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Device Simulation for SingleEvent Effects

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Title: Device Simulation for SingleEvent Effects


1
Device Simulation for Single-Event Effects
  • Mark E. Law
  • Eric Dattoli, Dan Cummings
  • NCAA Basketball Champions - University of Florida
  • SWAMP Center

2
Objectives
  • Provide SEE device simulation environment
  • Address SEE specific issues
  • Physics - strain
  • Numerics - automatic operation
  • Long term
  • Simulate 1000s of events to get statistics
  • With SEE appropriate physics
  • Without extensive human intervention

3
Outline
  • Background - FLOODS Code
  • Numeric Issues and Enhancements
  • Grid Refinement
  • Parallel Computing Platforms
  • Physical Issues and Enhancements
  • Transient / Base Materials
  • Mobility
  • Coupling to MRED / GEANT

4
FLOOPS / FLOODS
  • Object-oriented codes
  • Multi-dimensional
  • P Process / D Device 90 code shared
  • Scripting capability for PDEs - Alagator
  • Commercialized - ISE / Synopsis
  • Sentaurus - Process is based on FLOOPS
  • Licensed at over 200 sites world-wide

5
What is Alagator?
  • Scripting language for PDEs
  • Parsed into an expression tree
  • Assembled using FV / FE techniques
  • Stored in hierarchical parameter data base
  • Models are accessible, easily modified

6
What is Alagator?
  • Example use of operators for diffusion equation
  • Ficks Second Law of Diffusion
  • ddt(Boron) - 9.0e-16 grad(Boron)
  • ?C(x,t) / ?t D ?2C(x,t) / ?x2

7
Basic Upgrades
  • FLOODS has been used for
  • Bipolar devices (SiGe)
  • GaN based heterostructures MEMs
  • Coupled H diffusion to device operation
  • 4 equations ?, n, p, H
  • Noise simulations for RF bipolar devices
  • Enhancements for modern MOS
  • More flexible contacting options (transients)
  • Accurate mobility - transverse field
  • Alternate channel materials

8
Outline
  • Background - FLOODS Code
  • Numeric Issues and Enhancements
  • Grid Refinement
  • Parallel Computing Platforms
  • Physical Issues and Enhancements
  • Transient / Base Materials
  • Mobility
  • Coupling to MRED

9
Adaptive Refinement
  • Charge Deposition is not on grid lines

Charge Spreads in time Fine grid at zero
time Coarser grid as time goes Simulate many
hits, we cant have user defined grid
10
Object Oriented
  • Modular - Grid / Operators / Fields
  • Code written for elements works in all dimensions
  • Example - every element can compute Size

11
Example - Isotropic Refinement
  • Local Error Estimate - Bank Weiser Based
  • Remove
  • Replace an edge w/ a node
  • Dose Stays Constant
  • Position new node at optimal quality position
  • Addition
  • Subdivide an edge
  • Find effected volumes (Voronoi)
  • Centroidal positioning

SRC Supported
12
Anisotropic Grid - Initial
  • Rectangular region created at the command line
  • Remainder of the silicon is smoothed
  • Silicon Elements 478
  • Joint Quality 0.936
  • Average Quality 0.944

SRC Supported
13
Anisotropic Grid
  • Refinement of both extension and deep source /
    drain
  • LevelSet Spacer
  • Note - etch onto rectangular regions
  • Silicon Elements 1150
  • Joint Quality 0.937
  • Average Quality 0.961
  • Improved Quality on Add!

SRC Supported
14
Good for Process Simulation
  • Device Simulation is Different!
  • Channel Needs Anisotropic refinement
  • Unrefinement difficult
  • Global Operations and Data Structures

15
Device Simulation Driven Refinement
  • All brick elements (2D example)
  • Refine and terminate
  • Unrefinement easier to track
  • Glue elements together
  • Remove excess discretization nodes
  • Requires Multi-point Templates
  • 4, 5, and 6 point square discretization (2D)
  • Virtual functions in an Object Oriented Scheme

16
Object Oriented
  • Derived Specific Geometry Elements
  • Working on refinement
  • Working on Discretization

Element Class
Volume
Face
Edge
Node
Face
2 -Edge
3 -Edge
Tri
Quad
17
Parallel Computing
  • 3D Transient is time consuming
  • What can be done to accelerate?

18
Numerical Approximations
  • Discretization
  • Replace continuous functions w/ piecewise linear
    approximations
  • Grid Spacing, Time
  • Linearization
  • Reduce nonlinear terms using multi-dimension
    Newtons method
  • Mobility, Statistics,
  • Linear Matrix Problem
  • Number of PDEs x number of nodes square
  • Direct Solver

Nonlinear set of PDE
Poisson Carrier Continuity Lattice Temperature
Temporal and Spatial Discretization
Nonlinear algebraic equations
Flux (n1 - n2) / x12
Multi-dimensional Newton Linearization
Linear Matrix Problem
19
CPU Effort and Time
  • Assembly of Matrix
  • Calculate the large, linear system
  • Lots of Data read
  • Potential for Overlapping writes
  • Lots of Parallel Potential
  • Linear in number of elements
  • Solution of Matrix
  • Large Sparse System
  • Established means for parallel solve
  • Leverage Argonne Natl Lab Code
  • Low power of equations n1.5

Nonlinear set of PDE
Poisson Carrier Continuity Lattice Temperature
Temporal and Spatial Discretization
Nonlinear algebraic equations
Flux (n1 - n2) / x12
Multi-dimensional Newton Linearization
Linear Matrix Problem
20
Alagator Assembly
  • Equations are split
  • Edge pieces (current, electric field)
  • Node pieces (recombination, time derivative)
  • Element pieces (perpendicular field)
  • Pieces are vectorized
  • 128 pieces in tight BLAS loops for performance
  • Operations are broken down in scripting
  • Overall CPU linear in of pieces

21
Parallel Assembly
  • Two Options
  • High Level Parallel
  • Assemble Different PDEs on Different CPUs
  • Limited Parallel Speedup
  • Low Level Parallel
  • Split Grid, assemble pieces
  • Match to Linear Solve

22
Parallel Assembly
  • Partition the work on different processors
  • Assemble pieces on processor that will solve

23
Parallel Performance - Assembly
  • High Level Partition
  • Poisson on Node 1
  • Electrons on Node 0

24
Linear Solve Speedup - PETSC Package
  • Amdahls Law Clearly Visible

25
Linear Solve Speedup - Options
  • Ordering Algorithms are not helpful
  • Some Parallel Methods increase solve time

26
Outline
  • Background - FLOODS Code
  • Numeric Issues and Enhancements
  • Grid Refinement
  • Parallel Computing Platforms
  • Physical Issues and Enhancements
  • Transient / Base Materials
  • Mobility
  • Coupling to MRED

27
Todays Transistor
Scaled MOSFETS and alternate materials to extend
Moores Law
S. Thompson et al., IEEE EDL. 191-193, 2004.
  • Technology scaling is driven by cost per
    transistor
  • Channel length scaling is slowing in bulk planar
    devices
  • Limited by leakage current
  • Strained Si devices

S. Thompson et al., IEDM Tech. Dig. 61-64, 2003.
28
Enable Transients for Devices
  • Added transient device command
  • Extended Contacts to allow switching
  • Contact Templates Available Now

Example NMOS Switching Transient Gate Ramped
from 3V to 0V in 1ps
29
Enable Transients for Devices
  • 1D Diode
  • Charge added to depletion region at time 0
  • Simplest possible SEE

30
Mobility Modeling
  • Combination of terms
  • Ionized Dopants
  • Carrier-Carrier
  • Surface Roughness
  • Strain
  • Combined using Mathiessens rule

31
Low-Field Mobility
  • Lots of models - implemented Phillips unified
    model
  • Includes
  • Dopant (dependent on dopant type)
  • Carrier - Carrier scattering
  • Minority carrier scattering

32
Low-Field Mobility - Carrier-Carrier
  • In single event simulation
  • Dominant term can be carrier - carrier
  • Serious mistakes by ignoring these terms

Donor Density of 1016
33
Surface Scattering
  • Acoustic Phonons
  • Surface Roughness
  • Both depend on perpendicular field
  • Decay factor applies only in channel
  • Tuned to measured MOS results
  • In progress!

34
Normal Field Computation
SiO2
  • Requires element assembly
  • Increased computation
  • More complex matrix
  • Compute field perpendicular to an interface
  • Fixed geometry
  • Might interact w/ single event
  • Field perpendicular to current flow
  • Convergence difficulties at low current
  • Assumes current is perpendicular..
  • Make sure it doesnt apply in bulk

Current
Field
35
Channel Materials
  • Heterostructure Boundaries
  • Fairly Easy, since we had heterostructure
    experience in FLOODS before
  • Development of Ge channel simulations

500Å Ge Channel 30Å Gate Nitride Poly Gate Bias
Swept Up 0.1?m Channel Length Ideal Doping
Profiles Note Concentration Discontinuity at
interface
36
Boundary Conditions
  • Commercial simulators only allow BC at contacts
  • FLOODS has large flexibility at boundaries
  • Example - Sink on sides
  • pdbSetString ReflectLeft Equation
    1.0e-3(Elec-Doping)
  • Simulation as function of device simulation size
  • Reflecting boundaries at edges and back change
    current collected at contacts

Courtesy of Ron Schrimpf, Andrew Sternberg
37
Finite Element Method Mechanics
  • Theory of Elasticity linear elastic materials
  • - Silicon is modeled as an isotropic material
    for simplicity
  • Enhanced Alagator
  • Added elastic operator for displacement
  • Added source term operators
  • Elastic(displacement) BodyStrain(Boronk)

SRC Supported
38
Stress Contours
MPa
Source FLOOPS
39
Future - Strain and SEU Upgrades
  • Anisotropic operators
  • Current direction, strain interaction
  • Mobility has an orientation
  • Density of States
  • Recombination
  • Driving Forces?

Connection to Thompson
40
Trajectory Read
  • Trajectory Read Command

41
Summary
  • Numerics
  • Started Developing refinement appropriate to SEE
  • Parallel Port, Begun Testing
  • Physics
  • Built some basic capability for SEE
  • Read Tracks
  • Next Year
  • Demonstrate link, run demos on parallel machines
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