Title: Device Simulation for SingleEvent Effects
1Device Simulation for Single-Event Effects
- Mark E. Law
- Eric Dattoli, Dan Cummings
- NCAA Basketball Champions - University of Florida
- SWAMP Center
2Objectives
- 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
3Outline
- Background - FLOODS Code
- Numeric Issues and Enhancements
- Grid Refinement
- Parallel Computing Platforms
- Physical Issues and Enhancements
- Transient / Base Materials
- Mobility
- Coupling to MRED / GEANT
4FLOOPS / 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
5What 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
6What 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
7Basic 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
8Outline
- Background - FLOODS Code
- Numeric Issues and Enhancements
- Grid Refinement
- Parallel Computing Platforms
- Physical Issues and Enhancements
- Transient / Base Materials
- Mobility
- Coupling to MRED
9Adaptive 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
10Object Oriented
- Modular - Grid / Operators / Fields
- Code written for elements works in all dimensions
- Example - every element can compute Size
11Example - 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
12Anisotropic 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
13Anisotropic 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
14Good for Process Simulation
- Device Simulation is Different!
- Channel Needs Anisotropic refinement
- Unrefinement difficult
- Global Operations and Data Structures
15Device 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
16Object Oriented
- Derived Specific Geometry Elements
- Working on refinement
- Working on Discretization
Element Class
Volume
Face
Edge
Node
Face
2 -Edge
3 -Edge
Tri
Quad
17Parallel Computing
- 3D Transient is time consuming
- What can be done to accelerate?
18Numerical 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
19CPU 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
20Alagator 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
21Parallel 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
22Parallel Assembly
- Partition the work on different processors
- Assemble pieces on processor that will solve
23Parallel Performance - Assembly
- High Level Partition
- Poisson on Node 1
- Electrons on Node 0
24Linear Solve Speedup - PETSC Package
- Amdahls Law Clearly Visible
25Linear Solve Speedup - Options
- Ordering Algorithms are not helpful
- Some Parallel Methods increase solve time
26Outline
- Background - FLOODS Code
- Numeric Issues and Enhancements
- Grid Refinement
- Parallel Computing Platforms
- Physical Issues and Enhancements
- Transient / Base Materials
- Mobility
- Coupling to MRED
27Todays 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.
28Enable 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
29Enable Transients for Devices
- 1D Diode
- Charge added to depletion region at time 0
- Simplest possible SEE
30Mobility Modeling
- Combination of terms
- Ionized Dopants
- Carrier-Carrier
- Surface Roughness
- Strain
- Combined using Mathiessens rule
31Low-Field Mobility
- Lots of models - implemented Phillips unified
model - Includes
- Dopant (dependent on dopant type)
- Carrier - Carrier scattering
- Minority carrier scattering
32Low-Field Mobility - Carrier-Carrier
- In single event simulation
- Dominant term can be carrier - carrier
- Serious mistakes by ignoring these terms
Donor Density of 1016
33Surface Scattering
- Acoustic Phonons
- Surface Roughness
- Both depend on perpendicular field
- Decay factor applies only in channel
- Tuned to measured MOS results
- In progress!
34Normal 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
35Channel 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
36Boundary 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
37Finite 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
38Stress Contours
MPa
Source FLOOPS
39Future - Strain and SEU Upgrades
- Anisotropic operators
- Current direction, strain interaction
- Mobility has an orientation
- Density of States
- Recombination
- Driving Forces?
Connection to Thompson
40Trajectory Read
41Summary
- 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