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Jesse Maassen (Supervisor : Prof. Hong Guo)

crash. quantum physics. Atomic, materials, chemistry modeling. device modeling < 50nm (1000 atoms). Semi-classical device modeling. device parameters. Towards parameter-free device modeling. Jesse Maassen (Supervisor : Prof. Hong Guo)

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Jesse Maassen (Supervisor : Prof. Hong Guo)

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  1. crash quantum physics Atomic, materials, chemistry modeling device modeling < 50nm (1000 atoms) Semi-classical device modeling device parameters Towards parameter-free device modeling Jesse Maassen (Supervisor : Prof. Hong Guo) Department of Physics, McGill University, Montreal, QC Canada engineering science May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  2. The first electronic computer: ENIAC --- large sizes This computer is made of vacuum tubes, 17,000 of them. People work inside the CPU of this computer. 1800 square feet ENIAC: Electronic Numerical Integrator and Computer. It was 2400 times faster than human computing. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  3. Today: transistors are very small Line of ~ 50 atoms How to compute charge conduction in these atomic systems? 200 million transistors can fit on each of these pin head. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  4. As the size of a device goes down, physics change Channel Length, L 1 mm 0.1 mm 10 µm 1 µ m 0.1 µm 10 nm 1 nm 0.1 nm Macroscopic dimensions Top Transistor L 1975 2000 2016 Bottom Atomic dimensions May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  5. Mobility Scattering time n = ? m = ? Conduction is usually studied “top down” V = I R or I = V G Conductance G = 1/R Conductivity Channel “Not obvious” May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  6. What device parameters? Device parameters These parameters specify properties of each individual device. How to obtain device parameters? --- by experimental measurements - now; --- by computational modeling; May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  7. Practical modeling method: need for many parameters capacitance Transconductance diodes Geometry scaling More than a 400 parameters are needed. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  8. Moore’s law for model parameters • Number of parameter double every 18 months • Reflects the complexity in modern technology 103 PSP BSIM4 BSIM2 102 BSIM3v3 Implemented feature (arbitrary unit in log scale) Number of parameters BSIM1 Level 2 10 Level 3 Level 1 parameter per feature 1 1980 2000 1990 1965 Year of introduction May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  9. Different modeling method: includes quantum and discrete material properties (all parameter free, no m, n or ) Quantum: Tunneling – cannot turn off transistor; Size quantization ; electron-phonon scattering during current flow; Quantum dissipation; Spin transport; Spin-orbital effects … Atomistic structures: Materials are no longer a continuous medium. Atomic simulations are useful when: more atomic species are used in nano-systems; charge transfer; interfaces, surfaces, domain boundaries; external potential drop; disorder … It is highly desirable to develop parameter-free theory and modeling method. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  10. crash quantum mechanics Physics atomic simulations materials, chemistry, physics device modeling < 50nm (1000 atoms) large scale device modeling device parameters Goal of nanoelectronics theory and modeling engineering science Nanoelectronic device physics This is largely applied physics: it is absolutely important that our theory is not only fundamentally correct, but also practical. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  11. Basic ingredients of a theory: • A transport model • Device Hamiltonian • Non-equilibrium Physics • Transmission • Fermi level alignment • Calculable! Picture from: Nitzan & Ratner, Science, 300, 1384 (2003). May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  12. Theoretical transport model A scattering region; semi-infinite leads; coherence; external potentials; coupling to other bath (the X-probe), etc.. We build an atomic model for this picture (for material specific properties). May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  13. empty Left reservoir Theoretical transport model (cont.): Landauer theory Under a voltage bias, electrons elastically (coherent) traverse the device from left to the right. They are “hot” electrons on the right, and some dissipation occurs and electrons end up inside the right reservoir. Right reservoir We compute the transmission process from left to the right. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  14. Device Hamiltonian • The Hamiltonian determines the energy levels of the device. (How to fill these levels  non-equilibrium statistics.) • What kind of H to use is an issue of accuracy (tight-binding, DFT, GW, …). • In the end, we want to compare our results with experimental data without adjusting theoretical parameters. • DFT offers a good trade-off between accuracy and speed. H = Hleads + Hdevice + Hcoupling May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  15. Density functional theory : Kohn-Sham Hamiltonian Hamiltonian Potential of ions Potential of electrons (Poisson equation) Quantum/ many-body effects Assumption : All electrons are independent May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  16. DFT approximately solves how atoms interact : DFT for materials: put atoms in a simulation box, compute interactions between electrons and nucleus. But, DFT solves only 2 kinds of problems: finite or periodic systems. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  17. A device is neither finite nor periodic • For a device: • There is no periodicity. • There are infinite number of atoms because the device is hooked up to external leads… These difficulties must be overcome in first principles modeling of transport. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  18. Essentially, must solve two problems: How to reduce the infinitely large system to something calculable on a computer? Right lead Left lead Effective scattering region May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  19. Left lead Scattering region Right lead Screening approximation --- reducing the infinitely large problem: Within DFT, once the potential is matched at the boundary, charge density automatically goes to the bulk-electrode values at the boundaries: Charge density Within screen approx., we only have to worry about a finite scattering region. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  20. Another example Using the screening approximation and solving Poisson Equation in real space, we can deal with systems with different leads. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  21. Keldysh non-equilibrium Green’s function (NEGF): NEGF: Right lead Left lead Effective scattering region Correct non-equilibrium physics, correct transport boundary conditions, easiness of adding new physics (e-p). Book of Jauho; book of Datta; Wang, Wang, Guo PRL 82, 398(1999) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  22. Transmission (This is one of several ways of getting T) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  23. NEGF-DFT: Taylor, Guo and Wang, PRB 63, 245407 (2001). • Use density functional theory (DFT) to compute the electronic structure and all other materials properties of the open device structure; • Use Keldysh non-equilibrium Green’s function (NEGF) to populate the electronic states (non-equilibrium quantum statistics); • Use numerical techniques to deal with the open boundary conditions. Molecular transport junctions Solid state devices May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  24. Recently developed modeling tool allows for: • Large-scale systems (~1000 atoms & ~10 nm). • Disorder: Surface/interface roughness, dopants, impurities. Wide range of research has been carried out by NEGF-DFT • Leakage current in MOSFET; • Transport in semiconductor devices, photocells; • Transport in carbon nanostructures; • Resistivity of Cu interconnects; • Conductance, I-V curves of molecular transport junctions; • Computation of capacitance, diodes, inductance, current density; • TMR, spin currents, and spin injection in magnetic tunnel junctions; • Transport in nanowires, rods, films, clusters, nanotubes; • Resistance of surface, interface, grain boundaries; • STM image simulations; • Strongly correlated electrons in transport; • Transport through short peptides; • …. it is a progressing field and not all is perfect yet. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  25. An example: • Graphene-metal interface May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  26. Motivation (graphene-metal interface) • Experimental studies: Phys. Rev. B 79, 245430 (2009) Nature Nanotechnology 3, 486 (2008) Photocurrent experiments May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  27. Parameter-free transport (NEGF-DFT*) calculation of a graphene / metal interface Our goal * Jeremy Taylor, Hong Guo and Jian Wang, PRB 63, 245407 (2001). May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  28. Atomic structure • Which metals? What configuration at the interface? • Cu, Ni and Co (111) have in-place lattice constants that almost match that of graphene. • Previous study found most stable configuration (PRL 101, 26803 (2008)). Metal May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  29. Graphene-Cu interface Bandstructure of hybrid graphene | Cu(111) system • Graphene states in black • Weak hybridization • n-type graphene Metal Appl. Phys. Lett. 97, 142105 (2010) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  30. Graphene-Cu interface Transport properties: graphene-Cu(111) system • Double minimum T. • T almost perfectly described by pure graphene at TMIN. Appl. Phys. Lett. 97, 142105 (2010) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  31. Graphene-Cu interface Transport properties: graphene-Cu(111) system • One Dirac point pinned, while other moves with V. • Peak in conductance  doping level of graphene Appl. Phys. Lett. 97, 142105 (2010) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  32. : A-site C(pz) : B-site C(pz) : Ni(dZ2) Graphene-Ni interface Band structure : graphene-Ni(111) system • Strong hybridization with metal • Band gap opening • Graphene is spin-polarized Nano. Lett. 11, 151 (2011) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  33. Graphene-Ni interface Transport properties : graphene-Ni(111) system Nano. Lett. 11, 151 (2011) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  34. Graphene-Ni interface Transport properties : graphene-Ni(111) system Nano. Lett. 11, 151 (2011) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  35. Graphene-Ni interface Transport properties : graphene-Ni(111) system Nano. Lett. 11, 151 (2011) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  36. Graphene-metal interface SUMMARY • Cu merely n-dopes the graphene resulting in: • Peak in dI/dV provides doping level • Can be simply modeled assuming a n-i junction • Similar trends for Al, Ag, Au & Pt • Ni & Co create spin-dependent (pseudo-) band gaps in graphene. • Large spin injection efficiencies ~80% May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  37. Take home message: 9nm 1. Quantum physics Eigler (IBM) 2. Materials physics Williams (HP) To make quantitative predictions without phenomenological parameters, a formalism has been developed that includes these ingredients. 3. Nonequilibrium statistical physics (picture from Ratner) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  38. Thank you ! (and to my supervisor and colleagues) $: NSERC, FQRNT, CIFAR, DRDC; Computers : SRC, LuXin Energy. RQCHP,CLUMEQ maassenj@physics.mcgill.ca May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  39. Another example: • Graphene-metal interface • Ultrathin Si films May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  40. Motivation (Si nano-film) • The main motivation for our research was the experimental work by Pengpeng Zhang et al. with silicon-on-insulators. Nature 439, 703 (2006) Used STM to image 10 nm Si film on SiO2 Charge traps Surface states SiO2 Vacuum SiO2 Si May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  41. Our goal Current Electrode Electrode May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  42. Our goal Surface Current Thickness Electrode Electrode Length Doping level (lead or channel) Orientation May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  43. Atomic structure (surface) • Hydrogenated surface vs. clean surface Clean [P(22)] H terminated [21:H] H Si (top:1) Si (top) Si (top:2) Si Si May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  44. Electronic structure (surface) • Atomic structure & bandstructure H terminated [21:H] Clean [P(22)] || dimers  dimers  dimers || dimers || dimers  dimers  dimers || dimers • Large gap ~0.7 eV • Small gap ~0.1 eV May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  45. H Si (top) Si i n++ n++ n++ i n++ n++ n++ i Ultrathin Si films • Two-probe system • Channel : intrinsic Si • Leads : n++ doped Si • 21:H surface • Periodic  to transport L = 3.8 nm T = 1.7 nm L = 19.2 nm May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  46. i n++ n++ Ultrathin Si films • Conductance vs. k-points ( dimers) • Shows contribution from k-points  to transport • Transport occurs near  point. • Conductance drops very rapidly  TOP VIEW i n+ n+  May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  47. i n++ n++  TOP VIEW i n++ n++  Ultrathin Si films • Conductance vs. k-points ( || dimers) • Largest G near  point • Conductance drops rapidly, but slower than for transport  to dimers. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  48. i n++ n++ Ultrathin Si films • Conductance vs. Length • Conductance has exponential dependence on length, i.e. transport = tunneling. • Large difference due to orientation. • Better transport in the direction of the dimer rows. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  49. i n++ n++ Ultrathin Si films SUMMARY • Electronic structure • 21:H [~0.7 eV gap] • p(22) [~0.1 eV gap] • Transport properties • Large effect of orientation in G for 21:H • More complete study to come soon! May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

  50. Some (more) examples: • Effect of dephasing on electron transport • Scattering properties of a nano-electromechanical system [Published in Phys. Rev. Lett. 105, 217206 (2010)] • Raman spectra of graphene on Cu substrate [Submitted to Phys. Rev. Lett.] • Effect of disorder and vacancies on electronic transport through a Au conductor [in progress] • Electron transport through a Si/Ge interface [in progress]

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