modeling of hot-carrier degradation: physics and ... · employment of ldd structures v ds is scaled...
TRANSCRIPT
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Institute for Microelectronics
Vienna University of Technology
http://www.iue.tuwien.ac.at
Modeling of Hot-carrier Degradation: Physics and Controversial Issues
S.E. Tyaginov
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Acknowledgement
This work would not have been possible without the support of:
My Colleagues at TU Wien:
I. Starkov, O. Triebl, D. Osintsev, M. Bina, and T. Grasser
Industrial Partners From AMS:
H. Enichlmair, J.M. Park, and R. Minixhofer
RWTH Aachen
Prof. Ch. Jungemann
Colleagues from IMEC:
J. Franco and B. Kazcer
Colleagues from the Ioffe Institute, Russia
M.I. Vexler and I.V. Grekhov
ISEN-IM2NP
Prof. A. Bravaix
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Outline
Hot-carrier degradation: what is it?
Main peculiarities
Physical picture behind hot-carrier degradation
Physics-based modeling of HCD
The modeling paradigm which integrates:
Carrier transport
Microscopic mechanisms of defect creation
Modeling of degraded devices
Controversial/open issues
Conclusions
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HCD Basics: Definition
Hot-carrier degradation (HCD)
Build-up of defects
At/near the Si/SiO2 interface
Field acceleration → gained sufficiently high energy → “hot” carriers
Interface states → density Nit
Nit is a distributed quantity
Varies with the coordinate along the interface
And in energy
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HCD Basics: Nit
Interface states
Can capture electrons/holes
Become charged
Perturbs the electrostatics
Result in a threshold voltage shift ΔVth
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HCD Basics: Nit
Interface states
Act as additional scattering centers
Thereby degrading:
Mobility
Transconductance ΔGm
Linear drain current ΔIdlin
etc
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HCD Basics: What about Not?
Oxide traps with the density Not: contribute?
Trapping/detrapping in the oxide bulk:
Plays a crucial role in BTI
BTI and HCD: similar microscopic origin
Therefore, bulk oxide traps are expected in HCD
Responsible for
SILC
And for TDDB
T. Grasser et al., TED, 2011
D. Varghese et al., EDL, 2005
H. Park et al., IIRW, 2008
R. O’Connor et al., IRPS, 2008
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HCD Basics: What about Not?
Turn-around effects in HCD:
These effects are due to the partial compensation of the:
Charge stored in oxide traps
By interface state trapped charge
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HCD Basics: What is the Driving Force?
Field-driven paradigm
Lucky Electron Model
The main assumptions is that the “lucky-electron”:
Has energy enough to overcome the barrier
Impinges the interface without collisions
And without being scattered back
This energy is gained by the electric field:
φit – the potential barrier
λ – the electron free path
Em is the maximum electric field
C. Hu et al., TED, 1985
n
Eqdit
miteW
ItCN
/
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HCD Basics: What is the Driving Force?
Measures to suppress HCD In 80s device linear dimensions were reduced rather quickly
Accompanied by a slower supply voltage scaling
Result:
High electric fields
And severe hot-carrier degradation
Strategies:
Supply voltage has to reduce faster vs. device dimensions
Constant field scaling
Introduction of LDD structures
T-.Y. Huang et al., IEDM, 1985
T. Hori et al., TED, 1992
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HCD Basics: What is the Driving Force?
Energy deposited by carriers is the driving force
The IBM group investigated:
Fowler-Nordheim, direct tunneling stresses
Substrate hot-electron/hole stresses
Channel hot-electron/hole stresses
Interface state generation probability
Depends only on the carrier energy
Not on the field
Insensitive to stress mechanisms
Energy deposited by carriers
drives degradation
D.J. DiMaria, S.W. Stasiak, JAP, 1989
D.J. DiMaria, J.H. Stathis. JAP, 2001
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HCD Basics: What is the Driving Force?
Possible driving forces
Electric field, carrier average energy
Are distributed quantities
With a maximum close to the drain end of the gate
Hints that HCD is a strongly localized phenomenon
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Outline
Hot-carrier degradation: what is it?
Main peculiarities
Physical picture behind hot-carrier degradation
Physics-based modeling of HCD
The modeling paradigm which integrates:
Carrier transport
Microscopic mechanisms of defect creation
Modeling of degraded devices
Controversial/open issues
Conclusions
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Main Peculiarities: Localization
Strong localization of HCD
Interface state density lateral profile Nit(x)
Extracted from charge-pumping (CP) data
For two different oxide thicknesses
Nit(x) profiles feature peaks
Near the electric field maximum
M.G. Ancona et al., TED 1988
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Main Peculiarities: Carrier Ensemble
Carrier ensemble, not a solitary carrier
Si-H bond-breakage is a stochastic process
Carrier with a certain energy → certain probability to break a bond
Carrier packet has substantially different energies
Each carrier/energy → a certain contribution to HCD
Evolution of the ensemble along the interface
Macroscopic quantity which
Describes the cumulative ability
to rupture Si-H bonds
Different quantities used as driving force:
Different lateral distributions
Different Nit profiles
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Main Peculiarities: From Hot to Cold Carriers
HCD suppression by a proper supply voltage scaling?
Device dimensions were reduced rather quickly
Slower scaling of power supply
High electric field in the MOSFET channel
Carrier acceleration → high energy → Si-H bond rupture by solitary carrier
Measures to suppress carrier heating:
Fast scaling of power supply
Employment of LDD structures
Vds is scaled down to 1.0-1.5 V
Threshold energy for Si-H dissociation: 3.0-3.5 eV
Halt of degradation? NO!
K. Hess et al., Circ. Dev. Mag., 2001
A. Bravaix et al., IRPS-2009
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Main Peculiarities: From Hot to Cold Carriers
Energy exchange mechanisms Populating high energy fraction of the ensemble
Impact ionization
Auger recombination
Electron-phonon scattering
Electron-electron scattering
Is of special importance in
Ultra-scaled devices
K. Hess et al., Circ. Dev. Mag., 2001 A. Bravaix et al., IRPS-2009
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Main Peculiarities: From Hot to Cold Carriers
Si-H bond-breakage mechanisms
Ultra-scaled devices Electron-electron scattering
Change of the dominant dissociation mechanism:
Single-particle (SP) → multiple-particle (MP) process
Long-channel/high-voltage devices
Carriers are rather hot
Bond rupture in a single collision
SP-process
Scaled devices
Several “colder” particles → subsequently bombard a bond
Bond excitation → rupture
MP-process
Interplay between SP- and MP-mechanisms
Change of the HCD worst-case conditions
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Main Peculiarities: Worst-Case Conditions
Long-channel/high-voltage n-MOSFET Corresponds to the maximal substrate current Isub
Maximal impact ionization rate
Vgs = (0.4-0.5)Vds
Long-channel/high-voltage p-MOSFET Worst-case conditions (WCC) ↔ the maximum gate current Ig
Empirical link between the voltages is not established
Scaled devices: A single carrier is unlikely to trigger an SP-process
Carriers contributing to the MP-mechanism:
Require only a low energy
A large number of carriers
Carrier flux rather than the single-carrier energy becomes important
WCC ↔ Vds = Vgs
For both scaled n- and p-MOSFETs
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Main Peculiarities: Temperature Behevior
HCD becomes less pronounced at elevated temperatures Contrary to BTI
An n-MOSFET was stressed at WCC
Threshold voltage shift due to HC stress
∆Vth(t) is less pronounced at higher T
This traditional tendency is typical only for long-channel devices
Ultra-scaled MOSFETs HCD becomes more significant at higher T
Dominant role of electron-electron scattering
Impacts the carrier ensemble
F.-C. Hsu and K.-Y. Chu, EDL,1984.
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Main Peculiarities: Conclusions
Important: how carriers are distributed over energy
In a particular point in the device
By the carrier energy distribution function (DF)
Interplay between hotter and colder carriers
Interplay between SP- and MP-mechanisms
Strong localization of HCD ↔ driving force ↔ carrier transport
Temperature behavior ↔ scattering mechanisms ↔ carrier transport
Carrier transport
Intimately related to hot-carrier degradation
It is an essential fragment of the whole physical picture
↔ carrier transport
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Outline
Hot-carrier degradation: what is it?
Main peculiarities
Physical picture behind hot-carrier degradation
Physics-based modeling of HCD
The modeling paradigm which integrates:
Carrier transport
Microscopic mechanisms of defect creation
Modeling of degraded devices
Controversial/open issues
Conclusions
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Physical Picture: Carrier Transport
The carrier ensemble moved from the source to drain
Carriers are being accelerated by the electric field
Experience scattering events
Evolution of the carrier ensemble
The ensemble is described
By the energy distribution function
Probability to find a particle within [E; E+dE]
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Physical Picture: Carrier Transport
The evolution of the DF with the coordinate x
Source: carriers in equilibrium → Maxwellian distribution
Drain end of the gate: the carrier distribution is severely non-Maxwellian
Near the Nit peak: high-energy tails, plateau
Drain: again Maxwellian
5V n-MOSFET
standard 0.35 μm process
channel length: 0.5μm
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Physical Picture: Carrier Transport
Main scattering mechanisms in MOSFETs
Electron-phonon scattering
Scattering at ionized impurities
Impact ionization
Surface scattering
Auger recombination
Electron-electron scattering
In degraded devices: scattering on charged interface states
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Physical Picture: Carrier Transport
Carrier ensemble
Gains energy from the electric field
Loses and intermixes energy
Due to scattering
High-energetical fraction is depopulated
High-energy tail of the DF is distorted
Temperature behavior of HCD
Elevated temperatures
Scattering mechanisms are reinforced
High-energy tails of the DF is suppressed
“Hot” carriers are “frozen out”
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Physical Picture: Vague Issues [not really]
We focused on the high-energetical fraction
How to distinguish between “hot” and “colder” carriers?
Why are we primarily interested in hot carriers?
Why is HCD observed even in ultra-scaled devices?
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Physical Picture: Hydrogen in MOSFETs
Hydrogen is intentionally incorporated into CMOS devices
Si/SiO2 interface is non-regular
Dangling bonds
Pb centers
The electrostatics are disturbed
The mobility is reduced
Remedy: post-grow anneal
Hydrogen passivates dangling bonds
C.R. Helms, H.E. Poindexter, Rep. Prog. Phys, 1994
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Physical Picture: Si-H Bonds
Si-H bond dissociation
Leads to electrically active centers
Contribute into HCD and (N/P)BTI
Si-H bond energetics are important
Ab initio calculations using density functional theory
Si-H dissociation reaction pathway:
Bonded hydrogen → transport state
Potential barrier: ~2eV
Portion of energy delivered to H: 2eV
High-energetical fraction of the ensemble
With energies above 2eV
To trigger the Si-H bond dissociation
Hot carriers!
K. Hess et al, Physica E 3, 1998
B. Tuttle and Ch.G. Van de Walle, PRB, 1999
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Physical Picture: Si-H Bonds
Disparity: electron mass and the mass of the H nucleus
Difference ~1000 times
Total moment conservation
Direct bombardment: negligible portion of energy transferred
Bond dissociation is unlikely
Most probable pathway
Excitation of one of the bonding electrons to an antibonding state
A repulsive force acting on the H atom is induced
Followed by H release
K. Hess et al., Physica E 3, 1998
W. McMahon et al., Int. Conf. Mod. Sim. Micro, 2002
W. McMahon et al., IEEE Trans. Nanotech., 2003
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Physical Picture: HCD in Scaled Devices
Is there any HCD?
The supply voltage in scaled devices is 1.0-1.5 V
Carriers with energies above the threshold for Si-H dissociation?
Unlikely!
Isn’t HCD still a concern?
Pioneering paper by Mizuno et al
Lch = 0.12μm
Stressed at WCC
Vds = 1.5V, Vgs = 0.7V
Severe linear drain current degradation
T. Mizuno et al., IEDM, 1992
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Physical Picture: HCD in Scaled Devices
Factors responsible for HCD in scaled devices:
Energy exchange mechanisms
Populating high energy fraction of the ensemble
Single-particle process of Si-H bond dissociation
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Physical Picture: Scattering Mechanisms
Impact ionization induced high-energy tails
Gate currents Ig is measure of high-energy tails
n-MOSFET (0.1μm process) → investigated using a Monte-Carlo simulator
Mechanism responsible for Ig:
Impact ionization feedback through
The vertical fields of the drain-substrate junction
High-energy tails of the DF: pronounced
J.D. Bude, VLSI Techn. Dig, 1995
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Physical Picture: Scattering Mechanisms
The role of Auger recombination
n-MOSFETs: Lch = 0.3μm, dox = 40nm → tunneling is suppressed
Stressed: at Vds = 1.4-1.6V and T = 77, 300 K
Gate current Ig and the threshold voltage shift ΔVth
Ig is a criterion of hot-carriers
And carriers are hot
Physical mechanism
Vds ≥1.4 V → II contributes
Drain concentrations:
n = 1020 cm-3, p = 5·1014 cm-3
Recombination cannot be neglected
Auger recombination:
Two recombining carriers give their energy electron
Because n >> p
B. Ricco et al., IEDM, 1984
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Physical Picture: Scattering Mechanisms
Electron-phonon interactions
Electrons can gain energy from phonons if
Number of absorbed phonons exceeds
Number of emitted phonons
DF expands beyond |e|Vds
This scenario was supported
By Monte-Carlo simulations
For an n-MOSFET, Leff = 0.1 μm
A. Abramo et al., IEDM, 1995
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Physical Picture: Scattering Mechanisms
Electron-electron scattering (EES)
Is of special interest in nano-scale devices
1D Boltzmann transport equation with EES is included
Energies available from the electric field: |e|Vds
Calculated DFs for Vds = 0.5, 1.0, 1.5V
With and w/o EES
EES dramatically changes
the shape of the DF
DF propagates deeper than |e|Vds
P.A. Childs, C.C.C. Leung, JAP, 1996
M. Fischetti, S.E. Laux, IEDM, 1995, A. Ghetti et al, IEDM, 1998
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Physical Picture: Multivibrational Excitation
Multivibrational excitation (MVE)
First success of the concept
H/D desorption
Bombardment by electrons
Tunneling from STM tip
D-passivated surfaces: more resistant
Difference in depassivation rates: 2 orders
Giant isotope effect
B.N.J. Persson, Ph. Avouris, Surf. Sci.,1997
J.W. Lyding et al., Appl. Surf. Sci., 1998
K. Stokbro et al., PRL, 1998
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38
Physical Picture: Multivibrational Excitation
Si-H bond
Treated as a truncated harmonic oscillator
Eigenstates in the quantum well
Dissociation:
H hopping: last bonded → transport state
Vice versa = passivation
Electron flux
Phonon absorbtion → bond heating
With the rate Pu
Desorption → MVE decay
With the rate Pd
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39
Physical Picture: Multivibrational Excitation
Explanation of the giant isotope effect
Biswas and collaborators simulated vibrational excitations
Using tight-binding molecular dynamics
Two types of vibrational modes:
Stretch mode
Very stable for both Si-H and Si-D
Up to 0.8 ns
Bending mode
Si-H: no decay within 0.8 ps
Si-D: bending mode
Dumps down within 1-2 oscillations
Si/SiO2 interfaces:
H emission via bend-bending distortion
Giant isotope effect is explained
R. Biswas et al., PRB 1998 R. Biswas et al., APL, 1998
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40
Outline
Hot-carrier degradation: what is it?
Main peculiarities
Physical picture behind hot-carrier degradation
Physics-based modeling of HCD
The modeling paradigm which integrates:
Carrier transport
Microscopic mechanisms of defect creation
Modeling of degraded devices
Controversial/open issues
Conclusions
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41
Physics-Based Models: Hess Model
The main breakthrough of the Hess model
Introduction of two competing mechanisms
SP- and MP-processes
Dominating HCD in
Long-channel/HV devices (SP-process)
Scaled devices (MP-process)
Related to
“Hot” (SP-process)
And “colder” carriers (MP-process)
HCD is controlled by the carrier distribution function
Or by another quantity derived from the DF
The carrier acceleration integral (AI)
K. Hess et al., Physica E, 1998
W. McMahon et al., Int. Conf. Mod. Sim. Micro, 2002
W. McMahon et al., IEEE Trans. Nanotech., 2003
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42
Physics-Based Models: Hess Model
The acceleration integral Desorption rate via: the bonding electron → antibonding state
F(E) is the carrier impact frequency
Per unit area
Per unit energy
σ(E) is the scattering cross section
P(E) is the probability of the desorption
Eth is the threshold energy for scattering
Flux F(E):
F(E) = f(E)g(E)v(E)
f(E) is the carrier DF, g(E) the DOS, v(E) the carrier velocity
K. Hess et al., Physica E, 1998 W. McMahon et al., Int. Conf. Mod. Sim. Micro, 2002
dEEPEEFIEth
e )()()(
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43
Hess Model: Multivibrational Mode Concept
The MP-process The Si-H bond is treated as
Truncated harmonic oscillator
1/we – phonon life-time
– distance between the levels
Occupation number: Bose-Einstein
Phonon absorbtion = bond heating (Pu)
Desorption = multivibrational mode decay (Pd)
/
)/exp(exp1
BE
LBed
eu
LB
dB
MPTkwP
wP
TkP
ER
K. Hess et al., Physica E, 1998
dEEfEEFP
dEEfEEFP
phemi
Eth
u
phab
Eth
d
1)()(~
1)()(~
The MP-process rate:
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44
Physics-Based Models: Hess Model
Contribution of all levels
Not only SP- and MP-mechanisms
SP-process: excitation from the ground state
MP-process: from the last bonded state
Rate equations are simplified
Linked to the drain current Id
B.N.J. Persson, Ph. Avouris, Surf. Sci., 1997
W. McMahon et al., Int. Conf. Mod. Sim. Micro, 2002
edd
LBedu
wdEIP
TkwdEIP
)/exp(
lN
i
dd
i
i
evd
evd
fIAwfI
kTwfI
R0
exp
defines the population
of the i-th level
H hopping
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45
Physics-Based Models: Hess Model
Activation energy Ea for the Si-H bond-breakage
Statistically distributed
This is supported by ab initio calculations (DFT)
Dispersion of Ea → different power-law slopes:
21 )/(1)/(1~
2
2
1
1
t
p
t
pNit
2
2/1,
2/1,2/1,
2/1,
2/1,2/1,
2/1,
exp1
exp1
a
aam
a
aam
a
it
EE
EE
N
Two distributions with different:
Mean values Ea,1/2
Standard deviations σa,1/2
experimentally observed
K. Hess et al., Physica E 3, 1998;B. B.
Tuttle, PRB, 1999
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46
Physics-Based Models: Hess Model
H or D annealing of the dangling bonds?
Multivibrational mode concept
Giant isotope effect
MOSFETs with the Si/SiO2 interface passivated
By hydrogen
By deuterium
Subjected to hot-carrier stress
Devices with D-annealed interface
Demonstrate improved robustness
E.g. the transconductance degrades less
J.W. Lyding et al., APL, 1996
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47
Physics-Based Models: Hess Model
Advantages
A lot of pioneering concepts
Shortcomings Interface traps: microscopic level
Unconnected to the device level
Device life-time:
Time when Nit = Nit,critical
Degradation of such parameters as Gm, Idlin, etc:
Not really addressed
Necessity of the DF evaluation is acknowledged
But not incorporated into the approach
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48
Physics-Based Models: Penzin Model
Adaptation of the Hess model for TCAD simulators Phenomenological simplification
Microscopic level is sacrificed
The bond rupture → described by kinetic equation:
Ea depends on: Hydrogen density
Transversal F┴ component of the electric field
The vicinity of the interface → capacitor
Released H and dangling bonds = charges → electric field
Prevents hydrogen ions from leaving the system
HC
HCHCH
HLBa
Ik
kTkEkk
nNkndt
dn
1
)/exp(
)(
0
0
n –concentration of passivated bonds
N0 – total bond concentration
k, γ – forward, backward reaction rate
k0 – attempt rate
kH – hot-carrier acceleration factor
IHC – local hot-carrier current (?)
δHC, ρHC – fitting parameters
F
nN
nNTkFEE LBaa
1
ln)0(
0
00
O. Penzin et al., TED, 2003
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49
Physics-Based Models: Penzin Model
Activation energy dispersion
Captured by the model
Represents sublinear slope
Shortcomings
Carrier transport (?)
The hot-carrier acceleration factor (?)
“Local hot-carrier current”(?)
Criterion to distinguish “hot” and “cold” carriers
Based on the DF
Information about the Nit profile is hardly achievable
Kinetics of the trap generation and the device characteristics:
Are linked?
Rigorous comparison experimental/simulated device characteristics?
O. Penzin et al., TED, 2003
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50
Physics-Based Models: Reaction-Diffusion (RD)
NBTI and HCD are related to Si-H bond-breakage
Differing only in the driving force
HCD + NBTI → united within RD
HCD, NBTI: diffusion-limited
Some of experimental observations:
NBTI: ~ t1/4
HCD: ~ t1/2
NBTI is a 1D problem
HCD is a 2D phenomenon
non-uniform Nit(x)
2/1)(
4/1)(
)(
0
)0(2/1)0()(
2/1
)(
0
)0(2/1)0()(
)(~
)(~
)()12/()/(1)2/(
)()2/1()/(1)/1(
2/1
2/1
tDN
tDN
tDNArdrtDrNAN
tDNdrAtDrNAN
H
HCD
it
H
NBTI
it
H
tD
HdHHd
HCD
it
H
tD
HdHHd
NBTI
it
H
H
H. Kufluoglu and M. Alam, Journ. Comput. Electron., 2004.
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51
Physics-Based Models: Reaction-Diffusion
NBTI, HCD: diffusion limited
Stress is removed → recovery occurs rather quickly
NBTI: reaction limited
HCD: the recovery is rather weak
if there is any recovery at all
Model does not rely on carrier transport
Driving force behind the trap generation?
Nit distribution?
Localized nature of the damage
Not addressed
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52
Physics-Based Models: Energy-Driven Paradigm
Electron-electron scattering
Of special interest in scaled MOSFETs
Supply voltage: very low
SP- mechanism is suppressed
EES populates the high-energy tail
Hump in the carrier DF
SP-contribution is increased
EES defines the temperature behavior
Acceleration of HCD at elevated temperatures
In extremely-scaled MOSFETs
P.A. Childs, C.C.C. Leung, JAP, 1996
S.E. Rauch and G. LaRosa, TDMR, 2001
S.E. Rauch et al., EDL, 1998
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53
Physics-Based Models: Energy-Driven Paradigm
Driving force of HCD is the energy deposited by carriers
Not the maximal electric field
Beyond the 180 nm node
II rate/ Nit creation rate:
f(E) is a strongly decaying function
S(E) grows as a power-law
Trade-off results in:
Maximum at a certain energy
“Knee” energy
Weak function of Vds
dEESEf )()(f(E) – carrier DF
S(E) – reaction cross section
S.E. Rauch et al., EDL,1998
S.E. Rauch et al., TDMR, 2001
S.E. Rauch, G. LaRosa, IRPS, 2005
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54
Physics-Based Models: Energy-Driven Paradigm
Main advantages
Substantially simplifies modeling of HCD
Time-consuming calculations of the DF → Avoided!
Empirical parameter
Disadvantages
Maximum is not necessarily narrow
Width: 1.5 - 2 eV
Dominant energy?
The concept does not deal with Nit as a distributed quantity
Strong localization of HCD → not captured
Similar to the Hess approach:
Life-time: interface state generation rate
ΔGm, ΔIdlin → critical value
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55
Physics-Based Models: Bravaix Model
Main features from the Hess and the Rauch/LaRosa models
Interplay between SP- and MP-mechanisms
Idea: damage is defined by the carrier DF
Calculations of the DF → condition-related empirical factors
Rates in the Hess model
In the Bravaix model:
SMP is a fitting factor
Representing the reaction cross section
edd
LBedu
wdEIP
TkwdEIP
)/exp(
edMPd
LBedMPu
weISP
TkweISP
)/(
)/exp()/(
A. Bravaix et al., IRPS, 2009 C. Guerin et al., APL, 2009
)/( eISdEI dMPd
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56
Physics-Based Models: Bravaix Model
MP-process
Si-H → truncated harmonic oscillator
System of rate equations:
Finally: AI → empirical factor
The simplified solution for the MP-process:
Square root time dependence
edMPd
LBedMPu
weISP
TkweISP
)/(
)/exp()/( 2
1
11
010
)()(
-
MPpassNemiNdNu
N
iiuiidi
ud
NPnnPnPdt
dn
nnPnnPdt
dn
nPnPdt
dn
lll
l
tPPNtN lN
duemiMP /)( 0
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57
Physics-Based Models: Bravaix Model
Low Id regime High carrier energies
“Hot-carrier” regime
SP-mechanism plays the dominant role:
High electron flux
Low carrier energies
MP-process dominates
Intermediate case
Moderate Id and Vds
Governed by electron-electron scattering:
Real device stress/operation conditions → all the modes are present
KMP, KEES, KSP – prefactors
/2/1
/2/1
)]/([
)/exp()]/()[(~/1
B
B
E
dds
LBemi
E
sdsMP
WIV
TkEWIV
mdbdSPSPSP IIWICR //~/1
mdbdEESEESEES IIWICR //~/12
MPMPEESEESSPSPd KKK ///~/1
C. Guerin et al., IRPS, 2007
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58
Physics-Based Models: Bravaix Model
The fitting scheme for the SP-process rate
Used to better fit the CP data
Knee energy
From Rauch and LaRosa paradigm
No carrier transport sub-task
DF is substituted by empirical factors
Nit: agreement is good
eVEES
eVEES
eVEconstS
eVES
SP
SP
SP
SP
5.2,)5.1(
5.25.1),3exp(
9.15.1,
5.1,0
11
R.M. Randrimihaja et al., Microel. Reliab., 2012
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59
Physics-Based Models: Bravaix Model
Advantages
The microscopic and device levels are connected
Shortcomings
Simplified treatment of carrier transport
DF→ empirical factors
Electron-electron scattering cannot be treated as a separated mode because
It affects the carrier DF
Defines interplay between SP- and MP-processes
Final parameterization is
Based on fitting parameters
Not on physical mechanisms
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60
Outline
Hot-carrier degradation: what is it?
Main peculiarities
Physical picture behind hot-carrier degradation
Physics-based modeling of HCD
The modeling paradigm which integrates:
Carrier transport
Microscopic mechanisms of defect creation
Modeling of degraded devices
Controversial/open issues
Conclusions
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61
Our Model: Structure
The model
Features of previous approaches
Linking all the levels related to this effect
A physics-based model contains
Carrier transport module
Module describing the defect build-up
Module for simulation degraded devices
Carrier transport
Full-band Monte-Carlo simulator MONJU
Allows to thoroughly evaluate the DF
For a particular device architecture
Ch. Jungemann, B. Meinerzhagen, Hierarchical Device Simulation, Springer Verlag, 2003
MiniMOS-NT, Device and Circuit Simulator, Institute for Microelectronics, TU Wien
GTS Framework, Global TCAD Solutions, Vienna, Austria
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62
Our Model: Comprehensive?
Considers only the electron contribution Calibrated for 5V n-MOSFET (0.35 μm node), Lch = 0.5 μm
Successfully represented Idlin degradation
Further verification
Should properly describe HCD for different channel lengths
We used identical device architecture
Differing in channel lengths: Lch = 0.5, 1.2 and 2.0 μm
Stress conditions: Vgs = 2.0V
Vds = 6.25V
T = 250C
Calibration: to represent the Idlin degradation
S. Tyaginov et al., IPFA, 2010
S. Tyaginov et al., SISPAD, 2011
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63
Our Model: Comprehensive?
The first version of our model fails
While trying to capture Idlin degradation in different MOSFETs
ΔIdlin = (Idlin0 – Idlin(t))/Idlin0
Lch = 1.2, 2.0 μm:
Theoretical ΔIdlin is less than experimental
Nit by electrons: peaks outside the channel
Average interface trap density: <Nit>
Stronger degradation ↔ less <Nit>
Longer devices: less sensitive to electron-induced Nit
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64
Our Model: Missing Contribution
Mechanism generating interface states closer to the channel
Secondary generated holes
By impact ionization
Accelerated by the electric field
Interface states shifted to the source
The same Nit stronger affecting the device performance
Holes should be considered
S. Tyaginov et al., SISPAD, 2011
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65
Our Model: Electrons and Holes
Superposition of electron and hole AIs
Monte-Carlo simulator → DFs for electrons and holes
DFs → the carrier acceleration integral
The same functional structure for:
SP- and MP-processes and for electrons and holes
SP-process
First order kinetics
MP-process
Truncated harmonic oscillator
tII
SPhSPhSPeSPeSPeNtN ,,,,1)( 0
2/1
0 1)(
t
N
d
u
pass
emiMP
emi
l
eP
P
PNtN
thE
dEEEvEgEfI )()()()(
ehMPeMPd
LBehMPeMPu
wIIP
TkwIIP
,,
,, )/exp(
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66
Our Model: Verification and Results
Secondary holes
Generated by impact ionization
Due to the hot-electron injection
Holes are accelerated by the electric field
Towards the source
The hole AI is considerably shifted
towards the source
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67
Our Model: Verification and Results
Model represents degradation
For different channel lengths
With the same set of parameters
For Lch = 0.5:
Hole contribution may be neglected
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68
Outline
Hot-carrier degradation: what is it?
Main peculiarities
Physical picture behind hot-carrier degradation
Physics-based modeling of HCD
The modeling paradigm which integrates:
Carrier transport
Microscopic mechanisms of defect creation
Modeling of degraded devices
Controversial/open issues
Conclusions
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Our Model: Verification and Results
The driving force of HCD
Nit(x) profiles feature two peaks
In good agreement with the results of our HCD model
Peaks: by primary channel electrons and secondary generated holes
Correspond to the maxima of electron and hole acceleration integrals
S. Tyaginov et al., SISPAD, 2011 I. Starkov et al., IRPS, 2012
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Open Issues: Pro Not
Do bulk oxide traps contribute?
Arguments pro: Threshold voltage turn-around effect
Hot-carrier stress at WCC
The threshold voltage Vth was monitored up to 105s
First Vth decreases
Due to h+ trapping in the oxide bulk
After 10ks Vth increases
Due to trapping of e- by interface traps
At ~100 ks: compensation
Supported by Nit(x) and Not(x) profiles
Extracted from CP data
I. Starkov et al., IRPS, 2012
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Open Issues: Pro Not
Charge-pumping signal: no saturation plateau
Only interface traps
ICP vs. Vgh (varying high-level technique)
saturates, thereby demonstrating a plateau
This tendency is not pronounced
CP current continues to increase
Contribution of bulk oxide traps
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Open Issues: Pro Not
Turn-around effect of Idlin
p-DEMOS, 0.35 design
Stressed at Vds = -23V, Vgs = -12V
Short stress times:
Electrons stored in bulk oxide traps
In the Lp region
|Idlin| increases
Long stress times:
Holes trapped by interface states
In the Lov region
|Idlin| decreases
Result: turn-around effect
J.F. Chen et al., Jpn. JAP, 2009
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Open Issues: Contra Not
HCD demonstrates no (or weak) recovery
Switching oxide traps in BTI
Responsible for BTI recovery
By analogy
Oxide traps in HCD → Recovery should be pronounced
Only high-voltage devices (LDMOS, DEMOS) demonstrate recovery
Scaled CMOS transistors: No recovery
Contradictions → Reconciliation in further research
T. Grasser et al., TED, 2011 H. Park et al., IIRW, 2008 R. O’Connor et al., IRPS, 2008
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Conclusions part I: Experimental Facts
Due to generation of defects at or near the interface
Strongly localized
Temperature behavior
Long-channel devices: HCD is suppressed at elevated temperatures
Ultra-scaled devices: HCD becomes more severe at elevated temperatures
Contribution of bulk oxide traps
Results in turn-around effects
Charge-pumping current does not demonstrate a plateau
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Conclusions Part II: Complexity of HCD
Carrier transport
Scattering mechanisms
Carrier energy distribution: “cold” vs. “hot” carriers
Microscopic mechanisms of defect creation
Dissociation of Si-H bonds
Single- and multiple-carrier processes
Contributions of electrons and holes
Device level
Worst-case conditions of HCD
Their change with MOSFET downscaling
Degradation of device characteristics with time
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