Device Simulation for Single-Event Effects

Device Simulation for Single-Event Effects

Mark E. Law

Dan Cummings, Nicole Rowsey

SWAMP Center

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It all pales in comparison to….

Objectives

• Provide device simulation environment for rad-hard applications

• Address Rad-Hard specific issues– Physics - strain – Numerics - automatic operation– Coupled Device / Defect Simulations

Outline

• Background - FLOODS Code

• Numeric Issues and Enhancements

• Physical Issues and Enhancements

• Conclusions

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

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

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

Operator Description

“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

Outline

• Background - FLOODS Code

• Numeric Issues and Enhancements

• Physical Issues and Enhancements

• Conclusions

Object Oriented• Derived Specific Geometry Elements• Common properties so code is independent

Element Class

VolumeFaceEdgeNode

2 -Edge 3 -Edge Face

Quad

Tri

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

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)

Elastic Assembly - Element Assembly• Data Comes from ElementInfo Class• All are vectors - 128 long• Code Fragment of Assemblyfor(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();

}}

]63[]33[]36[]66[ xxxx

k e BT DB

Outline

• Background - FLOODS Code

• Numeric Issues and Enhancements

• Physical Issues and Enhancements

• Conclusions

Philips Unified Mobility Model

0

50

100

150

200

250

300

350

400

450

500

1E+14 1E+16 1E+18 1E+20 1E+22

Concentration (cm-3)

Ho

le M

ob

ilit

y [c

m2 /Vs]

Majority Minority

Unifies the description of majority and minority carrier bulk mobilities• temperature dependence• electron–hole scattering • screening of ionized impurities by carriers• clustering of impurities

Bandgap Narrowing

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1E+15 1E+16 1E+17 1E+18 1E+19 1E+20Concentration (cm-3)

app

aren

t b

and

gap

nar

row

ing

(eV

)

Unified (p & n type) Slotboom (p type)

del Alamo (n type)

is a function of doping levelGAPE

NDNA

pn diode band diagram Unified apparent bandgap narrowing

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 operationsCurrent

Field

SiO2

Mobility Degradation at Interfaces

ac B

E

C(N /N0)

E1/ 3(T /T0)k

sr E /E ref A

E

3

1

1

1

b

D

ac

D

sr

D e x /

“Surface Roughness” E = perpendicular field“Acoustic Phonon”

NMOS Transfer Characteristic ID vs VG

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0 0.2 0.4 0.6 0.8 1.0

VG (V)

I D (

mA

)

constant mobility Lombardi mobility

Anisotropic Mobility Enhancement

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

Vds (V)

|Ids|

(m

A)

250nm gate - anisotropic 250nm gate - isotropic65nm gate - anisotropic 65nm gate - isotropic

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.

Anisotropic Mobility Transient

PMOS Current Transient (Lgate=65 nm)

0

1

2

3

4

5

6

7

8

9

10

0 1E-11 2E-11 3E-11 4E-11 5E-11 6E-11 7E-11 8E-11 9E-11 1E-10

Time [s]

I D [

mA

]

isotropic anisotropic

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

Shockley-Read-Hall Recombination

2

trap trap

SRH inet E E

kT kTp i n i

np nR

n n e p n e

1n

n th tv N

1

pp th tv N

Nt trap density can be set as a function of distance

Diodes with different carrier lifetimes (increasing forward bias):

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

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

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

0.E+00 5.E-12 1.E-11 2.E-11 2.E-11 3.E-11 3.E-11 4.E-11 4.E-11 5.E-11 5.E-11

time [s]

Id [

mA

]

Boron S/D Boron+Carbon S/D

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