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Overview of Modeling and SimulationTCAD - FLOOPS / FLOODS

A 21st Century Approach to Reliability

Outline

• Modeling Overview– Strain Effects– Thermal Modeling

• TCAD Modeling– FLOOPS / FLOODS Introduction– Progress on GaN Devices– Prospects for Reliability Simulation


Self-consistent Procedure

• k•p self-consistent solution to Poisson andSchrödinger’s equation

)]()([/)(2

2

zNzNqzVdz

dDSi +=! "

)()()](2[

2

zEzzVm

P

nn!=!+

)(|)(|2)( 2

2 EfzzN D

n

n! "=


In and Out-of-Plane Masses (Ge)

m||

m|

m||

m|

kzkz

kyky

Uniaxial StressBiaxial Stress

kx kxUsing k•p methods to compute bands


Splitting (increases) / (decreases)

under confinement

Band splitting due to strain

EV

Low Vertical Field

Si02

Esecond

Etop

High Vertical Field

Uniaxial Biaxial

EV

Esecond

Etop

EV

Esecond

Etop

Confinement and Strain Sub-band Shifts


Same Physics for IV, III-V Materials

Si

Ge

GaAs

Unstressed 1GPa Biaxial Tension 1GPa Uniaxial Compression


Thermal Simulations

• Use finite element modeling to optimize package design• Most important factors in thermal management: heat transfer at the

system boundaries and substrate thickness• Couple w/ FLOOPS / FLOODS simulations as well


Thermal Simulations and IR Imaging

• T(Junc) of power devices is oftensignificantly hotter than T(stage)

• Accurate extraction of activationenergy requires knowledge of thetrue channel temperature.

• We have extensive experience inestimating heat transfer even incomplex structures

• Purchasing a high-resolution IRcamera for direct imaging of thedevice operating temperature. Wehave collaborated with Nitronexon thermal imaging-a typicalexample is shown at right for amulti-finger power HEMT.

• Possible Collaborations w/Samuel Graham, Georgia Tech

X (m)

Y (m)

Temp (°C)

Temp (°C)


Outline

• Modeling Overview– Strain Effects– Thermal Modeling– TCAD Based Approaches

• TCAD Modeling– FLOOPS / FLOODS Introduction– Progress on GaN Devices– Prospects for Reliability Simulation


FLOOPS / FLOODS

• Object-oriented codes• Multi-dimensional• 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– 2008 release– Manual is online (but needs updating)


What is Alagator?

• Scripting language for PDE’s• Parsed into an expression tree• Assembled using FV / FE techniques• Stored in hierarchical parameter data base

• Models are accessible, easily modified


What is Alagator?

• Example use of operators for diffusion equation• Fick’s Second Law of Diffusion

– ddt(Boron) - 9.0e-16 * grad(Boron) - K * (Boron - Trap)– ∂C(x,t) / ∂ t = D ∂ 2C(x,t) / ∂ x2

Compute elastic forces - FEM balance“elastic”

Returns the dot product of the gradient of two field – electric field in directionof current floq“dot”

Scharfetter / Gummel Discretization Operator“sgrad”

Spatial derivative“grad”

Time derivative“ddt”

DescriptionOperator


Strained PMOS

• To enhance channel mobility, PMOS strain processing includesembedded SiGe in the source/drain regions and compressive cappinglayers.

• FLOOXS predicts strain/stressprofiles where the channelstress is ~1 GPa

Cheng, et al. IEDM 2007

FLOOXS predicted stress profile [dyne/cm2](YY component - channel direction)

Horstmann, et al.IEDM 2005

compressiveSiGe SiGe

capping layer

X

Y


Complex Mobility Models Construction

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 [

cm

2/V

s]

Majority Minority

Unifies the description of majority andminority carrier bulk mobilities• temperature dependence• electron–hole scattering• screening of ionized impurities bycarriers• clustering of impurities

Surface scattering terms (Vertical Field)Velocity SaturationEffMass changes w/ strain (more later)


Piezoresistance

• Piezoresistivity is the change in electrical resistivity with mechanicalstress and involves the relationships between electric field Ei, currentdensity Jj, and mechanical stress σkl ( ) J + =E jklijkliji !" #

!!!!!!!!

"

#

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)

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'('('(

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)0(

)0(

)0(

/1//

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///1

)(

)(

)(

Z

Y

X

zzzzyzyzzxzx

yzyzyyyyxyxy

zxzxxyxyxxxx

Z

Y

X

J

J

J

J

J

J

µµµµµµ

µµµµµµ

µµµµµµ

)

)

)

Stress components

Piezoresistance coefficients

Mobility Change

pnpnpn qnJ,,,

!µ "#=

Resistivity Change

(Small Change Limit)


Piezoresistance example

• Silicon beam with an n-type surface• Bending induces tensile stress at the surface resulting in a increase in

mobility and current.

FLOOXS beam bending example

!

JX(") # 1+

$%µxx

µxx

&

' (

)

* + JX (0) = 1+ ,

11"xx( )JX (0)


Piezoresistance• The gradient of the quasi-fermi level gives Jn,p vector values for each

element

• Piezoresistance coefficient matrix can be definedfor any orientation usingdirectional cosines Z [001]

Y [010]

X [100]

X’ [110]

ϕ =45°

pnpnpn qnJ,,,

!µ "#=JX(0)

JY(0)

!"

#$%

&!"

#$%

&

'('(

'('(=!

"

#$%

&

)0(

)0(

/1/

//1

)(

)(

Y

X

yyyyxyxy

xyxyxxxx

Y

X

J

J

J

J

µµµµ

µµµµ

)

)


Piezoresistance• Piezoresistance coefficients can be set to spatially vary in FLOODS

– Extracted channel and bulk coefficients different (to do)• Piezoresistance coefficients are function of impurity concentration and

temperature P(N,T)

Kanda Y., IEEE Trans Electron Devices 1987 FLOODS simulated piezoresistance factor for T=300 K

T↑


Strained PMOS Simulations• PMOS with Lgate=30 nm• <110> channel orientation• 2007 ITRS dimensions• Charge strike dist. in drain


Double-Gate FinFET• Lgate=18 nm, wsi=11 nm• Midgap metal gate (typically TiN)• Gate-S/D doping underlap to control Vt and short channel effects• Undoped body

FinFET top cross-sectional view

nFinFET I-V characteristic


AlGaN/GaN HEMT Device

Sample IV curveEnergy Band Diagram

• Can handle heterostructure bands• Gate offsets• Field Dependence


Edge termination is critical forobtaining high breakdown voltage andreduced on-state resistance.

Severe electric field crowding aroundmetal contact periphery.

High leakage current and breakdownat the highest electric field

Depletion contour

Potential contour

nDepletion region contour

Electrode Oxide

Edge Termination


VB values are highly sensitive to thecharge in the JTE layer.

Multiple JTE termination technique(JTE1 + JTE2).

3x1017

4x1017

5x1017

1800

2000

2200

2400

2600

2800

Rev

erse

bre

akd

ow

n v

olt

age

(V)

JTE doping concentration (cm-3)

p+

N

p-

JTE layer

Depletion boundary

Junction Termination Extension


Reliability Simulation

• Simulate Device in Quasi-Steady State– Electrons and Holes equilibrate

quickly– Similar to assumption in process

simulation• Generation Events Triggered by

– Mechanical Stress– Current Flow / Electric Field

• Simultaneous solutions– Point Defects / Defect Cluster /

Interface Capture– Hydrogen

TNS, TBPVanderbilt+ UF


Example: 3.2µm x 90nm bulk nMOSFET

Low frequency measured and simulated noise data

Graphical depiction of Noise Producing oxide trap locations on meshfor simulating the low frequency noise features. Location 1 has 4 traps,locations 2 and 3 0.5 traps each.


Conclusions

• Modeling Integrated– Fundamental Physics k•p feeds TCAD– Thermal coupled to TCAD

• Experimentally Integrated– Failure Mechanism Identification feeds M&S– Electrical Measurement feeds

overview and tcad - university of · pdf fileoverview of modeling and simulation tcad - floops...

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