451, 168 (2008).

  41. Summary • ATK method is under development • Optimize algorithm: faster, better accuracy, larger system • Inelastic scattering • Multi-terminal systems: transistor • Temperature bias: thermoelectric effect • Better density functional 2009.11.28 ZJNU-JinHua

  42. Thanks for your attendance!

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