ATK 方法的扩展及其应用 王雪峰 苏州大学物理系 ZJNU-JinHua

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

SIESTA TranSIESTA KS Hamiltonian Matrix Nonequilibrium Green’s Function TranSIESTA-C ATK+VNL Other transport packages: Smeagol, OpenMX,WanT,PWSCF ZJNU-JinHua Jose M. Soler, et al., J. Phys.: CM 14, 2745 (2002); J. Taylor, H. Guo and J. Wang, Phys. Rev. B 63, (2001); M. Brandbyge, et al., Phys. Rev. B 65, (2002);

The system T 1,   T 2,   vibration ZJNU-JinHua

Band-diagram of the system in equilibrium

Effect of gate voltage Not just a shift in reality!

Effect of source-drain voltage

Escape time, contact coupling

Current N E Occupation number

Broadening ZJNU-JinHua N is then obtained

More general expression

Potential profile capacitance

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

Tight-binding model

Inflow and outflow

Coherent transport for one level model

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 : Formalism M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor, and K. Stokbro, PRB 65, (2002). K. Stokbro, J. Taylor, M. Brandbyge, and P. ordejon, Ann. NY. Acad. Sci. 1006, 212 (2003) ZJNU-JinHua

Density matrix:  In equilibrium:  In nonequilibrium:  The electron density: The current through the contact:

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

Phonon effect in the lowest order D G

Inelastic scattering p.287 p.336

Elastic scattering for one level model

Inelastic scattering for one level model D G

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, (2007) ZJNU-JinHua

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

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

Top-down technologies in traditional semiconductor industry -- Microelectronics mm 100nm10nmnm0.1nm Si lattice CPU wire ITRS Intl. Tech. Roadmap Semi. Bottom-up technologies Molecular electronics, Spintronics, Quantum computation mm 0.1nm nm 10 nm100nm DNA Si lattice H2OH2O Quantum dot nanotube, nanowire ZJNU-JinHua

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

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 Å Calculation Method ZJNU-JinHua L. N. Zhao, et al., J. Comp. Electronics 7, 500 (2008); X. F. Wang, et al., Int. J. Nanoscience 8, 113 (2009).

Si-slab based MOSFET capacitor Result: ZJNU-JinHua

Charge and electrostatic potential distribution X V  X ZJNU-JinHua

Total induced charge and surface potential versus gate voltage Q VsVs VsVs VgVg VgVg VgVg Q ZJNU-JinHua

Transmission spectrum under gate voltage T  T  ZJNU-JinHua

Thermoelectric effects

thermoelectric devices Thermal conductance ZJNU-JinHua

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

silicon nanowires A. I. Hochbaum et al., Nature 451, 163 (2008). silicon nanowires array Akram I. Boukai, ibid. 451, 168 (2008). ZT=S 2  T/ 

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 Summary ZJNU-JinHua