Device Simulation for SingleEvent Effects

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Device Simulation for Single-Event Effects

• Mark E. Law
• Eric Dattoli, Dan Cummings
• NCAA Basketball Champions - University of Florida
• SWAMP Center

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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

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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

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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

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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

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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

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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

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Outline

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

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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
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Object Oriented

• Modular - Grid / Operators / Fields
• Code written for elements works in all dimensions
• Example - every element can compute Size

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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
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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
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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
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Good for Process Simulation

• Device Simulation is Different!
• Channel Needs Anisotropic refinement
• Unrefinement difficult
• Global Operations and Data Structures

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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

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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
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Parallel Computing

• 3D Transient is time consuming
• What can be done to accelerate?

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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
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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
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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

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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

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Parallel Assembly

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

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Parallel Performance - Assembly

• High Level Partition
• Poisson on Node 1
• Electrons on Node 0

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Linear Solve Speedup - PETSC Package

• Amdahls Law Clearly Visible

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Linear Solve Speedup - Options

• Ordering Algorithms are not helpful
• Some Parallel Methods increase solve time

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Outline

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

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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.
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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
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Enable Transients for Devices

• 1D Diode
• Charge added to depletion region at time 0
• Simplest possible SEE

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Mobility Modeling

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

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Low-Field Mobility

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

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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
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Surface Scattering

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

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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
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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
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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
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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
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Stress Contours
MPa
Source FLOOPS
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Future - Strain and SEU Upgrades

• Anisotropic operators
• Current direction, strain interaction
• Mobility has an orientation
• Density of States
• Recombination
• Driving Forces?

Connection to Thompson
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Trajectory Read

• Trajectory Read Command

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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