Device Simulation for Single-Event Effects

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 ∂2C(x,t) / ∂x2 • All physics is defined on the command line • Rapidly evolve models for new devices / materials / physics

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 Node Edge Face Volume Face 2 -Edge 3 -Edge Tri Quad

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 BT, 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 pn diode band diagram Unified apparent bandgap narrowing NA ND is a function of doping level

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 SiO2 Current Field

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

21. Anisotropic Mobility Enhancement • PMOS (Lgate=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 (Lgate=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 Diodes with different carrier lifetimes (increasing forward bias): Nt trap density can be set as a function of distance

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