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AoE project-3: Modeling of new materials

AoE project-3: Modeling of new materials. G.H. Chen, J. Wang, H. Guo and Y.J. Yan. Research topics presented in the AoE Proposal:

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AoE project-3: Modeling of new materials

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  1. AoE project-3: Modeling of new materials G.H. Chen, J. Wang, H. Guo and Y.J. Yan Research topics presented in the AoE Proposal: Use tools from computational chemistry, computational physics and computational materials science to calculate the physical, chemical, mechanical and electric properties of materials such as insulator oxide layers and ultra thin metallic wires. Multi-scale approaches covering atomistic to continuum scales. Optical systems: materials and process models for on-chip/off-chip optoelectronic elements; the coupling between electrical and optical systems; optical interconnect models; semiconductor laser modeling. New topics suggested at the AoE Dec.17, 2009 meeting: 4. Phase changing materials AoE Team Meeting, Jan.26, 2010

  2. The chasm of first principles modeling chasm quantum mechanics Physics atomic simulations materials, chemistry, physics device modeling < 10nm (1000 atoms) large scale device modeling device parameters Nano-TCAD engineering science Goal of AoE The task of our research is to cross the chasm. AoE Team Meeting, Jan.26, 2010

  3. 1. Electronic materials Simulating gate leakage, thermal stability, interfacial layer formation, equivalent oxide thickness (EOT) control, and environmental stability, channel mobility, and high-k stability with poly silicon gates. Haffnium (Hf)-Based Materials for High-k Gate Stacks: growth, structure formation, and interface property. Simulating 0.5nm EOT: reducing dangling bonds, eliminating oxide layer, etc. Organic light emitting device (OLED) materials. Simulating Cu interconnects: sub-40nm lines. Surface roughness, grain boundary, bulk impurity scattering. Barrier layers to Cu lines: coating Cu lines with various barrier layers to reduce surface roughness scattering. Carbon nanotube interconnects. AoE Team Meeting, Jan.26, 2010

  4. 2. Multi-scale approaches Development of comprehensive database for kinetic Monte Carlo simulation of growth and thermal properties of materials. Step-1: literature evaluation. Step-2: first principles computation. Step-3: comparison to experimental measurements. Evaluate existing DFT codes of the AoE group, extend/modify/adapt/develop further materials simulation capabilities. Most likely is to adapt one of the real space DFT methods of the AoE group and extend it further using O(N). Phase-field methods. Develop phase-field and/or level-set methods for simulating growth of non-equilibrium structures within continuous model. Investigating and possibly develop the so called phase-field-crystal models where experimental scattering data is used to guide the numerical simulation of crystal formation process. Finite element and/or finite differencing calculations of strained materials. Develop linkages between all the above into a multi-scale electronics materials simulation package. AoE Team Meeting, Jan.26, 2010

  5. 3. Optical materials Simulating Gallium Nitride (GaN) films for optoelectronics and high temperature electronic devices. Modeling grow of GaN on nanoporous silicon carbide. Photonic bandgap materials – perhaps interacting with existing research groups in Hong Kong. Optical interconnect simulations: to be defined; Semiconductor laser modeling. Development of efficient and well controlled k.p methods. Development of million-atom pseudopotential based models for QD. Development of quantum Monte Carlo methods for excitons. Multi-scale: from CI to k.p. AoE Team Meeting, Jan.26, 2010

  6. 4*. Phase changing materials – new from Dec.17 meeting Prof. Mansun Chan’s talk will give more details on this class of important materials and the hot topic. AoE Team Meeting, Jan.26, 2010

  7. Materials modeling of AoE: AoE goal: come up with a suite of software tools for electronic materials modeling that provides atomic nanostructures for the device modeling project. Static properties: equilibrium structural determination by some kinds of total energy methods. Dynamic properties: nonequilibrium growth of nanostructures, meta-stable states, phase changing, current-induced, and complex systems. Software goal: through original research, develop atom-based quantitative software capable of dealing both static and dynamic modeling of electronic materials, including: Length scale --- 1nm to 22nm to continuum: 10,000 to 1M atoms to finite elements; Time scale --- sub-ps to milliseconds to continuous. (i) Large number of atoms, (ii) long time scales. AoE Team Meeting, Jan.26, 2010

  8. The AoE Materials modeling package Nano scale device N = 10,000 to 1,000,000 AoE Materials package collaboration Self-consistent module– O(N) DFT KMC module Phase-field atomic module Finite element module AoE Team Meeting, Jan.26, 2010

  9. Killer problem 1: Large number of atoms A cube of (10nm)3 has roughly 1 million atoms. Plus the leads, oxides, packaging layers, we have several million atoms. Self-consistent methods: typical DFT code VASP can do ~400 atoms; SIESTA did ~1000 atoms. For very special theory-oriented cases and running on supercomputers, one can do a few thousand atoms ab initio. (TB-LMTO can do ~4000 atoms but with bad total energy). It is very unlikely, if not impossible, to compute very large systems from atomic first principles, even with linear scaling methods (review later). We have to overcome this killer-problem for our AoE project. AoE Team Meeting, Jan.26, 2010

  10. Kill problem 2: Long time scales Time steps in atom based molecular dynamics is ~fs. Phonon time sales are ~0.1ps. To sample the energy landscape by MD we need 1M time steps and more. Typical DFT based MD can reach 100ps on a large computer cluster; empirical MD can reach 10ns; running supercomputer for one year, one probably can reach 1μs with empirical MD. It is unlikely that DFT based methods can ever reach 1ms, i.e. the relevant time scale for many material processing and formation problems. We have to use other approaches to overcome the time scale problem. AoE Team Meeting, Jan.26, 2010

  11. Atomistic modeling of materials from first principles • There are many electrons in a device: they interact via Coulomb interaction. Exact solution is impossible to obtain. • The de facto standard technique for atomistic calculation is DFT: DFT has been widely applied to solve problems of solid state physics, materials science, chemistry, molecular modeling, biological systems, drug design, … • DFT treats e-e interaction in a mean field manner: each electron is moving inside a mean field created by all other electrons. Hence, instead of solving an N-particle problem, DFT solves N 1-particle problems. • A typical DFT calculation can solve a system of a few tens to a few hundred atoms quite accurately. Linear scaling methods have solved problems involving ~2,000 or more atoms. AoE Team Meeting, Jan.26, 2010

  12. Basics for DFT and total energy methods: • Born-Oppenheimer approximation • Variational principle and Kohn-Sham equation • The Hellman-Feynman theorem • Total energy optimization • Molecular Mechanics and Molecular Dynamics Typical DFT computation scales as O(N3): a fast code runs ~200 atoms on a PC. AoE Team Meeting, Jan.26, 2010

  13. Progress in atomistic computation: physics underlying order-N Locality: properties of a certain observation region comprising one or a few atoms are only weakly influenced by factors that are spatially far away from this observation region. S. Geodecker Rev. Mod. Phys. (1999). Density matrix exhibits decaying property insulator metal LMTO (nanodsim) LCAO (nanodcal) Example: Si bulk AoE Team Meeting, Jan.26, 2010

  14. Concept of localization region Localization approximation: B A Density matrix of a single atom: it is sufficient to consider atoms within its localization region. So the system is divided into many localization regions surrounding each atom. AoE Team Meeting, Jan.26, 2010

  15. Order-N methods in literature: AoE Team Meeting, Jan.26, 2010

  16. ABEL on Si cluster (LMTO) – our best so far Si cluster (LMTO) with various radii is calculated on a single PC with ABEL (none-orth, adaptive block Lanczos ). The calculated on-site density matrix and occupation number is compared to Si bulk value: band gap (LMTO) = 0.525 eV band gap (Exp) = 1.17 eV • The calculated Si cluster has very long localization length (30 aB), which is due to underestimated band gap (well known problem in LDA). Currently we are working on a new type of XC which can solve the problem elegantly. • Assume the corrected localization length is 20 aB, a single atom needs 1 minute on a single processor (see 3rd row), 10000 atoms are expected to take 100 minutes on a 100-processor cluster. AoE Team Meeting, Jan.26, 2010

  17. We have repeated these calculations AoE Team Meeting, Jan.26, 2010

  18. MINRES on Si cluster (LCAO) – second best Si cluster (LCAO) with various radii is calculated on a single PC with MINRES (full-orth, Minimal Residue). The calculated on-site density matrix and occupation number is compared to Si bulk value: band gap (LMTO) = 0.727 eV band gap (Exp) = 1.17 eV • The calculated Si cluster has much shorter localization length (20 aB), which is due to relatively large band gap. • The computing time for LCAO + MINRES is 3 times slower than LMTO + ABEL. The efficiency can be somewhat improved by implementing partial orthogonalization. AoE Team Meeting, Jan.26, 2010

  19. Status of O(N) as we tested: We have tested all major O(N) techniques using both LCAO and LMTO DFT methods. The best has been Krylov subspace type; Tremendous progress have been achieved in literature in O(N) methods; But all O(N) methods have some problems, issues, errors, etc., and the comfort zone of DFT computation is limited to ~5,000 atoms or less. If one is willing to use large supercomputer, perhaps a bit more. Errors increase as systems become large so that convergence becomes slow --- we are entering unknown territory. Tentative conclusion: O(N) is useful for total energy computation. It is an on-going research and we need to speak to math people on Krylov. Cannot solve time scale problem with O(N). Our take: for materials project of AoE, we will develop O(N) capability for total energy computation; we will also use it to generate parameters for larger scale computation and for solving time scale problem. AoE Team Meeting, Jan.26, 2010

  20. Where the time is spent in DFT? Almost all the time are spent in the self-consistent loop. AoE Team Meeting, Jan.26, 2010

  21. Tight binding semi-empirical methods Tight binding (TB) method gets rid off the self-consistent computation of the potential. We first prepare TB potential parameters somehow. Compute forces and total energy by relaxation or by TBMD. Large systems: N=1M possible; Intermediate time scales: t ~ 10ns possible. Issues: how to obtain parameters that are accurate; charge transfer; external fields; etc. AoE Team Meeting, Jan.26, 2010

  22. Kinetic Monte Carlo – both length and time scales Pre-calculate the rates of reactions for relevant processes, put into a table; Do growth simulation by atomic dynamics using Monte Carlo: the rates are used to determine what the atoms do. Very fast, time scale problem gone, millions of atoms. AoE Team Meeting, Jan.26, 2010

  23. KMC (cont.) --- action plan Personnel: 1 undergrad (hired already) on KMC-1 for database collection; 1 PhD and 1 pdf to be hired to be on KMC-2. AoE Team Meeting, Jan.26, 2010

  24. KMC (cont.): It is crucial to cover all relevant chemical processes – collaborate experimentalists; It is crucial to accurately determine reaction rates --- we use first principles, probably O(N) type DFT method; Build database for relevant materials: Si, Ge, compound semiconductors, doping atoms, oxides, high-k, certain metals, etc. Literature search plus building; Test database --- collaborating with experimentalists. We expect to be able to reach million atom range and experimental time scales. The problem is accuracy, the saver is that we only have to work out accurate database for relevant electronic materials. AoE Team Meeting, Jan.26, 2010

  25. Phase-field crystal (PFC) model It is a classical density functional theory having atomic resolution for conserved fields, and having the correct classical non-equilibrium temperature field and thermal flow. Atomic information: by approximating the measured pair correlation to the dashed line (liquid side), very nice crystallization process can be simulated rather accurately. Freezing, phonons, binary alloy, dislocation, defects, grain boundary, eutectics, solidification, dendritic growth, nucleation, epitaxial, elasticity etc. AoE Team Meeting, Jan.26, 2010

  26. PFC (cont.): Martin Grant et al. (2009) PFC simulation of a hexagonal PFC crystal under externally applied shear. Left inset: probability density is peaked around the maximum likelihood positions of the atoms. Right: a dislocation and the associated Burger’s vector. PFC supports all crystal defects whose effects on device property is important. AoE Team Meeting, Jan.26, 2010

  27. AoE materials module --- DFT-KMC-PFC Front-end GUI O(N) DFT, TB <10,000, ps KMC < 1M, μs PFC Continuum, diffusive t Post analysis, parameter extraction, data presentation and back-end GUI AoE Team Meeting, Jan.26, 2010

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