M.I.T,
Reliability of semiconductor I Cs
plus spin-based electronics
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Read Campbell,p,425 -428 and Ch,20,Sec,20.1,20.2; Plummer,Sec,11.5.6
IC reliability:
Yield =(#ooperating parts) / (total # produced)
Failure of devices occurs over time (lifetime) by various mechanisms,
w Particles on surface interrupt depositions,flaw devices
w Oxides,dielectrics fail by charging or dielectric breakdown,
w Metals fail by corrosion and
Electro-migration,mass transport of one species
along grain boundaries in metal toward one of the electrodes
with subsequent failure there,(Ohring,p,379 - 383)
w Magnetic systems,interdiffusion,stress
Reliability in Spin-based electronics,spin valves and
magnetic random access memories (MRAM)
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6.12J / 3.155J Microelectronic processing
Reliability of semiconductor I Cs
Why is this an issue?
“Learning curve”,yield vs,lot number,yield vs,lot number
and average over last 7 lots.
Defect density,D,has decreased
with succeeding higher-densitywith succeeding higher-density
dynamic random access memoriesdynamic random access memories …
Net yield is product,Y
1
x Y
2
x Y
3
… (e.g.,a 10-step process each 95% =>60% yield)
1
Y =(1-G)e
-AD(d )
Fraction of disk area
in which all circuits fail
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Killer defects
Defect arealareal density
Simplest yield model assumes independent,randomly-distributed defects,
(Poisson distribution),
Particle control,Class (Max #/ft
3
) > 0.5 mm
1 1
10 10
100 100
1000 1000
A = chip area
D = defects/area
Yield
Y μe
-AD
AD
AD = probability
of defect
overlapping
chip
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Killer defects
Defect size
Defects are not randomly distributed spatially
(e.g,stress concentrations generate dislocations,stacking faults),
or by size,d,i.e,D = D(d)
D(d) =c
d
q
d
0
q+1
,0 <d<d
0
D(d) =c
d
0
p-1
d
p
,d
0
<d<d
max
Meander-line
process control
module
1-G
Empirical distribution of defect sizes,
Hard to measure,
Therefore Y (1-G) exp(-AD)
G is fractional area where all fail
2
Reliability definitions
6.12J / 3.155J Microelectronic processing
Cumulative failure distribution function,F (t),
F (t)
R (t)
1
F (t) = fraction of failures up to time,t.
Survival or reliability distribution function,R (t),
R (t)= 1 - F (t)
0
0
t
1
Failure probability density function,f (t),
f (t) = dF/dt
0
(This is key to predicting failure rates)
0
t
f (t)
Mean time to failure,MTTF,MTTF=
ú
t? f(t)dt
0
Median time to failure,t
50
,time after which half of devices have failed,
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Reliability definitions
6.12J / 3.155J Microelectronic processing
1
Failure probability density/number remaining,
l(t) = f(t)/R(t)
0
0
t
l(t)
Failure rate during time dt,l(t),
l(t) =
R(t) - R(t +dt)
dtR(t)
=-
1
R(t)
dR(t)
dt
1 dF(t)
=
R(t) dt
Failure rate
l(t) =-
1 dR(t)
=const,=l
0
(fractional failure frequency)
in steady state:
R(t) dt
Steady-state survival
Hence,
or reliability drops off
R(t) μe
-l
0
t
exponentially with time
steady state:
f (t) =
dF
=-
dR
μl
0
e
-l
0
t
MTTF =
ú
t? f (t)dt =
1
ss
dt dt
ss
0
l
0
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3
Different failure processes
mortality” state
Wearout
6.12J / 3.155J Microelectronic processing
l(t) =l
0
l (t)
t
0
“Infant Steady
Failure rate,
E
a
Different failure processes have
-
k
B
T
different thermally activated rates:
r = r
0
e
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6.12J / 3.155J Microelectronic processing
More realistic example,log-normal distribution
s = standard deviation
= time for 50% of devices to failt
50
ln(t)
1
[]
2
f (t) = expì-?
st 2p? 2s
2
ó?
s =ln(t
50
/ t
16
) and
MTTF =exp{ln(t
50
+s
2
/2)
Log-normal distribution,if ln of failure time is plotted vs,
fraction of chips failing within a range of times gives a
normal,i.e,Gaussian distribution,then the distribution is log-normal,
Lognormal distribution is hard to handle analytically
but can be represented more simply on a log-normal scale,
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4
s < 1
could represent
wearout
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6.12J / 3.155J Microelectronic processing
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm
log-normal distribution
f (t) =
1
st 2p
exp -
ln(t)[]
2
2s
2
ì
ó
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Log-normal distribution can represent any of the 3 regimes by varying s
s > 1
could represent
infant mortality
l
(t)
t
0
Infant
mortality
Steady
state
Wearout
Failure rate,
5
Log-normal distribution
6.12J / 3.155J Microelectronic processing
If data are linear on lognormal plot,then s can be found
s =ln(t
50
/ t
16
)
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6
Mean time to failure
6.12J / 3.155J Microelectronic processing
Expressed in log form as:
Plotted vs Log(J),right
in which case the slope gives the power,-n.
For increased operating current,
MTTF drops off as the -n
th
power of J.
For higher operating temperatures,
lifetime curve is shifted down,quicker failure,
Log(MTTF)
log(J)
ln <t
fail
>=ln( A) -nln(J)+
E
n
k
B
T
The mean time to failure (MTTF)
(related to inverse of rate),
n 2to3.
(Most activated mechanisms of failure have a form like this)
MTTF μ J
-n
e
+E
a
/ k
B
T
-
Or,ln(MTTF
1
),mean failure rate,could be plotted vs,1/T (Arrhenius plot)…
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Mitigating thermally activated failure
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Thermally activated failure rates,Caution on accelerated aging,
E
a
-
k
B
T
Operating
temperature
Accel,aging
r = r
0
e
test
Ln(r)
RT
Operate at lower temp.,
lower current density
Use,burn-out” to elim,early fails
1/k
B
T
…you may get
wrong activation energy,
Example,electromigration.,,
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7
Electromigration,electron wind moves atoms
6.12J / 3.155J Microelectronic processing
Electromigration,mode of failure in high-current-density heterostructures,
(Most literature on electromigration deals with metallic conductors in semiconductor devices)
Large current density,J => not only charge transport
J = nqv
but also mass transport of
charged particles,e’s or h’s,
When charge carriers collide with atoms (“electron wind”),
they impart a small momentum to atoms,
sweeping them in the direction of the carrier drift,
Expression for the electromigration flux of species A,j
A
= c
A
v
drift
,(Z*q
.
X nq v ) r
requires the force on an ion A due to the electric current,
Ion - carrier
**
interaction
F= qZ
A
E = qZ
A
Jr
Here q is the electronic charge,Z
A
* is the effective ion valence and E is the electric field
(force per unit charge) producing the electric current density,J = E/r
s =F / areaa2 ￥10
-2
lbs/ micron
2
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8
Electromigration,grain-boundary diffusion
6.12J / 3.155J Microelectronic processing
Most electromigration takes place along grain boundaries.
D
A
= D
A
o
exp[-E
a
/(k
B
T)]
D
A
is the grain boundary diffusion coefficient of A,
(D
A
typically 0.5 - 0.8 eV vs,bulk about 1.4 eV)
Flux of species A,J
A
,is proportional to the product
*
(volume concentration of A) x (velocity of A resulting from F= qZ
A
Jr ),
J
D
A
FD
A
qZ
A
*
Jr
A
= c
A
v
A
= c
A
=c
A
RT RT
Here use Nernst-Einstein equation for drift velocity of a particle
at temperature T under influence of force F,v = D
A
F/RT.
Electromigration is problematic? at high current density,
high resistivity (many electron-atom collisions),
for large grain-boundary diffusion,
at high T (which is in exponent of D
A
),
for light metals (D
A
0
is inverse function of mass of A)
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6.12J / 3.155J Microelectronic processing
Add temperature-dependent term to time rate of change of concentration as follows,
dc
A
dt
=-
J
A
x
-
J
A
T
dT
dx
temperature gradients
associated with
local hot or cold spots
couple with temperature
dependence of J
A
.
Isothermal mass transport
due to flux divergence
such as at
grain boundary junctions,
j
A
Fick's second law of diffusion states that change in concentration of species A
occurs as a result of a divergence in J
A
,i.e,a variable concentration gradient:
c
A
t
=-
J
A
x
= D
A
2
c
A
x
2
Electromigration damage,due to flux divergence or temperature gradients
9
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6.12J / 3.155J Microelectronic processing
Electromigration vs,linewidth/grain size
(Thompson-Frost model)
w/d
50
Yield
J
A
=
D
A
c
A
k
B
T
(qZ
A
*
Jr+W
ds
dx
)
ds
dx
=-
qZ
A
*
Jr
W
s =-ax +b
s
max
=±
Z
*
qJr
W
ê
á
ˉ
L
p
2
Equilibrium,
,
JL
p
<
s
crit
2W
Z
*
qr
w
d
50
w/d
50
3.0
w/d
50
0.3
w/d
50
1.3
L
p
Voids hillocks
Mass flow
Electromigration summary
6.12J / 3.155J Microelectronic processing
electron wind,
mass transport
Voids,depletion
Accumulation,hillocks
4 microns
Most electromigration takes place along grain boundaries,
Grain boundaries that run parallel to current direction are most problematic,
A factor cos (q) is often attached to the atomic flux expression to reflect this fact;
a is the angle between the current and the grain boundary,
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10
Grain growth
6.12J / 3.155J Microelectronic processing
Grain growth well described also by log-normal distribution
2
1 ln(d/ d
50
)
f (d) =
exp
2s
2
sd
]
2p
[
-
ì
ó
d
50
= median grain diameter
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Spin-based electronic devices,background
6.12J / 3.155J Microelectronic processing
Semiconductor review
E
Mobile holes
Immobile holes
Mobile e’s
E
Low
mass
electrons
P
E
FN
Immobile e’s
type
E
F
type
High
mass
holes
Semiconductors have two distinct types of carriers (e’s and h’s)
characterized by
w different mobilities,concentrations,conductivities
w different Fermi energies for N and P
w carriers scattered into dopant sites become trapped
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11
Spin-based devices
Two carrier types,e’s with spin parallel or antiparallel to local moments
6.12J / 3.155J Microelectronic processing
e
-
e
-
e
-
Mobile carrier
Scatters
from ion
Spin-dependent
resistivity
r << r < r
x
M (x)
Spin memory
is lost over x,t
e
-
M (x)
x
e
-
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Spintronics = spin (magnetism)-based electronic devices
6.12J / 3.155J Microelectronic processing
Spin-up and spin-down electrons form the basis for a number of spin-based devices including
spin valve (non-magnetic metal interposed) and the spin-tunnel junction (oxide layer interposed),
Separator Device
non-non-mag metal => low-impedance metal => low-impedance
spin valve or spin switch
insulator => high-impedance insulator =>
spin-tunnel junction
(Messervey and Tedrow,Phys.,Phys,Rpts,238,174 (‘96); Moodera et al,
Resistance
H
Phys,Rev.Phys,Rev,Lett,80,2941 (‘98))
Unlike semiconductor devices,performance of spin-based devices improves as thickness decreases
because screening lengths and spin diffusion lengths in metals << than in semiconductors,
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12
Magnetic Random Access Memory (MRAM)
(based on spin valve or spin-tunnel junction)(based on spin valve or spin-tunnel junction)
6.12J / 3.155J Microelectronic processing
No moving parts,non-volatile bits…but presently limited by lower density than hard disk
Array of spin valves
(or psuedo-SVs,PSVs)
…connected by
x and y electrode lines
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Magnetic Random-Access Memory (MRAM)
Bit read by weak
current pulses
(magnetic field)
in specific
x and y lines
Bit written by strong
coincident current pulses
(magnetic field)
in specific
x and y lines
14
Microelectronic processing
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6.12J / 3.155J
High Density Magnetic Random Access Memories
Word line (W)
Insulator (SiO2)
Sense line (W)
MR element
(Co/Cu/NiFe)
Magnetic nanostructures can be used in electronic components such as ultra-
sensitive magnetic field sensors,optical computing components,and a new
class of ‘spintronic’ devices,One example is an MRAM,which will replace the
semiconductor memory chips in computers with faster,lower power,non-
volatile storage using magnetoresistive (MR) elements,
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6.12J / 3.155J Microelectronic processing
Spintronics,processing,reliability issues
MTTF μ J
-n
e
+E
a
/ k
B
T
w Very large current densities (J > 10
7
A/cm
2
)
=> high operating temperatures (T > 100
0
C),
electrothermal failure:
w Chemical interaction of dissimilar metals
w Spin-valve magnetic layers < 8 nm thick
w Oxide layers in spin-tunnel jcts < 3 nm thick
w Track-width decreasing toward 100 nm
15