Towards parameter-free device modeling 4/16/2017 Towards parameter-free device modeling Jesse Maassen (Supervisor : Prof. Hong Guo) Department of Physics, McGill University, Montreal, QC Canada science engineering crash Semi-classical device modeling device parameters Atomic, materials, chemistry modeling quantum physics device modeling < 50nm (1000 atoms) May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial

The first electronic computer: ENIAC --- large sizes 2017/4/16 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 HP corporate template tutorial

Today: transistors are very small 2017/4/16 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 HP corporate template tutorial

As the size of a device goes down, physics change 2017/4/16 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 HP corporate template tutorial

Conduction is usually studied “top down” 2017/4/16 Conduction is usually studied “top down” V = I R or I = V G Conductance G = 1/R Conductivity Mobility Scattering time Channel m = ? n = ? “Not obvious” May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial

What device parameters? 2017/4/16 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 HP corporate template tutorial

Practical modeling method: need for many parameters 2017/4/16 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 HP corporate template tutorial

Moore’s law for model parameters 2017/4/16 Moore’s law for model parameters Number of parameter double every 18 months Reflects the complexity in modern technology 103 Year of introduction (arbitrary unit in log scale) Implemented feature 1 102 10 1965 1980 1990 2000 Level 1 Level 2 Level 3 BSIM1 BSIM2 BSIM3v3 BSIM4 Number of parameters parameter per feature PSP May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 8

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 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 HP corporate template tutorial

Goal of nanoelectronics theory and modeling 2017/4/16 Goal of nanoelectronics theory and modeling engineering science crash large scale device modeling device parameters atomic simulations materials, chemistry, physics quantum mechanics Physics device modeling < 50nm (1000 atoms) 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 HP corporate template tutorial

Basic ingredients of a theory: 2017/4/16 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 HP corporate template tutorial

Theoretical transport model 2017/4/16 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 HP corporate template tutorial

Theoretical transport model (cont.): Landauer theory 2017/4/16 Theoretical transport model (cont.): Landauer theory Left reservoir empty 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 HP corporate template tutorial

H = Hleads + Hdevice + Hcoupling 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

Density functional theory : Kohn-Sham 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

DFT approximately solves how atoms interact : 2017/4/16 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 HP corporate template tutorial

A device is neither finite nor periodic 2017/4/16 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 HP corporate template tutorial

Essentially, must solve two problems: 2017/4/16 Essentially, must solve two problems: How to reduce the infinitely large system to something calculable on a computer? Effective scattering region Left lead Right lead May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial

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: Left lead Right lead Scattering region 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

Roberto Car’s group, Chemistry Department, Princeton 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

Keldysh non-equilibrium Green’s function (NEGF): 2017/4/16 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 HP corporate template tutorial

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

NEGF-DFT: Taylor, Guo and Wang, PRB 63, 245407 (2001). 2017/4/16 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 HP corporate template tutorial

Wide range of research has been carried out by NEGF-DFT 2017/4/16 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; …. Recently developed modeling tool allows for: Large-scale systems (~1000 atoms & ~10 nm). Disorder: Surface/interface roughness, dopants, impurities. it is a progressing field and not all is perfect yet. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial

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

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

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

Roberto Car’s group, Chemistry Department, Princeton 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

Roberto Car’s group, Chemistry Department, Princeton 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

Roberto Car’s group, Chemistry Department, Princeton 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

Roberto Car’s group, Chemistry Department, Princeton Graphene-Cu interface Transport properties: graphene | Cu(111) E = 0.2 eV Transmission Momentum filtering k Nano. Lett. 11, 151 (2011) kz kx k E EF May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

Roberto Car’s group, Chemistry Department, Princeton 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

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

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

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

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

Roberto Car’s group, Chemistry Department, Princeton 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

Roberto Car’s group, Chemistry Department, Princeton 4/16/2017 Conclusions We have a first principles quantum transport theory valid at finite bias using a combination of NEGF-DFT. Large scale parameter-free modeling tool useful for device and materials engineering. Proper treatment of chemical bonding at interfaces and includes the effects of disorder (very important for practical calculations). Potential to treat ~104 atoms and lengths ~10nm. May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial

Roberto Car’s group, Chemistry Department, Princeton 4/16/2017 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 HP corporate template tutorial

Thank you ! (and to my supervisor and colleagues) 4/16/2017 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 HP corporate template tutorial

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

Roberto Car’s group, Chemistry Department, Princeton 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 SiO2 Si Vacuum May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Our goal Current Electrode Electrode May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 43

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Our goal Surface Current Thickness Electrode Electrode Length Doping level (lead or channel) Orientation May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 44

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Atomic structure (surface) Hydrogenated surface vs. clean surface H terminated [21:H] Clean [P(22)] H Si (top:1) Si (top) Si (top:2) Si Si May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 45

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 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 HP corporate template tutorial 46

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Ultrathin Si films n++ i H Si (top) Si Two-probe system Channel : intrinsic Si Leads : n++ doped Si 21:H surface Periodic  to transport L = 3.8 nm n++ i T = 1.7 nm L = 19.2 nm n++ i May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 47

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Ultrathin Si films n++ i 21:H surface n++ i L n++ EF VB i CB Potential profile Max potential varies with L Screening length > 10nm May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 48

Roberto Car’s group, Chemistry Department, Princeton 4/16/2017 Ultrathin Si films n++ i 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 HP corporate template tutorial 49

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Ultrathin Si films n++ i Conductance vs. k-points ( || dimers) Largest G near  point Conductance drops rapidly, but slower than for transport  to dimers. i n++  TOP VIEW May 4, 2011 Roberto Car’s group, Chemistry Department, Princeton HP corporate template tutorial 50

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Ultrathin Si films n++ i 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 HP corporate template tutorial 51

Roberto Car’s group, Chemistry Department, Princeton 2017/4/16 Ultrathin Si films n++ i 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 HP corporate template tutorial 52

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]

J. Maassen, F. Zahid and H. Guo PRB 80, 125423 (2009) Effect of dephasing on electron transport I(X) = 0 Phase breaking : Phenomenological model (Buttiker probe model) Self-energy : Simple implementation J. Maassen, F. Zahid and H. Guo PRB 80, 125423 (2009)

Effect of dephasing on electron transport Al - BDT - Al Left reservoir Right reservoir J. Maassen, F. Zahid and H. Guo PRB 80, 125423 (2009)

Effect of dephasing on electron transport Narrow Al nanowire V = 0.05 V Ballistic transport independent of length Ohm’s law behavior J. Maassen, F. Zahid and H. Guo PRB 80, 125423 (2009)