si l 1/sqrt(lw) [um]

Workshop November 5, 2010

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Acknowledgement

Sponsored by Applied Materials, ASML, Ebara, Global

Foundries, IBM, Intel, KLA-Tencor, Marvell, Mentor

Graphics, Novellus, Panoramic Tech, SanDisk,

Synopsis, Tokyo Electron and Xilinx with matching

support by the UC Discovery Program.

IMPACT Integrated Circuit Variability Modeling and Statistical Transistor Parameter Extraction

Kun Qian, Prof. Costas J. Spanos, University of California, Berkeley

Motivation

Decomposing Random Variability Capturing Systematic Effects Statistical Compact Model Extraction

Testchips in 22/16nm FDSOI and 45nm Bulk 2010 Main Objectives

Parameter Selection Example:

Single 65nm chip I-V data Experimental Results Systematic Spatial Variation

BSIM3v3 Batch Sequential Extraction Future Goals Correlation Structure

Goal 1

Goal 2

Funded by

YOUR

IMAGE

HERE

Sub-wavelength lithography:

Resolution enhancement techniques are

costly and increase process sensitivity

Design

Mask

Wafer

250nm250nm 180nm180nm

OPCOPC

90nm and Below90nm and Below

PSM

0°

180°

PSMPSM

0°

180°

0°

180°

OPC

0°

180°OPCOPCOPC

0°

180°

SiO2 Gate

A. Brown et al.,

IEEE Trans.

Nanotechnology,

p. 195, 2002

Source Drain

A. Asenov, Symp. VLSI Tech. Dig., p. 86, 2007

Gate line-edge roughness (LER):

Does not scale with gate length photoresist line

Random dopant fluctuations (RDF):

Atomistic effects become significant in

nanoscale FETs

Gate work function variation (WFV)

22/16nm Test Chip Design

– Random variability decoupling structures

– Systematic variability capture plan

Variability-Aware Compact Model Extraction

– Algorithmic analysis of parametric observability with

iterative (step-wise) parameter selection

– Implement a sequential parameter extractor that performs

optimization for large number of transistors.

Characterize random and systematic variability - Local and spatial variation

- Process and layout-induced variation

- SRAM and ring oscillator performance

22nm fully-depleted SOI process suppresses

random dopant fluctuation (RDP) and short channel

effect (SCE)

Padded-out SRAM

DUT-Tiles

Pad Ring

DRAM

C-V

Resistor

Ring Oscillator

NMOS

I-V

PMOS

I-V

45nm die photo

22/16nm target chip layout

Ultra-Thin Body

(UTB)

Buried Oxide

Substrate

Source Drain

Gate

tSi

Lg

tSi < (1/4) Lg

3D TCAD simulation results:

Without RDF, Tsi variation is

dominant at large gate lengths, and

both LER & Tsi at short gate lengths

Then LER & Tsi can be further

decoupled

Design for decomposition of

different sources of random

variability:

Low-temperate I-V measurement to

de-activate dopant atoms

Choice of W, LOD to eliminate

narrow width effect and stress-

induced variation, respectively.

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

LER + Tsi + RDF @ 50mV of VDS

LER + Tsi + RDF @ 1V of VDS

Avt = 1.06 [mV x um]

sig

ma(V

TH)

[mV

]

1/sqrt(LW) [um]

LER/Tsi/RDF

LER+Tsi

LER/Tsi/RDF

LER+Tsi


0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

LER + Tsi + RDF @ 50mV of VDS

LER + Tsi + RDF @ 1V of VDS


sig

ma(V

TH)

[mV

]

1/sqrt(LW) [um]

LER/Tsi simulated

LER/Tsi estimated

LER/Tsi simulated

LER/Tsi estimated


Vt .SCE2 VDS 1V

2 VDS 50mV2

Vt

L L

2

Vt

TSiTSi

2

Systematic variations are just as

important as random variations

– Spatial variations at different

hierarchical fabrication levels:

non-uniformity in CVD, PVD,

plasma etching, post exposure

bake (PEB), CMP, …

– Layout dependent effects (litho

proximity, CMP, etch loading, …)

Vertical STI size

Length of Diffusion

Horizontal STI size

Sample layouts for stress effect

Not every compact model parameter is suitable for describing

device variability.

Use a stepwise selection scheme to find proper parameters for

statistical extraction

Convert parameter statistics to a systematic + random

hierarchical spatial model

Parameters

Suitable for

Statistical

Extraction

SPICE

Model

Parameters

Check:

Fitting Quality

Extraction Quality

ADD

REMOVE

Distribution of

Electrical Data

Distribution of

Model Parameters:

Systematic + Random

Optimizer

vto, kp

vto, kp, lambda

vto, kp, lambda, ucrit

step2 step3 step4 step1

Full-set

Die-to-die variation

modeled as a

deterministic

parabolic function +

correlated

Gaussian random

variables

Fitting residual

45nm Padded-out SRAM data

Die-to-die variation

of extracted model

parameters are

fitted using a 2nd

order polynomial

spatial function

Experiment vs. prediction by statistically extracted model parameters

Experimental

SPICE

Variability-Aware Compact Model Extraction

– Study the effects of different parameter selection

scheme for given device parameter correlation

structure.

Explore key applications such as custom “corner”

generation, etc.

Non-linear least square optimization is not always accurate.

0.26 0.28 0.3 0.32 0.34 0.36 0.380.26

0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36

Extr

acte

d V

TH

0

"Actual" VTH0

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.4

Extr

acte

d K

1

"Actual" K1

1 2 3 4 5 6 7 8 9 10 11

x 10-3

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

"Actual" K2

Extr

acte

d K

2

0 1 2 3 4 5 6 7 8 9 10

x 1018

7

7.5

8

8.5

9

9.5

10

10.5x 10

17

"Actual" NCH

Extr

acte

d N

CH

Transistor data

simulated using

90nm BSIM3

NCH = NCH0+r1+k1*e1

VTH0=VTH00+r2+k2*e1

K1=K1+r3

K2=K2+r4

r1, …, r4, e1, e2 are

Gaussian random

variables

Artificial strong correlation between VTH0 and NCH induced by

the fitting process.

7 7.5 8 8.5 9 9.5 10 10.5

x 1017

0.26

0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0.36

"Actual" NCH

"Actu

al"

VT

H0

0 1 2 3 4 5 6 7 8 9 10

x 1018

0.26

0.28

0.3

0.32

0.34

0.36

0.38

Extracted NCH

Extr

acte

d V

TH

0

C-V data Fit NCH I-V data Fit VTH0,

K1, K2

si l 1/sqrt(lw) [um]

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