A Software Platform for Nanoscale Device Simulation and Visualization

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A Software Platform for Nanoscale Device
Simulation and Visualization
Google "nanofem platform"

• Marek Gayer and Giuseppe Iannaccone
• ACTEA 2009 - Conference on Advances in
  Computational Tools for Engineering Applications
• Notre Dame University, Faculty of Engineering,
  Zouk Mosbeh, Lebanon, July 15 July 17, 2009

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Goals of NanoFEM platform

• Create software platform for Technology CAD
  device simulation based on FEM
• Should be flexible modifiable (research)
• Interactive features Geometry, meshing and
  visualization with user interface
• Separation of IT (software) and physics
• Ability to run simulations on remote servers
• Able to run on Windows, Linux, Mac OS X
• Extendible users should be able to develop for
  the platform writing own modules
• Performance

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Finite Element Method

• Finding solution for Partial Differential
  equations for evaluation of characteristics (e.g.
  potential)
• Discretizes continuum (i.e. modeled object) into
  finite number of elements e.g. triangles,
  tetrahedron
• Characteristics are determined in the nodes of
  the element
• Solving of linear systems
• Complex to design and implement, solid
  mathematical and informatics understanding
  required for high performance

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3D Finite Element Mesh

• Suitable discretization of continuous domain to
  simple volume cell elements
• Partial differential equations (PDEs) can be
  replaced by system of non-linear algebraic
  equations
• Very complex to create code to generate FEM mesh
  on arbitrary structures
• Mesh need to be at least Delaunay mesh
• Tetrahedrons

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Related solutions / approaches

• Commercial codes (Synopsis, Silvaco, etc.)
• Disadvantages limited extendibility,
  modifications
• Free codes 2D, 3D
• Archimedes, nextnano
• Free Meshers - NETGEN, Tetgen
• Existing simulation frameworks
• Gmsh, Calculix, Salome Platform, Orcan,
• Finite Element Solvers
• FEniCS/DOLFIN, Libmesh, Getfem, Rheolef, Tahoe,
  OOFEM.org, OFELI

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Transistor modeled in NETGEN
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Gmsh Mesh of transistor Postprocessing
(tutorial dataset)
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Components of NanoFEM platform

• SALOME 3.2.6 supports limited number of OSs gt
• Developed as a VmWare image with
• Debian Linux 3.1 (codename Sarge)
• SALOME 3.2.6
• FEniCS/DOLFIN 0.7.1
• MeshAPI lib. for our FEM module/component
• Component and additional codes for SALOME
• KDevelop for development
• Additional tools (Krusader, )
• Running on VmWare Server 1 or Workstation 6
• Eventual distribution by providing this VmWare
  image

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NanoFEM platform modelling approach
Salome Platform
MeshAPI with DOLFIN/FEniCS
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SALOME platform (LGPL) www.salome-platform.org

• SALOME(LGPL) is a free software that provides a
  generic platform for Pre and Post-Processing for
  numerical simulation.
• Interactice geometry modelling, meshing
• Very good user interface (Qt4)
• Visualization (2D and 3D graphs)
• Can use Python scripting to replace or assist
  GUI all functionalities are also accessible
  through the programmatic integrated Python
  console
• Modular architecture, we can create own modules
• Components can run on remote servers (CORBA)
• Exchanging data MEDMEM API, .HDF, .MED
• Much more powerful then any other open source
  finite element component/software we found

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SALOME platform modular architecture
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MED / HDF data format

• Storing and loading data associated to numerical
  meshes and fields
• Exchange between codes and solvers
• Comes with C/Python API
• Data can be exchanged in memory
• 3. levels files, memory, CORBA (data on demand)
• The persistent data storage is based upon HDF
  format (developed by Boeing and NASA in the area
  of Computational Fluid Dynamic).

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FEniCS/ DOLFIN (L)GPLwww.fenics.org

• Free finite element library and solver
• Supports both direct and iterative solvers (LU,
  Krylov solvers)
• Uses PETSc and uBLAS libraries for systems of
  linear/nonlinear equations gt high performance
  linear algebra
• Automatic generation of finite elements,
  evaluation of variational form assembly of
  matrices for FEM linear systems
• Support for general families of finite elements,
  (Lagrange, BDM, RT, BDFM Nedelec and
  Crouzeix-Raviart elements)
• No deeper knowledge about FEM method is needed to
  use and develop
• Eigenvalue problems with SLEPSc
• Simple and intuitive C object interface

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FEniCS / DOLFIN

• UFC - unified framework for finite element
  assembly. More precisely, it defines a fixed
  (C) interface for communicating low level
  routines (functions) for evaluating and
  assembling finite element variational forms.
• SyFI generates an UFC form, from Symbolic
  Finite Elements
• FFC generates UFC from bi/linear form of
  equations in variational form generation goal
  any form, any finite element, maximum efficiency
• FIAT automatic finite element tabulator used
  by FFC or SyFI
• DOLFIN C finite element library / interface

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Our SALOME/DOLFIN bridge MeshAPI

• Core mesh, fields, groups
• Linear-Nonlinear PDE classes
• Selection from Krylov solver methods and
  preconditioners
• XML material database (SAX parser)
• Boundary conditions
• Inherited MeshAPI based solvers
• Wrappers for SALOME platform

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MeshAPI mesh, fields, groups

• Reading Salome mesh from files .med files (MEDMEM
  API)
• Processing mesh coordinates and connectivities
• Processing groups of mesh (can be defined in
  SALOME editor)
• Passing this information to DOLFIN (to build mesh
  in memory)
• Providing core fields (such as Source, Flux,
  Potential, some visual debug fields)
• Additional methods to work with mesh and fields
• Control of storing of core and custom fields to
  .MED files
• Clean code design in strictly object oriented C

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Example of XML material database

• lt?xml version"1.0" encoding"UTF-8"?gt
• ltmaterialDatabase xmlns"materials.xsd"gt
•   ltmaterial name"Si" description"(100)silicio"
  gt
•     ltparameter name"dielectricConstant"
  description"CostanteDielettricarelativa"
  type"double" value"11.8" /gt
•     ltparameter name"longitudeMassForElectrons"
  description"MassaLongitudinaleelettrone"
  type"double" value"0.98" /gt
•     ltparameter name"transversalMassForElectrons"
  description"MassaTrasversaleelettrone"
  type"double" value"0.19" /gt
•   lt/materialgt
•   ltmaterial name"SiO2" description"ossidodisilic
  io"gt
•     ltparameter name"dielectricConstant"
  type"double" value"3.9" /gt
•   lt/materialgt
•   ltmaterial name"Air" description"Aire"gt
•   lt/materialgt
• lt/materialDatabasegt

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Storing materials and boundary conditions in
MEDMEM mesh

• Implemented by correct naming of groups, which
  are then read in code to retrieve materials and
  boundary conditions
• Examples bottomoxideSi
  metalplate1dirichlet1.0
• From SALOME mesh, we get IDs of nodes and assign
  a group color number to them
• From group number, we determine material,
  Dirichlet boundary conditions etc. These data are
  stored in numeric arrays 0..n n is number of
  groups

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MeshAPI/Linear-Nonlinear PDE

• Classes allowing solving nonlinear and nonlinear
  PDE, using DOLFIN, allows to set preconditioners
  and Krylov methods
• Available Krylov methods
• cg - The conjugate gradient method
• gmres - The GMRES method (default)
• bicgstab - The stabilized biconjugate gradient
  squared method
• Preconditioners
• none - No preconditioning
• jacobi - Simple Jacobi preconditioning
• sor - SOR, successive over-relaxation
• ilu - Incomplete LU factorization (default)
• icc - Incomplete Cholesky factorization
• amg - Algebraic multigrid (through Hypre when
  available)

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MeshAPI based solvers

• Using MeshAPI, one can easily, in few lines
  define DOLFIN solvers as classes inherited from
  cl. Dolfin
• Behaviour that can be generalized and reused is
  already defined in Mesh API
• It can be used in any current and future examples
• There are 3 example solvers
• Poisson example from DOLFIN manual, but using
  Salome mesh
• Poisson equation computed on partitioned group
• Poisson equation computed on partitioned group
  with permittivity (Eps)
• Non-linear Poisson equation computed on
  partitioned group with permittivity (not 100
  done)

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Solving example linear Poisson

• Solving linear PDE Poisson equation
• f(x,y,z) source function (known), can be 0
• e(x,y,z) permittivity of material in given
  point
• u(x,y,z) potential, that we are computing

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Solving example linear Poisson

• Bi-linear and linear form of Poisson equation
• g(x,y,z) Neumann boundary condition

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Converting equation to variational form

• The bilinear form a(v, U) and linear form L(v)
  for
• Poisson's equation.
• Compile this form with FFC ffc -l dolfin
  PoissonEps.form
• element FiniteElement("Lagrange",
  "tetrahedron", 1)
• v TestFunction(element)
• u TrialFunction(element)
• f Function(element)
• g Function(element)
• eps Function(element)
• a dot(grad(v), grad(u))epsdx
• L vfdx epsvgds
• This generates 5239 lines, 191.359 characters

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Main solving routine in C

• include "PoissonEps.h
• include "LinearPDE.hxx"
• int SCPoissonEpssolve ()
• Source f (mesh)
• Flux g (mesh)
• DirichletFunction u0 (mesh)
• DirichletBoundary boundary(mesh)
• DirichletBC bc (u0, mesh.dolfinMesh, boundary)
• Eps eps (mesh)
• PoissonEpsBilinearForm a (eps)
• PoissonEpsLinearForm L (f, g, eps)
• SCLinearPDE pde (a, L, mesh.dolfinMesh, bc)
• pde.setupKrylov (mesh.krylovMethod,
  mesh.krylovPc)
• Function solution
• pde.solve(solution)
• mesh.nodePotential.init (u) mesh.nodeSource.init
  (f) mesh.nodeFlux.init (g)

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Dirichlet boundary in C

• class DirichletBoundary public SubDomain
• MeshAPI meshpublic
• DirichletBoundary(MeshAPI meshInstance)
  mesh(meshInstance)
• bool inside(const dolfinreal x, bool
  on_boundary) const
• int index mesh.getGroupNumberFromCoordinates(x)
  MaterialFunction nodeMaterial
  mesh.materialFunctionsindex return
  nodeMaterial-gtmaterialData NULL

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Dirichlet values in C

• class DirichletFunction public Function
• MeshAPI meshpublic
• DirichletFunction(MeshAPI meshInstance)
  mesh(meshInstance), Function(meshInstance.dolfinMe
  sh)
• dolfinreal eval(const dolfinreal x) const
• int index mesh.getGroupNumberFromCoordinates
  (x) MaterialFunction nodeMaterial
  mesh.materialFunctionsindex
• return nodeMaterial-gtdirichlet

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Source function in C

• class Source public Function
• MeshAPI meshpublic
• Source(MeshAPI meshInstance)
  mesh(meshInstance), Function(meshInstance.dolfinMe
  sh)
• dolfinreal eval(const dolfinreal x) const
• return 0

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Neumann boundary conditions C

• class Flux public Function
• MeshAPI meshpublic
• Flux(MeshAPI meshInstance) mesh(meshInstance),
  Function(meshInstance.dolfinMesh)
• dolfinreal eval(const dolfinreal x) const
• return 0

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Defining permittivity in C

• class Eps public Function
• MeshAPI meshpublic
• Eps (MeshAPI meshInstance) mesh(meshInstance),
  Function(meshInstance.dolfinMesh)
• dolfinreal eval(const dolfinreal x) const
• int index mesh.getGroupNumberFromCoordinates
  (x) MaterialFunction nodeMaterial
  mesh.materialFunctionsindex
• return nodeMaterial-gtpermitivity

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Geometry modelling of transistor
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Automatically generated mesh
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Scalar map of the electric potential
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Scalar map of the electric potential
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Conclusion - 1/2

• NanoFEM platform is a new research environment
  for TCAD simulations of nanoscale devices.
• Based on free LGPL components SALOME Platform and
  FEniCS/DOLFIN
• We can concentrate only on developing of our
  MeshAPI and computational modules
• Physicist/developers independent
• Simple definition of equations instead of
  programming

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Conclusion 2/2

• Interactive pre- and post-processing
• Automated meshing
• Modules can run on remote servers
• High performance
• Standard formats - .MED and .HDF
• .XML material database
• Good extendibility and modularity

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Possible future effort for the NanoFEM Platform

• More complex equations (drift, diffusion)
• Compare performance with commercial
• More modules with exchange of fields
• Control of simulation flow and coupling
• Tests of supervision (with scripting)
• More complex boundary conditions
• Run on native Debian and Windows

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Thank you for your attention.

• ???
• Do you have any questions ?