Lecture A4a On Reliability and Randomness in Electronic Devices

2009
NCN@Purdue‐Intel
Summer
School

 Notes
on
Percola9on
and
Reliability
Theory

Lecture
A4a
 On
Reliability
and
Randomness

 in
Electronic
Devices Muhammad A. Alam Electrical and Computer Engineering Purdue University West Lafayette, IN USA NCN
 www.nanohub.org


1


outline of lecture 7 1.  Background
informa5on
 2.  Principles
of
reliability
physics
 3.  Classifica5on
of
Electronic
Reliability

 4.  Structure
Defects
in
Electronic
Materials
 5.  Conclusions



2


process, reliability, and design Reliability

Process plus

t=0

-15%

-10%

-5%

ID

ID,nom

+15%

Design

We do not have too much margin

3


complexity of the reliability problem Mobility

 Improvement


TI


 
Ge
channel


 
Strained
silicon


 
uniaxial



 
bi‐axial


 
III‐V
materials


Improvement
in
Electrosta5cs
 Berkeley
 FINFET


IBM


 
Silicon
on
insulator
(SOI)


 
Double‐gated
devices


 
Tri‐gate
or
FINFET
devices


 
Surround
gate
devices







(VRG,
Si‐NW)


4


outline of lecture 7 1.  Background
informa5on
 2.  Principles
of
reliability
physics
 3.  Classifica5on
of
Electronic
Reliability

 4.  Structure
Defects
in
Electronic
Materials
 5.  Conclusions



5


Equivalence between Spatial/Temporal Fluctuation Process

Reliability plus

Side view (TDDB)

top view (RDF)

Spa5al
and
temporal
fluctua5on
should

 be
considered
with
same
framework
…


model

6


Equivalence of spatial/temporal fluctuations Process


Device


Process


Reliability
 Same
theore5cal
tools


Device


• 
Time‐ordered
(N~t)
 • 
Spa9al
Correla9on


Temp
 Manufacture


E‐field
 Store


Home/office


Time
 7


Gate
Current


reliability: stochastic process terminated by a threshold

Pey,
IRPS02
 HBD


ln
(5me)


8


reliability: physics of how things break A
child
drops
a
glass
 Bridges
(Tacoma
Narrows)

 ShuLle
(Challenger)
 Ligh9ng
in
a
rain‐soaked
night
 Volcano,
landslides
&
forest
fire
 Check‐out
queues,
scheduling
 A stochastic process terminated by threshold 9


theory of accelerated testing Nonlinear
projec5on
for
 processes
with
threshold


V3>
V2
>
V1


Days


Vop


Years



ln
(TBD)


Gate
Current


years
 Std.


Days


V G


Empirical projection is very difficult, if not impossible … 10


Nonlinear Projection: an illustrative example Stochas9c
Process


Stochas9c
Process
with
a
threshold
 Absorption site

v
 How far away from the trap-site do I need to inject the particles so that after TBD sec of diffusion no more than y percent of particles is lost? 11


accelerated testing: empirical approach m
 v


Absorption site q
 p


accelerate


p~1


ln
Tav


years
 decreasing
p


vsafe


p
or
velocity


5me
 12


average arrival time distribution q


x=0

p


x=xm

x‐d
 x
 x+d


Time
to
absorp9on
a\er
being
injected
at
x
….


13


average arrival time distribution x=0

q


p


x=xm

x‐d
 x
 x+d


Average lifetime diverges at small velocity, v or p -> 0 14


physical vs. empirical projection p


q


x=0

x=xm

Ln
T


x
 physical
 years


vsafe
 vsafe


  Empirical

meas. & comp. simulation would not do

  Prediction is possible because t=0- is smooth

15


outline of lecture 7 1.  Background
informa5on
 2.  Principles
of
reliability
physics
 3.  Classifica5on
of
Electronic
Reliability

 4.  Structure
Defects
in
Electronic
Materials
 5.  Conclusions



16


front and backend reliability

Transistor
Reliability
Issues




       

The
Oregonian,
2008


Gate
Dielectric
Breakdown
 Nega5ve
Bias
Temperature
Instability
 Hot
Carrier
Degrada5on
 Radia5on
Induced
damage


Interconnect
Reliability
Issues



  Electro‐migra5on/Stress‐migra5on.


  Inter‐level
dielectric
breakdown
 17


Initially ….

S


G


.... a few months later

D

Drain Current

front end transistor reliability VG2
 VG1


Drain Voltage Broken
Si‐H
bonds:
 
Nega5ve
Bias
Temperature
Instability
(NBTI)
 




































 
Hot
carrier
degrada5on
(HCI)
 Broken
Si‐O
bonds: 
Gate
dielectric
Breakdown
(TDDB)
 
 
 
Radia5on
induced
damage
 Trapping:






Posi5ve
bias
temperature
instability

 18


outline of lecture 7 1.  Background
informa5on
 2.  Principles
of
reliability
physics
 3.  Classifica5on
of
Electronic
Reliability

 4.  Structure
Defects
in
Electronic
Materials
 5.  Conclusions



19


Crystalline, Amorphous, and Random Materials Crystalline



Amorphous


Random


N

r 20


crystalline Si and SiO2 Crystalline
Si


Crystalline
SiO2


For
a
dynamic
view
of
SiO2
see,

 hdp://cst‐www.nrl.navy.mil/laece/struk.jmol/coesite.html


crystalline vs. amorphous SiO2 Fixed
bond
lengths


Sof
Si‐O‐Si

 bond
angles

 oxygen


Si
 22


composition vs. coordination

4
Si
atoms
x
1/8
=
½


1
Si
atoms
(white)


1
oxygen
atom
(white)
=
1


4
oxygen
atom
x
½/cell
=
2


Si1/2O
=
SiO2


SiO2
…..


Oxygen
coordina5on
…

4
 Hf

coordina5on
–
8



Oxygen

coordina5on
…
2
 Silicon
coordina5on
…
4


23


amorphous is neither completely Random, nor it is defective Amorphous


small scatter in ring distribution … 24


geometry defines ring statistics Euler
Rela5onship
in
2D



ver5ces
edges
 cell
number


Interpreted
as

 edges/cell


1/2
of
a
cell:
must
have

6‐sides!
 25


Ring Statistics in Random Structure Euler
Rela5onship
 Prob.
of

 k‐sided
ring


26


amorphous material and bandtail states

Ec


Ev
 27


origin of defects: Maxwell Constraints – a Poor Man’s MD Zero
T
approxima5on
 dimensionality


Points
to
be
stabilized
 constraints


q1

q2 q3 Maxwell,
Phil.
Mag.
27,
1864,
294.
 J.C.
Phillips,
1979.
Thorpe,
1982.


 28


examples: SiO2 and Si3N4

Maxwell,
Phil.
Mag.
27,
1864,
294.
 J.C.
Phillips,
1979.
Thorpe,
1982.


 29


meaning of an oxide/nitride defect

30


crystalline vs. amorphous oxides

NY
Times,
2007.



31


bulk defects of missing oxygen: E’, K, and P defects Courtesy:



Prof.
Lenahan


Responsible for gate dielectric breakdown Will discuss in Lecture 8 and 9

Pb centers – interface traps

Pb1
[211]


[111]


Responsible for NBTI degradation Detailed discussion in Lecture 10 33


Interface structures by Molecular dynamics A.  Bongiorno et al. PRL, 90, 2003.

34


electron spin resonance: a ‘microscope’ for defects Variable

 Fixed

 Microwave
 B‐field


ΔE
=
geμBB0
 hν
=
geμBB0


Microwaves
@
~
 10
GHz
 B
~
3500
G
(0.35
T)



Absorp5on
Spectra
 35


ESR invisible defects Paramagne5c
materials
may
appear
diamagne5c


Phonon assisted e-e attraction (superconductivity).

36


conclusions

  
Reliability
is
a
very
important
technology
problem.
The


success
or
failure
of
any
technology
depends
on
its
intrinsic
 reliability
(e.g.
Stone
vs.
Cu
age)



  
Historically
reliability
has
been
an
empirical
science;
it
has
 changed
drama5cally
since
WWII

(Military
applica5ons,
AT&T
 trans‐Atlan5c
cable,
IBM
mainframe,
Introduc5on
of
CMOS).



  
Reliability
as
a
‘Stochas5c
process
with
a
threshold’
provides
 the
physical
basis
for
wide
range
of
phenomena.



  
There
are
many
reliability
concerns
for
electronic
devices
–
an
 analysis
of
these
problems
beings
with
the
analysis
of
the
 nature
of
defects.
We
will
related
bulk
oxide
E’
centers
to
 TDDB
and
depassiva5on
of
SiH
bonds
at
the
interface
to
NBTI.



figure references Checkout:
hdp://vinlai.com/gallery2/v/1042‐2/heathrow_4.jpg
 hdp://i111.photobucket.com/albums/n125/woodz1415/broken20glass.gif
 Lightning:
hdp://www.uwec.edu/jolhm/EH3/
 Group2/Pictures/lightning.jpg
 Concord:
hdp://www.ahrtp.com/EG_Images2/ Concorde_crash_opt600x412_concordesst.jpg
 hdp://www.theharrowgroup.com/ar5cles/20020513/TacomaBridge.gif
 hdp://www.ifw‐dresden.de/ins5tutes/ikm/organisa5on/dep‐31/ research‐topics/electromigra5on/insituem_small.jpg
 38