akb2007 gondro statistical simulation methodology for smart … · 2007. 10. 26. · source: /ep/...

Copyright © Infineon Technologies 2007. All rights reserved. 19.10.2007

Statistical Simulation Methodologyfor a Smart Power Technology

I nfi

neo

nAutomotive Power CAD

Dr. Elmar Gondro

2007, Oct 19th

AK Bipolar 2007 / Munich


Outline

�Motivation�Modeling Flow�Model Quality�Conclusion


Motivation / Wake-Up

Zero DefectZero Defect

Design 4 Manufacturability

Design 4 Manufacturability Automotive

Excellence

Automotive Excellence

CAD PDTD

Model Quality

Flow Quality

YieldEnhancemen

t

YieldEnhancemen

t

Nominal & statisticalRepresentation of allfuture Fab Outputs


Five Steps Extraction Process of Electrical Parameters

NominalParameters

StatisticalParameters

PCM Targets

„Golden Wafer“

PCM Spec Limits

PCM Samples

Extraction

Centering µ

Deviations σ

Correlations

Mismatch Testchip Matching Consts


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 1: Nominal Parameters

0.6 0.8 1 1.2

I[µ

A]

simu

VBE [V]

IC meassimu

IB meas

100

0.40.2

1e6

10000

1

0.01

0.0001

1e−6

1e−8

source: /EP/-Docu (Bipolar / Tempsense)

PCM parameters:Vbe � Ic

β � IbVbd � none


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 1: Nominal Parameters

source: /PCM/-Docu (Bipolar)

Re-Simulation SchematicsSMART5 PCM: • 41 of 75 device types covered• 143 of 194 PCM setups can

be re-simulated simultaneously


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 2: Parameter Centering

µ

pro

pability

densi

ty

past (T7)


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


µ=Target

Definition!!!

pro

pability

densi

ty

Definition!!!


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


Nom

µ=Target

pro

pability

densi

ty


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


µ=Target=Nom

pro

pability

densi

ty


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 3: Process Deviations

Definition!!!

6 σ 6 σ

USLLSL µ=Target=Nom

pro

pability

densi

tyCentering and ±6σ

� cpk=2

Definition!!!


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


µ=Target=NomLSL USL

pro

pability

densi

ty

past (T7)today


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch



pro

pability

densi

ty

past (T7) futuretoday



pro

pability

densi

ty

PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch



3 σ


Definition!!!

3 σ

pro

pability

densi

ty

PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


Centering and ±3σ� cpk=1

Definition!!!


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


source: /MQ/-Docu (Low Volt NMOS)

Normalized PCM Window with 3 σ Process Variations

simu

YYIsat MNLE2

MMRon MNLE2

MMG MNLE2

YYVt MNLE2

ClassificationParameter

USLTargetLSL

MOSFET


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


source: /MQ/-Docu (qnbh Bipolar)

Normalized PCM Window with 3 σ Process Variations

Bipolar

MM

VBE QNBH 50u MM

VCEO QNBH RMno simulation possible

no simulation possibleVCB QNBH RM

VEB QNBH RMno simulation possible

simu

Parameter

VBE QNBH 1m

MMB QNBH 200u

YMB QNBH 20u

MMB QNBH 200n

Classification

USLTargetLSL


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch


source: /EP/-Docu (qnbh Bipolar)

Gummel Poon and beta Plot

Bipolar

0.8 1 1.2

I[µ

A]

simu

VBE [V]

IC meas

IB meassimu

1

0.60.40.2

10000

100

0.01

0.0001

1e−6

1e−8

1e−6 0.0001 0.01 1 100IC [µA]

10000

β[−

]

meassimu

40

90

80

70

60

50

30

20

10

0

beta @ Ic=200n, 20u, 200u

Vbe @ Ic=50u, 1m


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 4: Correlation Table


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 4: Correlations

source: /PCM/-Docu

0.95

0.75 0.8 0.85

Sim: c = 0.751

Vt

MN

NE2

[V]

PCM: c = 0.818

Nom=0.863

Nom=0.838

0.9

Vt MNLE2 [V]

0.9

0.85

0.8

0.75

USL=0.943

Target=0.852

LSL=0.761

USL=0.93Target=0.834LSL=0.738


PCM Targets

„Golden Wafer“

PCM Limits

PCM Samples

Mismatch

Step 5: Mismatch Parameters

Area

constmismatchmismatch

2=σ

Special Device Pair Measurements on Testchiprequired

• Threshold voltages of MOS transistors• Current gains of bipolar• Sheet resistances of poly resistors


Monte Carlo Sections

uniform distribution of samplesµ = Target = (USL+LSL)/2σ = (USL-µ)/sqrt(3)

= σ[nom]*sqrt(3)

unif

Gaussian distribution of samplesµ = Target = (USL+LSL)/2σ = (USL-µ)/3= (USL-LSL)/6

nom

DistributionComment

LSL USL

LSL USL



parameters shifted to their Spec Limits (USL or LSL)µ = Target = (USL+LSL)/2

σ = USL-µ= σ[nom]*3

specLimits

uniform distribution of samples within 2σ and 3σµ = Target = (USL+LSL)/2

σ ≈ (USL-µ)*0.84= σ[nom]*2.5

unif2s3s

uniform distribution of samplesµ = Target = (USL+LSL)/2

σ = (USL-µ)/sqrt(3)= σ[nom]*sqrt(3)

unif

Gaussian distribution of samplesµ = Target = (USL+LSL)/2

σ = (USL-µ)/3= (USL-LSL)/6

nom

DistributionComment

LSL USL

LSL USL

LSL USL

LSL USL



parameters shifted to their Spec Limits (USL or LSL)µ = Target = (USL+LSL)/2

σ = USL-µ= σ[nom]*3

specLimits_noParspecLimits

uniform distribution of samples within 2σ and 3σµ = Target = (USL+LSL)/2

σ ≈ (USL-µ)*0.84= σ[nom]*2.5

unif2s3s_noParunif2s3s

uniform distribution of samplesµ = Target = (USL+LSL)/2

σ = (USL-µ)/sqrt(3)= σ[nom]*sqrt(3)

unif_noParunif

Gaussian distribution of samplesµ = Target = (USL+LSL)/2

σ = (USL-µ)/3= (USL-LSL)/6

nom_noParnom

DistributionCommentw/o Parasiticsw/ Parasitics

LSL USL

LSL USL

LSL USL

LSL USL


Example 1: PCM Par Vt_MNLE2 — MC Section nom

LSL USL

source: /PCM/-Docu

0.85 0.9

pro

pability

density

[%]

Vth [V]

LSL=0.738 Target=0.834 USL=0.93

Nom=0.838

PCM µ=0.836 σ=0.0121 N =1677Sim µ=0.84 σ=0.032 N =1000Spec µ=0.834 σ=0.032

00.80.75

4000

3500

3000

2500

2000

1500

1000

500


Example 2: PCM Par Vt_MNLE2 — MC Section unif

LSL USL

0.85 0.9

pro

pability

density

[%]

Vth [V]

LSL=0.738 Target=0.834 USL=0.93

Nom=0.838


00.80.75

4000

3500

3000

2500

2000

1500

1000

500


Example 3: PCM Par Vt_MNLE2 — MC Section unif2s3s

LSL USL

0.85 0.9

pro

pability

density

[%]

Vth [V]

LSL=0.738 Target=0.834 USL=0.93

Nom=0.838


00.80.75

4000

3500

3000

2500

2000

1500

1000

500


Example 4: PCM Par Vt_MNLE2 — MC Section specLimits

LSL USL

0.85 0.9

pro

pability

density

[%]

Vth [V]

LSL=0.738 Target=0.834 USL=0.93

Nom=0.838


00.80.75

8000

7000

6000

5000

4000

3000

2000

1000


Corner Sections

δVth(MNND, MNND2)=0.243V

δlcap(MNTE, MNSE2)=0.32µm

δVth(MNND)=-0.139VδVth(MNND2)=-0.154Vδlcap(MNTE, MNSE2)=-0.25µm

depSlow:

dmosSlow:

depFast:

dmosFast:

Comment

depSlow_dmosSlowdepFast_dmosSlow

depSlow_dmosFastdepFast_dmosFast

There are no universally valid “worst cases” in BCD Technologies�Corners have to be defined by Device Team according to the needs of Product Development!


Corner Sections

δVth(PMOS)=-3σ

δ wint =-3σ

δVth(PMOS)=-3σ

δVth(PMOS)=3σ

δwint =+3σ

δVth(PMOS)=3σ

δVth(NMOS)=3σδtox =+3σδlint =+3σδCj =+3σδVth(NMOS)=-3σ

SlowSlow:

FastSlow:

SlowSlowFastSlow

δVth(NMOS)=-3σδtox =-3σδlint =-3σδCj =-3σδVth(NMOS)=3σ

FastFast:

SlowFast:

SlowFastFastFast

δVth(MNND, MNND2)=0.243V

δlcap(MNTE, MNSE2)=0.32µm

δVth(MNND)=-0.139VδVth(MNND2)=-0.154Vδlcap(MNTE, MNSE2)=-0.25µm

depSlow:

dmosSlow:

depFast:

dmosFast:

Comment

depSlow_dmosSlowdepFast_dmosSlow

depSlow_dmosFastdepFast_dmosFast


Model Sections

� 8 Monte Carlo Sections

� 4 sections with different distributions� 4 “no Parasitics” sections (noPar) with neglect of:

- (substrate) parasitic devices- voltage/current/power warnings- paramTests (geometry checks)

� Corresponding noPar sections speed up simulation by ≥ 25%.� No section toggle required for nominal and Gaussian MC

simulation� 8 Corner Sections

� 4 corners for NMOS/PMOS speed� 4 corners for leakage current of depletion MOS and slew rate

of DMOS� Performing Monte Carlo analysis issues an error.


Model Quality

� The SMART5 PCM comprises 194 measurements (ASM52).� 143 of them can be re-simulated.� PCM evaluations may serve as a testbench to quantify the

model quality (w/o correlation and mismatch).

1. Does the nominal simulation reproduce the PCM Target?nom = Target

2. Does the mean value of the Monte Carlo simulation reproduce the nominal value?

µ = nom3. Does the standard deviation of the Monte Carlo simulation

reproduce one third of the distance between the PCM Upper Spec Limit and the PCM Target (cpk=1)?

3 σ = USL-Target


Model Quality

source: /MQ/-Docu


Model Quality

source: /MQ/-Docu

meas

simu

YYIsat MNLE2

MMRon MNLE2

MMG MNLE2

Vt MNLE2 YY

ClassificationParameter

USLTargetLSL


Conclusion

� PCM: not only Process Monitoring (TD), but also Device Monitoring (CAD)

� Recommended Usage of

� Monte Carlo Section nom with ≥100 runs for small circuits� Monte Carlo Section unif2s3s_noPar with ≤100 runs for

large circuits� Corner Sections only if you know what you are doing

(worst-worst case)� Reproduction of Correlations

� Monte Carlo Section nom� Monte Carlo Section unif, unif2s3s, specLimits� Corner Sections

� To be discussed

� Benefits of Quarterly Monitoring?� Device type coverage (SMART5 PCM: 41 of 75 types)?� PCM measuring regions?� PCM AC and Temp measurements needed?

akb2007 gondro statistical simulation methodology for smart … · 2007. 10. 26. · source: /ep/...

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