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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 2 C(x,t) / x 2 OperatorDescription ddtTime derivative gradSpatial derivative sgradScharfetter / Gummel Discretization Operator diff Returns the magnitude of the derivative of the argument parallel to the edge of evaluation – electric field applications for mobility in a device – returns a scalar trans Returns the magnitude of the derivative of the argument perpendicular to the edge of evaluation – electric field application for mobility in a device – returns a scalar elasticCompute elastic forces - FEM balance

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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 Element Class VolumeFaceEdgeNode

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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 Average Quality 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 Average Quality 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 VolumeFaceEdgeNode 2 -Edge3 -Edge Face Quad Tri

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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 Nonlinear algebraic equations Linear Matrix Problem Temporal and Spatial Discretization Poisson Carrier Continuity Lattice Temperature Multi-dimensional Newton Linearization Flux = (n 1 - n 2 ) / x 12

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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 n 1.5 Nonlinear set of PDE Nonlinear algebraic equations Linear Matrix Problem Temporal and Spatial Discretization Poisson Carrier Continuity Lattice Temperature Multi-dimensional Newton Linearization Flux = (n 1 - n 2 ) / x 12

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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 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., IEEE EDL , S. Thompson et al., IEDM Tech. Dig , 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 10 16

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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 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 SiO 2

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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(Boron*k) σ ε SRC Supported

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(μm) 45 nm 140 nm 120 nm 30 nm Si 0.83 Ge 0.17 STI Source FLOOPS MPa Stress Contours

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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

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