1. Device Simulation for Single-Event Effects Mark E. Law Dan Cummings, Nicole Rowsey SWAMP Center

2. 2006 Basketball Champs

3. 2006 Football Champs

4. 2007 Basketball Champs

5. It all pales in comparison to….

6. Objectives Provide device simulation environment for rad-hard applications Address Rad-Hard specific issues –Physics - strain –Numerics - automatic operation –Coupled Device / Defect Simulations

7. Outline Background - FLOODS Code Numeric Issues and Enhancements Physical Issues and Enhancements Conclusions

8. FLOOPS / FLOODS Multi-dimensional, Object-oriented codes P = Process / D = Device 90% code shared Scripting capability for PDE’s - Alagator Commercialized - ISE / Synopsis –Sentaurus - Process is based on FLOOPS Licensed at over 300 sites world-wide Short Course at Vandy Jan. 11-12

9. What is Alagator? Scripting language for PDE’s Models are accessible, easily modified Equations are split –Node pieces (recombination, time derivative) –Element pieces (current, fields) Pieces are vectorized –128 pieces in tight BLAS loops for performance –Operations are broken down in scripting Precomputation and Caching automatic Overall CPU linear in # of pieces

10. What is Alagator? Example use of operators for diffusion equation Fick’s Second Law of Diffusion –ddt(Boron) - 9.0e-16 * grad(Boron) –∂C(x,t) / ∂t = D ∂ 2 C(x,t) / ∂x 2 All physics is defined on the command line Rapidly evolve models for new devices / materials / physics OperatorDescription “ddt”Time derivative “grad”Spatial derivative “sgrad”Scharfetter / Gummel Discretization Operator “dot”Returns the dot product of the gradient of two scalar arguments “cross” Returns the magnitude of the cross produce of the gradient of two scalar arguments “elastic”Compute elastic forces - FEM balance

11. Outline Background - FLOODS Code Numeric Issues and Enhancements Physical Issues and Enhancements Conclusions

12. Object Oriented Derived Specific Geometry Elements Common properties so code is independent Element Class VolumeFaceEdgeNode 2 -Edge3 -Edge Face Quad Tri

13. Anisotropic Grid - Mixed Elements For many reasons, quads are better shapes for device simulation Rectangular region created at the command line Refinement creates mixed elements and terminated lines Assembly runs on generalized elements

14. ElementInfo Derived Classes NodeInfo Base Class - for nodes EdgeFluxInfo - Edge Flux Terms ReflectInfo - Boundary conditions, contacts InterfaceInfo - Interface layers and Material boundaries ElementInfo - Base Element Assembly Class Derived Classes - Allow more element types –EleEdgeInfo (1D) –EleTriInfo, EleQuadInfo (2D) –EleTetInfo (3D) (will add EleBrickInfo)

15. Elastic Assembly - Element Assembly Data Comes from ElementInfo Class All are vectors - 128 long Code Fragment of Assembly for(i = 0; i < BDim; i++) { for(j = 0; j < BDim; j++) { sij = 0.0; for(l = 0; l < Ddim; l++) { for(k = 0; k < Ddim; k++) { //multiply B T, D, B tmp.Mult(ev.BM(k, i),ev.BM(l, j), D[k][l]); sij += tmp; } sij *= ev.Size(); }

16. Outline Background - FLOODS Code Numeric Issues and Enhancements Physical Issues and Enhancements Conclusions

17. Philips Unified Mobility Model Unifies the description of majority and minority carrier bulk mobilities temperature dependence electron–hole scattering screening of ionized impurities by carriers clustering of impurities

18. Bandgap Narrowing is a function of doping level NDND NANA pn diode band diagramUnified apparent bandgap narrowing

19. Normal Field Computation Dot, magnitude, cross operators Compute gradient of scalar terms, vector operations dot(DevPsi, x) –Determines magnitude of the gradient of the first argument –In the direction of the second –dot(DevPsi, x) - vertical (channel) field dot(DevPsi,qfn) / Magnitude(qfn) –Produce field in the current flow direction dot(DevPsi, x) - vertical field for mobility reduction Leads to strain tensor operations Current Field SiO 2

20. Mobility Degradation at Interfaces “Surface Roughness” = perpendicular field “Acoustic Phonon”

21. Anisotropic Mobility Enhancement  PMOS (L gate =65 nm)  Mobility enhanced by a factor of 2.5 in the lateral direction uniformly  DC Drain curves with the gate at -1.0V for a 65nm and 250 nm gate length, with and without a strain enhanced mobility in the lateral direction.

22. Anisotropic Mobility Transient  PMOS (L gate =65 nm)  Mobility enhanced by a factor of 2.5 in the lateral direction uniformly  To observe strain differences, assumed no recombination  Charge was deposited along a vertical line through the drain junction  Charge cloud was assumed to be Gaussian in the lateral direction and uniform vertically *Issue: total charge collected is not the same for both cases

23. Shockley-Read-Hall Recombination N t trap density can be set as a function of distance Diodes with different carrier lifetimes (increasing forward bias):

24. Example - Modern USJ Formation State of the Art USJ Technology Si Preamorphization Carbon Implant at End of Range Significant increase in junction leakage (but still small compared to S-D leakage) Large local recombination centers at C Felch, et al., INSIGHT 2007

25. Example - Modern USJ Formation Centered SRH increase at C sites Order of magnitude increase in junction leakage (measured was larger) 65nm MOS transistor (larger technology node than this is aimed at) Single event response w/ and w/o carbon

26. Summary Generalized Element Assembly, Refinement –Need to work on bricks, unrefinement Added Physical Operators –Directional terms included –Add Strain Built Standard MOS models for distribution –Lombardi, Phillips, Bandgap, Recombination