recent developments in device reliability modeling: the

Recent Developments in

Device Reliability Modeling:

The Bias Temperature Instability

Tibor Grasser

Institute for Microelectronics, TU ViennaGußhausstraße 27–29, A-1040 Wien, Austria

TU Wien, Vienna, Austria

1/37

The Negative Bias Temperature InstabilityThe Negative Bias Temperature Instability

Huard et al., MR ’06

Negative bias temperature stress of pMOSFETs[1] [2] [3]

Large negative gate voltage (≈ 5 − 8 MV/cm), all other terminals grounded

Elevated temperatures (typically 100 ◦C– 200 ◦C, but also at room temperature)

Degradation of critical device parametersThreshold voltage

Subthreshold slope

Transconductance

Mobility

Drain current

...

Occurs in all four configurationsStrongest in pMOS with negative bias

Serious reliability concern in pMOSFETs[1]

Schroder and Babcock, JAP ’03[2]

Alam and Mahapatra, MR ’05[3]

Huard et al., MR ’06

2/37

The Negative Bias Temperature InstabilityThe Negative Bias Temperature Instability

When does the NBTI scenario occur?NBTI: VG ≪ 0 V, VS = VD = 0 V

Example: inverter with Vin = 0 V

Similar scenarios in ring-oscillators, SRAM cells, etc.

VDD

Vin Vout

What happens to the pMOS transistor?

Kimizuka et al., VLSI Symp. ’00

3/37

Origin of the Negative Bias Temperature InstabilityOrigin of the Negative Bias Temperature Instability

[Courtesy: PennState Univ.]

[Courtesy: PennState Univ.]

What happens during negative bias temperature stress?

Creation of SiO2/Si interface defects (dangling Si bonds, Pb centers)Pre-existing, but passivated by hydrogen anneal

Si–H bonds can be broken

Results in trapping sites inside the Si bandgap

Universally acknowledged [1] [2]

Different defect in SiON and high-k? [3]

Creation of oxide chargeMost likely E ′ centers

Charge exchange mechanism?

Controversial! [4]

[1]Mahapatra et al., IRPS ’07

[2]Huard et al., MR ’06

[3]Campbell et al., TDMR ’07

[4]Mahapatra et al., IRPS ’07

4/37

NBTI Measurement TechniquesNBTI Measurement Techniques

Main problem: it is impossible to perfectly measure NBTI

As soon as stress is removed, extremely fast recovery is observed [1] [2]

Strong bias dependence, in particular to positive bias [3] [4] [5]

A number of techniques have been suggest and used

Conventional Measure/Stress/Measure [6]

On-the-fly (during stress, no interruption) [7]

Charge-pumping and DCIV techniques [8]

Various problemsDelays lead to recovery

How to quantify the degradation (∆Vth, ∆ID, ???)

Biggest problem: results do not match!!!No exact theory available that unanimously links and explains all the data

[1]Ershov et al., IRPS ’03

[2]Reisinger et al., IRPS ’06

[3]Ang, EDL ’06

[4]Huard et al., MR ’06

[5]Grasser et al., IEDM ’07

[6]Kaczer et al., IRPS ’05

[7]Denais et al., IEDM ’04

[8]Neugroschel et al., IEDM ’06

5/37

Influence of DelayInfluence of Delay

Measurement delay has a significant impact on measurement[1] [2] [3]

Curvature in data becomes more obvious, larger (time-dependent) ’slope’

Impact of delay does not disappear at longer stress times

Impact of delay is temperature dependent

100

101

102

103

104

105

Net Stress Time [s]

10

100

∆Vth

[m

V]

200oC

125oC

50oC

10 ms10 s10 ms10 s

10 ms

10 s

10-2

10-1

100

101

Delay Time [s]

0.12

0.14

0.16

0.18

0.2

Eff

ectiv

e Po

wer

Law

Slo

pe

200oC

150oC

100oC

50oC

[1]Ershov et al., IRPS ’03

[2]Denais et al., IEDM ’04


6/37

Standard Model: Reaction-Diffusion ModelStandard Model: Reaction-Diffusion Model

Successful in describing constant bias stress [1] [2]

Cannot describe relaxation[3] [4] [5]

Relaxation sets in too late and is then too fast, bias independent

Wrong duty-factor dependence in AC stress: 80% (theory) vs. 50% (measured)

10-10

10-8

10-6

10-4

10-2

100

102

104

106

108

Normalized Relaxation Time ξ

0

0.2

0.4

0.6

0.8

1

Uni

vers

al R

elax

atio

n Fu

nctio

n r

(ξ)

Numerical H0

Numerical H2

1/(1+ξ1/2)

Reisinger

Model is wrong!!! [6] [7] [8] [9] [10]

[1]Alam et al., MR ’06

[2]Kufluoglu et al., T-ED ’07


[4]Grasser et al., IRPS ’07

[5]Huard et al., IEDM ’07





[10]Huard et al., IRPS ’10

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OverviewOverview

IntroductionStochastic NBTI on small-area devices: link NBTI and RTN

New measurement techniqueThe time dependent defect spectroscopy

Anomalous defect behaviorPresent in all defects

Stochastic modelAdditional metastable states, multiphonon theory

Compact modeling attemptRC ladders

Implications on lifetimes

Conclusions

8/37

What is Really Going On?What is Really Going On?

Study of NBTI recovery on small-area devices [1] [2] [3] [4] [5] [6]

Stochastic and discrete charge emission events, no diffusion

[1]Huard et al., IIRW ’05

[2]Reisinger et al., IIRW ’09





9/37

Recoverable NBTI due to the same Defects as RTNRecoverable NBTI due to the same Defects as RTN

Quasi-equilibrium:Some defects neutral, others positive, a few produce random telegraph noise (RTN)

Stress:Defects switch to new equilibrium (mostly positive), a few may produce RTN

Recovery:Slow transition (broad distribution of timescales) to initial quasi-equilibrium

0 200 400 600 800 1000Time [s]

Sum

#11

#10

#8

#4

#3

+

0

Equilibrium: RTN

VG = -0.5V

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Charging Time [s]

Non-Equilibrium: Charging

VG = -1.8V

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

Discharging Time [s]

EquilibriumRTN

Non-Equilibrium: Discharging

VG = -0.5V

10/37

The Time Dependent Defect Spectroscopy (TDDS)The Time Dependent Defect Spectroscopy (TDDS)

Analyzes contributions from multiple traps via spectral maps [1] [2]

0

5

10∆V

th [

mV

]

10-5

10-4

10-3

10-2

10-1

100

101

102

Emission Time [s]

0

2

4

6

Ste

p H

eigh

t [m

V]

ts = 1msT = 100

oC

VG = -1.7V

Time Domain


[2]For a discussion on the step heights see Kaczer et al., IRPS ’10

10/37


Analyzes contributions from multiple traps via spectral maps

0

5

10∆V

th [

mV

]

10-5

10-4

10-3

10-2

10-1

100

101

102

Emission Time [s]

0

2

4

6

Ste

p H

eigh

t [m

V]

Spectrum

ts = 1msT = 100

oC

VG = -1.7V

Time Domain

[0] [0]

10/37


Analyzes contributions from multiple traps via spectral maps

0

5

10∆V

th [

mV

]

10-5

10-4

10-3

10-2

10-1

100

101

102

Emission Time [s]

0

2

4

6

Ste

p H

eigh

t [m

V]

Spectrum

#3

#4

#1

#2

#12

#3

#4

#1

#2

#12

#3

#4

#1

#2

#12 ts = 1msT = 100

oC

VG = -1.7V

Time Domain

[0] [0]

11/37

The Time Dependent Defect SpectroscopyThe Time Dependent Defect Spectroscopy

Function of stress time ts

12/37


Function of temperature

13/37


Different non-linear field dependence of the capture time constants

Different bias dependence of emission time constant: two defect types?

0.5 1 1.5 2 2.5 -VG [V]

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Cap

ture

Tim

e C

onst

ant

[s]

#1 125oC

#3 125oC

#4 125oC

#6 125oC

#8 125oC

tRTN: τcs 125

oC

#1 175oC

#3 175oC

#4 175oC

#8 175oC

#10 175oC

#11 175oC

tRTN: τcs 175

oC

~1/ID

VthVDD

10-4

10-3

10-2

10-1

100

#2 (lin/125oC)

#4 (lin/125oC)

#4 (lin/175oC)

#1 (sat/125oC)

#2 (sat/125oC)

#4 (sat/125oC)

0.2 0.4 0.6 0.8 1 1.2Negative Readout Voltage (-VG) [V]

10-4

10-3

10-2

10-1

100

101

E

mis

sion

Tim

e C

onst

ant

[s]

#1 (lin/125oC)

#3 (lin/125oC)

#1 (lin/175oC)

#3 (lin/175oC)

#3 (sat/125oC)

#6 (sat/125oC)

ID

Disappearing Switching Traps

Compare SRH-like model: τc = τ0 eβ∆EBNv

pτe = τ0 eβ∆EB eβ∆ET exF/VT

14/37

Anomalous Defect BehaviorAnomalous Defect BehaviorDefects disappear temporarily from the map (#7)

Long term stability: defect #6 missing for a few months now

15/37

Anomalous Defect BehaviorAnomalous Defect Behavior

Temporary random telegraph noise (tRTN)

0 2 4 6 8 10 12 14 16 18Relaxation Time [ms]

0

5

10

15

0

5

10

15

-∆V

th [

mV

]

0

5

10

15

Trace 23

Trace 16

Trace 14

T = 150oC / ts = 1s / Vs = -1.7V

#1 #4

#4#1

#14

#1

#4

No ModulationModulation

0 2 4 6 8 10 12 14 16 18Relaxation Time [ms]

0

5

10

15

0

5

10

15

-∆V

th [

mV

]

0

5

10

15T = 125

oC / ts = 100ms / Vs = -1.5VVr = -0.668V

Vr = -0.556V

Vr = -0.459V

16/37

Tewksbury ModelTewksbury Model

Tewksbury model[1]: charging and discharging of traps via elastic tunnelingEquilibrium Stress Recovery

[1]Tewksbury and Lee, SSC ’94

17/37

How Can We Model All That Properly?

18/37

Standard Model for RTNStandard Model for RTN

Model suggested by Kirton & Uren[1]

Noticed that elastic tunneling cannot be ’it’

Also used lattice-relaxation multiphonon emission (LRME)

Time constants depend on activation energy ∆EB and depth x

τc = τ0 eβ∆EBNv

pτ−10 = Nv vth σ e−x/x0

τe = τ0 eβ∆EB eβ∆ET exF/VT

B

Neutral DefectPrecursor Hole Capture

A

Standard Charge Capture/Emission Model

Charged TrapPositive Defect

Hole Emission

Kirton/Uren Model

LRME

LRME

+

[1]Kirton & Uren, Adv.Phys ’89

19/37

Lattice Relaxation and MetastabilityLattice Relaxation and Metastability

Density functional calculations (DFT) of E′ center ’charging & puckering’

-10 -5 0 5 10Reaction Coordinates [a.u.]

-0.4

-0.2

0

0.2

0.4

Tot

al E

nerg

y [e

V]

Positive

Neutral

Silicon

Oxygen

20/37

Detailed Defect Model RequiredDetailed Defect Model Required

Substratewith

ExchangeCharge

1 2

RelaxationStructural

NeutralStable

2’

PositiveMetastable

1’

NeutralMetastable

RelaxationStructural

Substratewith

ExchangeCharge

PositiveStable

+

+

21/37

ModelModel

Different adiabatic potentials for the neutral and positive defect

Metastable states 2’ and 1’ are secondary minimaThermal transitions to ground states 1 and 2

Stochastic Markov-model for defect kinetics based on multiphonon theory

-4 0 4 8 12Reaction Coordinates [a.u.]

-1

-0.5

0

0.5

1

1.5

2

2.5

Latti

ce +

Ele

ctro

nic

Ene

rgy

- E

V [

eV]

1

2’

2 1

Stress

EV

EC

1’

+

+

22/37

Qualitative Model EvaluationQualitative Model Evaluation

Normal random telegraph noise (RTN)Very similar energetical position of the minimas 1 and 2

0

1

f 2 (+

)

0

1

f 1’ (

Neu

tral

)

1 2 3 4Time [s]

0

1

f 1 (N

eutr

al)

-1 0 1 2 3 4 5 6 7 8 9Reaction Coordinates [a.u.]

0

0.5

1

1.5

2

Latti

ce +

Ele

ctro

nic

Ene

rgy

- E

V [

eV]

❏1❏2’

❏2❏1’

Kirton and Uren, Adv. Phys. ’89

23/37


Anomalous RTNVery similar energetical position of the three minima 1, 2, and 1’

0

1

f 2 (+

)

0

1

f 1’ (

Neu

tral

)

0 10 20 30 40 50 60Time [s]

0

1

f 1 (N

eutr

al)


0

0.5

1

1.5

2

Latti

ce +

Ele

ctro

nic

Ene

rgy

- E

V [

eV]

❏1❏2’

❏2 ❏1’

Uren et al., PRB ’88

24/37


Temporary random telegraph noise (tRTN)Very similar energetical position of the minima 2 and 1’

0

1

f 2 (+

)

0

1

f 1’ (

Neu

tral

)

0 1 2 3 4Relaxation Time [s]

0

1

f 1 (N

eutr

al)


-1

-0.5

0

0.5

1

1.5

2

Latti

ce +

Ele

ctro

nic

Ene

rgy

- E

V [

eV]

❏1

❏2’

❏2 ❏1’

❏1Stress tRTN Relax

25/37

Quantitative Model EvaluationQuantitative Model Evaluation

Excellent agreement for both capture and emission time constantsCapture time: particularly important for back-extrapolation of stress data

Emission time: determines recovery behavior

Does the defect act like a switching trap?Depends on the defect configuration

0 0.5 1 1.5 2 2.5 -VG [V]

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102 τc @125

oC

τc @175oC

τe @125oC

τe @175oC

fp @125oC

fp @125oC

Defect #1

0 0.5 1 1.5 2 2.5 -VG [V]

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102 τc @125

oC

τc @175oC

τe @125oC

τe @175oC

fp @125oC

fp @125oC

Defect #4

26/37

How to Model This with SPICE?

Ck1

Ld

V0

Va

1

Re

C2

Ck2

T

LR2

R1C

27/37

Compact ModelingCompact Modeling

First attempt: approximate multi-state model by two-state model[1] [2]

Try to capture the notoriously difficult dynamics first

Effective capture and emission time constants

Differential equation for a two-state modelCorresponds to an RC equivalent circuit

Two branches: charging vs. discharging



28/37


Example: modeling of recovery[1]

Crude approximation: 1 RC element every 3 decades


29/37


Example: modeling of recovery[1]

Finer approximation: 2 RC elements every 3 decades


30/37


Extraction of the time constants[1]


31/37


Application examples[1]


32/37


Notorious: duty factor dependence[1] [2] [3]


[2]Grasser et al., IRPS Tutorial ’08


33/37

Why Would We Care?

34/37

Why Would We Care?Why Would We Care?

Defects determine the lifetime of the device

Statistics of individual defects become important in nanoscale MOSFETsRandom number of traps

Random distribution of traps in space

Random defect properties

Interaction with random discrete dopants

Discrete stochastic charge capture and emission events

Fundamental implications on device reliabilityLifetime is a stochastic quantity

Lifetime will have a huge variance

35/37

How to Determine the Lifetime?How to Determine the Lifetime?

Small area devices: lifetime is a stochastic quantity [1] [2]

Charge capture/emission stochastic events

Capture and emission times distributed

Number of defects follow Poisson distribution

For details see Grasser et al. IEDM ’10

[1]Kaczer et al. IRPS ’09

[2]Grasser et al. IEDM ’10

36/37

ConclusionsConclusions

NBTI/PBTI is a challenging problem to understand and model

Dynamics are of utmost importanceFor example: DC vs. AC stress, duty factor dependence, bias dependence, etc.

What happens in a circuit?

Cannot be captured by existing models

Measurement method: time dependent defect spectroscopy (TDDS)Operates on nanoscale MOSFETs with a handful of defects

Allows extraction of τe, τc, and step-height over very wide range

Allows simultaneous analysis of multiple defects

New defect modelMetastable defect states, nonradiative multiphonon theory, stochastic behavior

First attempts towards compact modelingEquivalent RC circuits which deliver ∆Vth

Can capture the main features, e.g. DC vs. AC

Lifetime becomes a stochastic quantity

37/37

This work would have been impossible without the support of ...This work would have been impossible without the support of ...

The Institute for MicroelectronicsE. Langer, S. Selberherr, ...

My Ph.D. students W. Gos, Ph. Hehenberger, F. Schanovsky, and P.-J. Wagner

B. Kaczer and G. Groeseneken (IMEC)

Longstanding collaboration, tons of measurement data, discussion/theory

M. Nelhiebel, Th. Aichinger, J. Fugger, and O. Haberlen (Infineon Villach)Financial support, measurement data, and discussion

R. Minixhofer and H. Enichlmair (austriamicrosystems)Financial support, measurement data, and discussion

H. Reisinger, C. Schlunder, and W. Gustin (Infineon Munich)

Ultra fast measurement data, discussion/theory

‘Reliability community’P. Lenahan, J. Campbell, G. Bersuker, V. Huard, N. Mielke, A.T. Krishnan, ...

Funding byEU FP7 contract n◦216436 (ATHENIS), ENIAC project n◦820379 (MODERN), CDG

recent developments in device reliability modeling: the

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