Jesse Maassen (Supervisor : Prof. Hong Guo)

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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) - PowerPoint PPT Presentation

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  • Jesse Maassen (Supervisor : Prof. Hong Guo)Department of Physics, McGill University, Montreal, QC Canada

    May 4, 2011Roberto Cars group, Chemistry Department, PrincetonTowards parameter-free device modeling

  • 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, 2011Roberto Cars group, Chemistry Department, Princeton

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

  • As the size of a device goes down, physics changeChannel Length, L

    1 mm

    0.1 mm

    10 m

    1 m

    0.1 m

    10 nm

    1 nm

    0.1 nm

    Transistor2000Atomic dimensions19752016 TopBottomMacroscopicdimensions L May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • V = I R or I = V G

    Conductance G = 1/RConductivityNot obviousConduction is usually studied top downChannelMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • What device parameters?Device parametersThese parameters specify properties of each individual device.

    How to obtain device parameters? --- by experimental measurements - now; --- by computational modeling;

    May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • Practical modeling method: need for many parameterscapacitanceTransconductanceGeometry scalingdiodesMore than a 400 parameters are needed.May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • Moores law for model parameters Number of parameter double every 18 months Reflects the complexity in modern technologyMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • 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, 2011Roberto Cars group, Chemistry Department, Princeton

  • Nanoelectronic device physicsscienceengineeringGoal of nanoelectronics theory and modelingThis is largely applied physics: it is absolutely important that our theory is not only fundamentally correct, but also practical.May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • Basic ingredients of a theory:Picture from: Nitzan & Ratner, Science, 300, 1384 (2003).A transport modelDevice HamiltonianNon-equilibrium PhysicsTransmissionFermi level alignmentCalculable!

    May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • 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, 2011Roberto Cars group, Chemistry Department, Princeton

  • Theoretical transport model (cont.): Landauer theoryUnder 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.We compute the transmission process from left to the right.Right reservoirMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • 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 + HcouplingMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • Density functional theory : Kohn-Sham HamiltonianHamiltonianPotential of ionsPotential of electrons (Poisson equation)Quantum/ many-body effectsAssumption : All electrons are independentMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • DFT approximately solves how atoms interact :DFT for materials: put atoms in a simulation box, compute interactions between electrons and nucleus.May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • A device is neither finite nor periodicFor a device: There is no periodicity. There are infinite number of atoms because the device is hooked up to external leadsThese difficulties must be overcome in first principles modeling of transport.May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • Essentially, must solve two problems:How to reduce the infinitely large system to something calculable on a computer?May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • 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:Within screen approx., we only have to worry about a finite scattering region.Charge densityMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • Another exampleUsing the screening approximation and solving Poisson Equation in real space, we can deal with systems with different leads.May 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • Keldysh non-equilibrium Greens function (NEGF):Book of Jauho; book of Datta; Wang, Wang, Guo PRL 82, 398(1999)NEGF: Correct non-equilibrium physics, correct transport boundary conditions, easiness of adding new physics (e-p). Effective scattering regionLeft leadRight leadMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

  • Transmission (This is one of several ways of getting T)May 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • 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 Greens function (NEGF) to populate the electronic states (non-equilibrium quantum statistics);

    Use numerical techniques to deal with the open boundary conditions.Molecular transport junctionsSolid state devicesMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • Wide range of research has been carried out by NEGF-DFTLeakage 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, 2011Roberto Cars group, Chemistry Department, Princeton

  • An example: Graphene-metal interfaceMay 4, 2011Roberto Cars group, Chemistry Department, Princeton

    *Physics & Astronomy, Pitt

  • May 4, 2011Roberto Cars group, Chemistry Department, PrincetonExperimental studies:Nature Nanotechnology 3, 486 (2008)Phys. Rev. B 79, 245430 (2009)PhotocurrentexperimentsMotivation (graphene-metal interface)

    *Physics & Astronomy, Pitt

  • May 4, 2011Roberto Cars group, Chemistry Department, Princeton* Jeremy Taylor, Hong Guo and Jian Wang, PRB 63, 245407 (2001).Our goal

    *Physics & Astronomy, Pitt

  • May 4, 2011Roberto Cars group, Chemistry Department, Princeton 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)). MetalAtomic structure

    *Physics & Astronomy, Pitt

  • Graphene-Cu interfaceMay 4, 2011Roberto Cars group, Chemistry Department, PrincetonAppl. Phys. Lett. 97, 142105 (2010)Bandstructure of hybrid graphene | Cu(111) system Graphene states in black Weak hybridization n-type grapheneMetal

    *Physics & Astronomy, Pitt

  • Graphene-Cu interfaceTransport properties: graphene-Cu(111) system Appl. Phys. Lett. 97, 142105 (2010)May 4, 2011Roberto Cars group, Chemistry Department, Princeton Double minimum T.

    T almost perfectly described by pure graphene at TMIN.

    *Physics & Astronomy, Pitt

  • Graphene-Cu interfaceMay 4, 2011Roberto Cars group, Chemistry Department, PrincetonEFkETransport properties: graphene | Cu(111) E = 0.2 eVkxkz Momentum filteringkNano. Lett. 11, 151 (2011)Transmission

    *Physics & Astronomy, Pitt

  • Graphene-Cu interfaceTransport properties: grap