Download Noise modeling at quantum level for multi

Noise Modeling at Quantum Level for MultiStack Gate Dielectric MOSFETs.
Zeynep Çelik-Butler
Industrial Liaisons: Ajit Shanware, Luigi Colombo, Keith
Green, TI; Hsing-Huang Tseng, SEMATECH, Ania
Zlotnicka, Freescale
Students:
Bigang Min, Siva Prasad Devireddy, Tanvir Morshed,
Shahriar Rahman
University of Texas at Arlington
P. O. BOX 19072
Arlington, TX 76019
UTA Noise and Reliability Laboratory
1
Outline

Noise Modeling



Experimental Verification



Unified Flicker Noise Model
Multi-Stack Unified Noise Model (MSUN)
Metal-Gated HfO2/SiO2 NMOSFETs – different interfacial layer processing
Poly-Gated HfSiON/SiON NMOSFETs – variable interfacial layer thickness
Conclusions and Future Work
UTA Noise and Reliability Laboratory
2
Unified Flicker Noise Model*






Based on correlated number and mobility fluctuations
theory.
Equi-energy tunneling process.
Traps in the gate dielectric trap/de-trap channel carriers
Trapping/de-trapping phenomenon causes fluctuations in
the carrier number.
Fluctuations in carrier mobility due to remote Coulomb
scattering from trapped charge.
Uniform distribution of traps in the gate dielectric with
respect to distance and energy level.
*K. K. Hung, P. K. Ko, C. Hu, Y. C. Cheng, “A unified model for the flicker noise in metal-oxide-semiconductor field-effect transistors,”
IEEE Trans. Electron Devices, vol. 37, pp.654-665, 1990.
UTA Noise and Reliability Laboratory
3
Physical Mechanism for Noise
z
L
x
W
y
SiO2
Tox
Traps
Source
Carriers
Drain
Substrate
K. K. Hung, P. K. Ko, C. Hu, Y. C. Cheng, “A unified model for the flicker noise
in metal-oxide-semiconductor field-effect transistors,”
IEEE Trans. Electron Devices, vol. 37, pp.654-665, 1990.
Channel carriers tunnel
back and forth from the
traps in the gate oxide
causing fluctuations in the
number of carriers. By
virtue of Coulomb
scattering from oxide
trapped charges there are
fluctuations in carrier
mobility that cause
additional noise in
correlation with the carrier
number fluctuations.
UTA Noise and Reliability Laboratory
4
Unified Flicker Noise Model Expressions
   0 exp(z )
SI 
d
kTI d2

1
  sc  eff ) 2 N t
fWL N
(
4
2m  
h
K. K. Hung, P. K. Ko, C. Hu, and Y. C. Cheng
IEEE Trans. Electron Devices, vol. 37, pp.654-665,1990
BSIM Low Frequency Noise Model
S Id
kTq 2 I d  eff 
 N0  N * 

  NOIB N  N   NOIC N 2  N 2

NOIA
log

0
L
0
L
 N  N* 
2
C ox f EF Leff 2 
 L






2
2
kTI d Lclm  NOIA  NOIB.N L  NOIC .N L 



EF
2
2
*
Wf Leff 

NL  N



UTA Noise and Reliability Laboratory
5
High-k Gate Stack Scenario
z
L
x
THK
W
y
High-k
Traps
y
x
TIL
z
Source
Carriers
Drain
Substrate
Channel carriers tunnel
into the traps in high-k
and interfacial layer
causing fluctuations in
carrier number and
mobility in a correlated
way.
Interfacial layer
The uniform dielectric trap density assumption does not hold.
The different trap profiles and various physical properties of highk/interfacial layer materials like physical thicknesses, barrier
heights etc. affect the 1/f noise.
UTA Noise and Reliability Laboratory
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Multi-Stack Unified Noise Model (MSUN)








Based on correlated number and mobility fluctuations theory
Equi-energy tunneling process
Traps in the gate dielectric layers trap/de-trap channel carriers
Trapping/de-trapping phenomenon causes fluctuations in the
carrier number
Fluctuations in carrier mobility due to remote Coulomb
scattering from trapped charge
Scalable with regards to the high-k/interfacial layer physical
thicknesses
Takes different dielectric material properties into account
Considers non-uniform distribution of traps in the highk/interfacial layer with respect to distance and energy level
UTA Noise and Reliability Laboratory
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Typical Band Diagram for High-k Stack
NtIL0
Carrier tunneling probability
into the gate dielectric is an
exponentially decaying
function with attenuation
rates corresponding to the
dielectric material.
NtIL0 – IL/Si interface trap
density at intrinsic Fermi
level
NtHK0 – HK/IL interface trap
density at intrinsic Fermi
   exp( 
level
0
Ec
exp(-γILz)
exp[-γHK(zTIL)]
Ei
Efn
Ev
THK
TIL
NtHK0
T   HK TIL ) exp(  HK z )
IL IL
   0 exp(  IL z )
UTA Noise and Reliability Laboratory
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Trap Density Profile in SiO2
Nt0 exp(ξ(Efn-Ei))
Nt0 exp(ξ(Efn-Ei))
=Nt(Efn)
Nt0
0
Ei
Nt(Efn) exp(ηz)
1.2
Nt0 is the trap density at the Si/SiO2 interface
and intrinsic Fermi level. Trap density
increases exponentially towards the band
edges at a rate defined by parameter ξ.
N tIL ( E fn , z)  N tIL0 exp[ IL ( E fn  Ei )  (qILVgIL TIL ) z   IL z]
Nt(Efn)
0
z
Nt(Efn) is the trap density at the Si/SiO2
interface and quasi-Fermi level. Trap density
increases exponentially into the gate
dielectric.
N tHK ( E fn , z)  N tHK0 exp[ HK ( E fn  Ei )  (qHKVgHK THK ) z   HK z]
Z. Çelik-Butler, and T. Y. Hsiang, “Spectral dependence of 1/fγ noise on gate bias in n-MOSFETs,” Solid State Electron., vol. 30, pp. 419–423, 1987.
UTA Noise and Reliability Laboratory
9
Modified Trap Profile by Energy Band Bending
NtIL0
The energy bands bend in both
high-k and interfacial layers
due to the applied gate
voltage. Higher trap density
towards the band edges means
that the trap profile
encountered by channel
carriers at a particular location
in the dielectric is altered due
to band bending. This effect is
reflected by the parameters λIL
and λHK.
Ec
Ei
Ef
Ev
High-K
N tIL ( E fn , z)  N tIL0 exp[ IL ( E fn  Ei )  (qILVgIL TIL ) z   IL z]
Interfacial
Layer
NtHK0
N tHK ( E fn , z)  N tHK0 exp[ HK ( E fn  Ei )  (qHKVgHK THK ) z   HK z]
Z. Çelik-Butler, and T. Y. Hsiang, “Spectral dependence of 1/fγ noise on gate bias in n-MOSFETs,” Solid State Electron., vol. 30, pp. 419–423, 1987.
UTA Noise and Reliability Laboratory
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Trap Density in High-k Stack
Trap density for (0<z<TIL)
N tIL ( E fn , z)  N tIL0 exp[ IL ( E fn  Ei )  (qILVgIL TIL ) z   IL z]
   0 exp(  IL z )
Trap density for (TIL<z<THK+TIL)
N tHK ( E fn , z)  N tHK0 exp[ HK ( E fn  Ei )  (qHKVgHK THK ) z   HK z]
   0 exp(  IL TIL   HK TIL ) exp(  HK z )
UTA Noise and Reliability Laboratory
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Total Noise
Power spectral density of the mean square fluctuations in the number
of occupied traps for high-k/interfacial layer stack
S N ( x, f ) 
t
Ec W TIL

 4 N tIL ( E, x, y, z )xft (1  f t )
Ev 0 0

 ( E , x, y , z )
dEdydz
2 2
1    ( E , x, y , z )
Ec W THK TIL

Ev 0
 ( E , x, y , z )
T 4 N t HK ( E, x, y, z )xft (1  f t ) 1   2 2 ( E, x, y, z ) dEdydz
IL
Z. Çelik-Butler, “Different noise mechanisms in high-k dielectric gate stacks,” in Proc. SPIE—Noise and Fluctuations, pp. 177–184, 2005.
B. Min, S. P. Devireddy, Z. Çelik-Butler, A. Shanware, L. Colombo, K. Green, J. J. Chambers, M. R. Visokay, and A. L. P. Rotondaro,
“Impact of interfacial layer on low-frequency noise of HfSiON dielectric MOSFETs,” IEEE Trans. Electron Devices, vol. 53, pp. 1459–1466, 2006.
UTA Noise and Reliability Laboratory
12
MSUN Noise Model Simplification




ft(1-ft) ensures that only traps within few kT of Efn contribute to
fluctuations.
Integral along the channel (x) approximated.
The shape of the spectral density is modified from pure 1/f through
functional form of Nt.
Contribution to fluctuations from the high-k dielectric layer is much
higher than that from the interfacial layer.
UTA Noise and Reliability Laboratory
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MSUN Noise Model Expressions
After appropriate substitution of various parameters, the power spectral density of the mean
square fluctuations can be written as
 N tIL0 exp[ IL ( E fn  Ei )]  0 exp(  ILTIL ) u (  IL  IL )

du


(  IL  IL )
2

1 u
 IL  0 


 0
S N ( x, f )  

 0 exp(  HK THK  ILTIL ) ( 
t
HK  HK )
N
exp[

(
E

E
)]
u


tHK 0
HK
fn
i

du
 T ) 1  u 2 
   exp{(    )T }(  HK  HK )

exp(
IL
HK
IL
0
IL IL
 HK 0

4kTWx
X

Conduction Band Offset with Si
4

2m IL  IL
h
4


2m HK  HK
h
 IL 
 IL  [(qILVgIL TIL )   IL ]
 HK
 HK  [(qHKVgHK THK )  HK ]
Tunneling Coefficients
UTA Noise and Reliability Laboratory
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MSUN Model Expressions (con.)
Power spectral density for local current fluctuations
2
 Id

1
S I ( x, f )  
(
  sc  eff ) S N ( x, f )
d
t
Wx N ( x)

Total noise power spectral density
L
1
S I d ( f )  2  SI d ( x, f )xdx
L 0
UTA Noise and Reliability Laboratory
15
Outline

Noise Modeling



Experimental Verification



Unified Flicker Noise Model
Multi-Stack Unified Noise Model (MSUN)
Metal-Gated HfO2/SiO2 NMOSFETs – different interfacial layer processing
Poly-Gated HfSiON/SiON NMOSFETs – variable interfacial layer thickness
Conclusions and Future Work
UTA Noise and Reliability Laboratory
16
Experimental Verification

Split C-V and DC Measurements
•
10µm  10µm devices
•
78K & 100K – 350K in steps of 25K (metal gate)
•
172K – 300K (poly gate)

Noise and DC Measurements
•
Metal gate
•
0.165µm  10µm devices
•
78K & 100K – 350K in steps of 25K
•
Poly gate
•
(0.20-0.25)µm  10µm devices
•
172K – 300K

Noise Modeling and Analysis
•
Unified Flicker Noise Model
•
Multi-Stack Unified Model
UTA Noise and Reliability Laboratory
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Metal Gated HfO2/SiO2 MOSFETs
Gate
Electrode
High-k
IL Type
IL Thickness
TaSiN
27Å HfO2
(ALD)
SRPO SiO2
10Å
27Å HfO2
(ALD)
RCA SiO2
10Å
TaSiN
UTA Noise and Reliability Laboratory
18
(V -V ) = 0.3V
g
3
(F / Hz cm )
Normalized Noise vs. Temperature
t
V = 50mV
Normalized noise for the two
process splits shows no clear
dependence on temperature at all
bias points.
10Å SRPO SiO
2
10Å RCA SiO
2
CET
10
-25
Generally, the magnitude of 10Å
SRPO device is lower.
d
Metal-Gated HfO2/SiO2
Id
2
(S / I ).L.C
2
2
d
10
-26
50
100
300
200 250
150
Temperature (K)
350
400
UTA Noise and Reliability Laboratory
19
Parameter Extraction
1.4
1.2
10Å SRPO SiO
The dependence of noise power
spectral density on frequency mainly
comes from the term,
2
1
Frequency Exponent
0.8
 (1 
0.6
W/L = 10m/0.165m
V = 50mV
0.4
d
10Å RCA SiO
1.2
where,
2
The frequency exponent  for the
1-100Hz region is plotted against
the applied gate bias.
A straight line fit is made to the data
from which ηHK ,λHK are extracted
0.8
0.6
W/L = 10m/0.165m
V = 50mV
0.4
d
0.4
 HK )
 HK  [(qHKVgHK THK )   HK ]
1
0.2
0.2
HK
0.6
0.8
V (V)
g
1
1.2
1.4
Metal-Gated HfO2/SiO2
UTA Noise and Reliability Laboratory
20
Energy Dependence of Trap Density
Energy Dependence of Trap Density
3 10
N
tHK0
18
exp( (E -E ))
HK
 = 0.1eV
fn
The trap density variation with
respect to energy is represented
as an exponentially varying
function.
The energy interval swept by the
quasi Fermi level for the
temperature and the bias range
considered in this work is 0.05eV.
i
-1
HK
N
tHK0
2 10
=2x10
18
-3
cm eV
-1
18
0.05eV
0
0.2
0.4
0.6
0.8
1
1.2
Band Gap Energy (E)
Metal-Gated HfO2/SiO2
UTA Noise and Reliability Laboratory
21
MSUN Model
Metal-Gated HfO2/SiO2
N
t
= 2.0x10
18
3
cm eV
-1
9
  = 9.0x10 cm/Vs

c0
10
10

-15
7




= -1.27x10 cm
 = 4.68 eV
 = 0.1 eV
-1
= 4.0x10
t
18
3
cm eV
-1
9
  = 9.0x10 cm/Vs
-1


c0
-1
7




= -1.27x10 cm
 = 4.68 eV
-1
-1
-15
 = 0.1 eV
10
-1
-16
-16
10
SRPO SiO (1nm)
SRPO SiO (1nm)
(V -V ) = 0.7V
(V -V ) = 0.3V
T = 275K
T = 78K
2
2
t
g
t
Id
g
S (A /Hz)
S (A /Hz)
2
Id
2
N
t
= 2.0x10
18
3
cm eV
-1
8
  = 4.5x10 cm/Vs
10
-15
10
-16


c0

7



= -0.85x10 cm
 = 0.045 eV
 = 0.1 eV
-1
N
t
= 2.0x10
18
3
cm eV
8
  = 6x10 cm/Vs
-1
-1


c0

-1
7



= -0.85x10 cm
 = 0.045 eV
 = 0.1 eV
-1
-1
-15
-1
10
-16
10
RCA SiO (1nm)
RCA SiO (1nm)
(V -V ) = 0.7V
(V -V ) = 0.3V
T = 275K
T = 78K
2
g
10
N
2
t
g
t
-17
-17
10
1
10
10
100
f (Hz)
UTA Noise and Reliability Laboratory
22
MSUN Model
T = 275K
SRPO SiO (1nm)
2
Metal-Gated HfO2/SiO2
18
N
t
3
= 2.0x10 cm eV
-1
T = 78K
SRPO SiO (1nm)
2
9
  = 9.0x10 cm/Vs
c0
10
18
N
-15
t
3
= 4.0x10 cm eV
-1
10
-15
10
-16
9
  = 9.0x10 cm/Vs
c0

7

= -1.27x10 cm
  = 4.68 eV
-1

-1
  = 0.1 eV
-16
-1
-1

-1
  = 0.1 eV

-1

2
Id
S (A /Hz)
S (A /Hz)
= -1.27x10 cm
  = 4.68 eV

10
7

Id
18
N
t
2
3
= 2.0x10 cm eV
T = 78K
RCA SiO (1nm)
-1
2
T = 275K
RCA SiO (1nm)
2
8
  = 4.5x10 cm/Vs
c0
10
-15
18
N
t
3
= 2.0x10 cm eV
-1
10
-15
10
-16
8

7

= -0.85x10 cm
  = 0.045 eV
  = 6x10 cm/Vs
c0
-1

-1

10
  = 0.1 eV
-16
7

= -0.85x10 cm
  = 0.045 eV
-1
-1

-1

  = 0.1 eV
-1

0
0.2
0.4
0.6
0.1
0.8
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(V -V ) (V)
g
t
UTA Noise and Reliability Laboratory
23
19
10
18
4 10
18
10
10
10
9
-1
10
SRPO SiO (1nm)
-3
Nt0HK is constant for all temperatures
and the non-uniformity in trap density
is modeled by ηHK ,λHK
(cm eV )
Effective Oxide Trap Density vs. Temperature
tHK0
c0
6 10
8
4 10
8
2 10
400
8
RCA SiO (1nm)
2
10
18
50
100
150
200
250
300
Temperature (K)
UTA Noise and Reliability Laboratory
350
24
-1 -1
MSUN Model
Metal-Gated HfO2/SiO2
 (cmV S )
N
2
Effective Oxide Trap Density vs. Temperature
10
10Å SRPO SiO
2
10Å RCA SiO
2
10
18
t
-3
-1
N (cm eV )
The overall effective trap density
(Nt) is extracted using the Unified
Flicker Noise Model.
In general, the values tend to
increase with a decrease in
temperature.
19
This is not consistent with the
uniform trap density assumption
at the core of the model.
10
17
10
16
50
Original Unified Noise Model
100
150
200 250
300
Temperature (K)
350
400
Metal-Gated HfO2/SiO2
UTA Noise and Reliability Laboratory
25
Outline

Noise Modeling



Experimental Verification



Unified Flicker Noise Model
Multi-Stack Unified Noise Model (MSUN)
Metal-Gated HfO2/SiO2 NMOSFETs – different interfacial layer processing
Poly-Gated HfSiON/SiON NMOSFETs – variable interfacial layer thickness
Conclusions and Future Work
UTA Noise and Reliability Laboratory
26
Poly Gated HfSiON/SiON MOSFETs

NMOS HfSiON with same high-k thickness (3.0 nm) and different
interfacial layers (IL)
Dielectrics EOT (nm)
HfSiON
HfSiON
HfSiON
HfSiON
1.24
IL (nm)
Length (μm)
Width
(μm)
0.8
0.20
10
1.33
1.0
0.20,0.25
10
1.46
1.5
0.20,0.25
10
1.66
1.8
0.14 ~ 0.25
10
Variable temperature
1/f noise
measurement
has been done.
UTA Noise and Reliability Laboratory
27
Temperature Dependence of Low
Frequency Noise Spectral Density
-18
10
•Normalized current noise spectral
density did not show any noticeable
dependence on temperature.
EOT=1.46nm
-19
4
(S /I ) (F /Hz-cm )
10
10-20
-21
10
EOT=1.24nm
-19
10
C
EOT
2
Id d
2
2
•The observed noise behavior is not
affected by any temperature sensitive
process.
10-20
-21
10
Vg -Vt=0.2V
Vg -Vt=0.3V
Vg -Vt=0.4V
Vg -Vt=0.5V
Vg -Vt=0.6V
Vg -Vt=0.7V
160 180 200 220 240 260 280 300 320
•Remote optical phonon scattering
may not have a significant impact on
low frequency noise characteristics
although it has a profound effect on
mobility behavior (presented last
year).
Poly-Gated HfSiON / SiON
Temperature (K)
UTA Noise and Reliability Laboratory
28
Low Frequency Noise Mechanism
Correlated Number and Mobility Fluctuation
Model1:
10
-8
10 1
10
-9
10
10
-8
10
2
10
-9
10
1
-10
10
0
10
-5
10
-4
Hooge’s Bulk Mobility Fluctuation Model9:
0
10
10
S Id
2 gm 2

(1


C
I
/
g
)
( ) SVfb
eff ox d
m
I d2
Id
10
-2
S /I
2
2
EOT=1.66 nm L=0.25m T=270K
Id d
-1
-7
m d
2
10
(g /I ) (V )
(Hz )
EOT=1.24 nm L=0.20m T=172K
2
S Id q  h  eff  Vd

2
Id
fL2 I d
Correlated number and surface mobility
fluctuation mechanism was observed to dominate
for devices with different interfacial layer
thicknesses in the experimental temperature range
-3
I (A)
d
9
Poly-Gated HfSiON / SiON
F.N. Hooge. IEEE Trans. Electron Devices 41. 1926 (1994).
UTA Noise and Reliability Laboratory
29
The MSUN Model
According to original Unified Model, current noise spectral density can be shown as
2
I

S I d ( x, f )   d (1  N ) S Nt ( x, f )
 N

(1)
Considering tunneling through a double step barrier, we can show
S N t  4kTWx 
TIL
0
 4kTWx 
TIL THK
TIL
N tIL0 exp[ IL ( E fn  Ei )  qIL
VIL
 IL
z   IL z ]
dz
2
TIL
1   2 IL
N tHK 0 exp[ HK ( E fn  Ei )  qHK
VHK
 HK
z   HK z ]
dz
2
2
THK
1    HK
(2)
The final expression of Sid(A2/Hz) using the new model for high-k gate devices becomes
( q ILV IL / TIL  IL ) /  IL


2f IL 0 exp(  IL TIL ) u
NtIL0 exp[ IL ( E fn  Ei )]
IL
du


2
IL
(
q

V
/
T


)
/

2
1 ( q V / T  ) /  
2
1  uIL
4kTId L 
1    IL IL 0 IL IL IL IL IL (2f ) IL IL IL IL IL 2f IL 0
 dx
 eff 

SI d ( f ) 
2 0 
( q HK V HK / THK  HK ) /  HK


WL
N ( x) 
2f HK 0 exp(  HK THK ) u
NtHK 0 exp[ HK ( E fn  Ei )]

HK

duHK 
( q HK V HK / THK  HK ) /  HK
2
1 ( q HK VHK / THK  HK ) /  HK 2f
HK
0
  HK HK 0

(2f )
1  uHK
(3)
UTA Noise and Reliability Laboratory
30
MSUN Model Parameter List
High-k dielectric layer parameters
Interfacial layer parameters
NtHK0
Mid-gap trap density at the IL/high-k
interface
NtIL0
Mid-gap trap density at the substrate/IL
interface
μc0
Mobility fluctuation coefficient
μc0
Mobility fluctuation coefficient
λHK
Band bending parameter corresponding
to the high-k layer
λIL
Band bending parameter corresponding
to the IL
ηHK
Spatial trap distribution parameter for
the high-k layer
ηIL
Spatial trap distribution parameter for
the interfacial layer
ξHK
Parameter for the energy distribution of
traps in the high-k dielectric layer
ξIL
Parameter for the energy distribution of
traps in the interfacial layer
• If the published trap density values are chosen for NtIL0 and NtHK0 the noise contribution of the interfacial layer is
insignificant when compared to the total device noise. The interfacial layer parameters do not play any
effective role in the data fitting
• For the high-k layer, as discussed earlier, λHK= ξHK, so the number of effective fitting parameters reduce to 4.
UTA Noise and Reliability Laboratory
31
Extracted ξ, λ, η
From Eq (3) we can show
1.4
EOT=1.24nm
1.2
EOT=1.33nm
Frequency exponent ( )
1
0.8
α=
1 ( q HKVHK / THK  HK ) /  HK
0.6
0.4
0.2
0

=
HK
 =
=1.53 eV -1
HK
HK
6
 HK=-7.99x10 cm
=-0.4056 eV
6
 =-5.38x10 cm
-1
-1
HK
-1
HK
EOT=1.46nm
1.2
EOT=1.66nm
1
0.8
0.6
0.4

0.2
 HK=-4.67x10 cm
=
HK
=-0.455 eV -1
 =
HK
6
HK
-1
0.6
0.8
-1
 =-3.53x10 6 cm -1
HK
0
0.4
=-0.947 eV
HK
1
0.6
0.4
1.2
V (V)
g
0.8
1
1.2
From a linear fit of α as a function of
Vg for individual devices at all
temperatures, the energy dependence
parameters ξ, λ and the spatial
distribution parameter η were
extracted. The extracted values
are shown on the plots.
1.4
Poly-Gated HfSiON / SiON
UTA Noise and Reliability Laboratory
32
Data Vs MSUN Model Predictions for
LF Noise Spectra
)
cy(Hz
en
qu
rFe
10
0
1
0
1
g
10
10

=1.7x10
19
tHK0
t0HK
=1.7x10
N
HK
6
=-7.99x10 cm
-1
HK
-17
10
cm
-1
-3 eV
cm eV
T=300K EOT=1.24nm V =0.58V
10
 =5x10 10 cm/Vs
c0 =5x10 cm/Vs
g
-18
-15
10
c0
NN
Id
=3.0x10
tHK0
t0HK
T=172K EOT=1.33nm V =0.94V
10
g
-15
 =5x10
c0

10
N
=6.4x10
t0H K
tHK0
10
1
HK

-16
-17
-16
10
 =1.1x10
c0
10
19
cm
-3
eV
=
HK
=-0.4056 eV
6
=-5.38x10 cm
10
19
-3
cm eV
cm/Vs
-1
2
-17
HK
=1.53 eV
10
c0
-1
-3
19
NN
=
c0
Id
2
-16
t0
10
 =5x10
cm/Vs
 =5x10cm/Vs
-1
S (A /Hz)
S (A /Hz)
10
t0
-15

-1
-3
19
-1
-3
19
N N=1.3x10
cm eVeV
=1.3x10 cm
tHK 0
T=172K EOT=1.24nm V =0.96V
-16
10
-1
-1
-17
HK
10
-1
T=300K EOT=1.33nm V =0.67V
g
cm/Vs
10
100
Frequency (Hz)
10
100
Poly-Gated HfSiON / SiON
The calculated current noise spectral density SId is compared to the data for devices with
four different IL thicknesses and in the experimental temperature range of 172K-300K.
UTA Noise and Reliability Laboratory
33
Data Vs MSUN Model Predictions for
LF Noise Spectra
NN
tH
K0K=1.6x10
t0H
T=172K EOT=1.46nm V =0.74V
g
10
 =2.5x10
-16
c0

10
HK

-17
=3.8x10
 =5x10
10
2
c0
cm
-3
eV
6
eV
-1
cm/Vs
10
-16
-1
=-0.455 eV
=-4.67x10 cm
-3
-1
HK
10 -17
-1
T=300K EOT=1.46nm V =0.76V
Id
S (A /Hz)
tH
K0
t0H
K
19
HK
cm
S (A /Hz)
N
=
10
19
g
cm/Vs
Id
2
18 18 -3 -3 -1 -1
=6.0x10
=6.0x10 cmcmeVeV
tH
K0N
t0HK
t0
N
N
T=172K EOT=1.66nm V =1.01V
g
10
10
10
 =1.75x10
 =1.75x10
cm/Vs
cm/Vs 10 -16
c0
c0
-15

10 -16
19
19 -3
-3-1
NN
cm cm
eV eV
N=2.6x10
=2.6x10
t0tH K0
-1

=
HK
=-0.947 eV
-1
HK
6
=-3.53x10 cm
10 -17
-1
HK
t0HK
T=300K EOT=1.66nm V =1.13V
10
 =5x10
=5x10 cm/Vs
cm/Vs
10
10
-17
g
c0 c0
1
10
100
Frequency (Hz)
10
10
100
-18
Poly-Gated HfSiON / SiON
Excellent agreement between data and model predictions was observed irrespective
of IL thickness at all temperatures.
UTA Noise and Reliability Laboratory
34
Data Vs MSUN Model Predictions for
LF Noise Spectra
f c1  1 (2HK 0 exp( HKTHK ))
10
-15
10
-16
10
-17
10
-18
10
-19
10
-20
10
-21
f 
α=0
f c 2  1 (2HK 0 )
α~1
EOT=1.66nm
α~2
Frequency (Hz)
S
Id Total
S
Id high-
S
Id
2
S (A /Hz)
SId
(A2/Hz)
A special phenomena was observed for the
devices with the thickest gate oxide.
Id IL
1
The higher frequency components in the
device noise are contributed by traps closer to
the interface, where as the traps further away
contribute to the lower frequency components.
10
100
Frequency (Hz)
1000
For the devices with TIL=1.8nm, the
characteristic corner frequency was calculated
to be fc2~ 33Hz. Below 33 Hz the noise was
contributed by the high-k layer. Above this limit
noise contribution was primarily from the IL
layer.
UTA Noise and Reliability Laboratory
35
Data Vs MSUN Model Predictions for
Bias Dependence
10
-14
-1

= =1.53
=
eV eV
HK =1.53
HK
-1
 =
HK
6
-1
=-7.99x10
 =-7.99x10cmcm
6
-1

HK
-1
=-0.4056 eV
HK
6
-1
=-5.38x10 cm
HK
10 -15
NN =1.9x101919cm-3-3eV-1-1
NtHK 0=1.9x10 cm eV
N =6.4x1019 cm-3 eV-1
N
tHK 0
=2.75x1010 cm/Vs
cm/Vs
c0=2.75x10
c0
EOT=1.28nm T=230K
EOT=1.24nm T=230K
 =1.1x10 cm/Vs
t0 K
t0H
t0HK
2
10
-16
10
c0
EOT=1.33nm T=172K
=
=-0.947
eV eV -1
 =
=-0.947
-1

Id
S (A /Hz)
10

=
HK
-1
=-0.455 eV
HK
=-3.53x10 cm
6
-1
 =-3.53x10 cm
HK
6
HK
-1
=-4.67x10 cm
6
-1
• The fit was good in
the bias range of
moderate inversion
to strong inversion,
for devices with all
different IL thicknesses in the
experimental
temperature range.
HK
HK
10 -15
19
-3
-1
N
NtHK 0 =2.3x10 cm eV
19
-3
-1
N
NtHK 0 =1.9x10 cm eV
t0HK
t0HK
 =5.0x10 cm/Vs
10
 =5.0x10
c0
10
0
c0
0.1
0.2
0.3
0.4
0.5
0.6
10
-3
cm e V
-1
cm/Vs
10
 =5 .0x 10
c0
EOT=1.46nm T=261K
-16
19
N t0 =2 .3x 10
cm/Vs
EOT=1.66nm T=188K
EOT =1.66nm T =18 8K
0.1
0.7
(V -V ) (V)
g
t
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Poly-Gated HfSiON / SiON
UTA Noise and Reliability Laboratory
36
Extracted MSUN Model Parameters
EOT=1.28nm, λHK=ξHK =1.538eV-1, ηHK =-7.99x10 6 cm-1
EOT=1.33nm, λHK=ξHK =-0.4056eV-1, ηHK=-5.38x10 6 cm-1
T(K)
NtHK0(cm-3 eV-1)
μc0(cm/Vs)
T(K)
NtHK0(cm-3 eV-1)
μc0(cm/Vs)
172
1.7x1019
5.0x1010
172
6.4x1019
1.1x1010
188
1.8x1019
5.0x1010
188
6.1x1019
3.0x1010
207
1.7x1019
3.0x1010
207
5.6x1019
4.5x1010
230
1.9x1019
2.75x1010
230
5.9x1019
3.5x1010
261
1.4x1019
5.0x1010
261
3.6x1019
1.7x1010
300
1.3x1019
5.0x1010
300
3.0x1019
5.0x1010
EOT=1.46nm, λHK=ξ HK = -0.455eV-1, η HK=-4.67x10 6 cm-1
EOT=1.66nm, λHK=ξ HK = -0.947eV-1, η HK=-3.53x10 6 cm-1
T(K)
NtHK0(cm-3 eV-1)
μc0(cm/Vs)
T(K)
NtHK0(cm-3 eV-1)
μc0(cm/Vs)
172
3.8x1019
5.0x1010
172
2.6x1019
5.0x1010
188
3.1x1019
5.0x1010
188
2.3x1019
5.0x1010
207
2.4x1019
5.0x1010
207
1.4x1019
7.5x1010
230
1.5x1019
2.25x1010
230
1.6x1019
5.0x1010
261
1.9x1019
5.0x1010
250
1.6x1019
5.0x1010
300
1.6x1019
2.5x1010
270
9.0x1018
3.0x1010
300
6.0x1018
1.75x1010
Poly-Gated HfSiON / SiON
UTA Noise and Reliability Laboratory
37
Extracted NtHK0
22
10
21
10
20
10
19
10
18
10
17
160
tHK0
-3
N
•NtHK0 values extracted using
the MSUN Model
•Shows consistency over
the whole experimental
temperature range
•Shows consistency with
devices having different IL
thickness
EOT=1.66nm
EOT=1.46nm
EOT=1.33nm
EOT=1.28nm
-1
(cm eV )
10
Poly-Gated HfSiON / SiON
180
200
220
240
260
280
300
320
Temperature (K)
UTA Noise and Reliability Laboratory
38
Dependence of NtHK on Energy
Poly-Gated HfSiON / SiON
NtHK =NtHK0 exp( |E-Ei |) (cm -3 eV-1)
1020
10
19 19 -3 -3 -1 -1
NNN =1.3x10
=1.3x10
cmeVeV  =
-1 -1
cm
==1.53
=1.53
eVeV
tHK0
t0HK
t0
HK
19
-3
-1
N
19
-3
-1
NNtHK0
=3.0x10
=3.0x10
cm cm
eV eV = =-0.4056 eV-1
t0HK
t0
HK
=-7.99x10 6cm -1
 =-7.99x10 cm
HK
Fermi energy sweep range
10
6
=5x1010 cm/Vs
cm/Vs
c0=5x10
c0
19
19
-3
-1
6 eV-1
 ==-5.38x10
=-0.4056
cm
-1
 =5x10 10cm/Vs
10
 c0=5x10
cm/Vs
c0
HK

EOT=1.33nm
-1
(3.0x10 ~ 3.4x10 )cm eV
HK
6
=-5.38x10 cm
-1
HK
EOT=1.24nm
19
2 10
20
19
EC
EV
EV
2 10
Fermi energy sweep range
19
19
-3
EC
-1
(2.33x10 ~ 2.39x10 )cm eV
10
19
10
4 10 19 N
N
=1.60x10
19
tHK0
t0 HK
 =2.5x10
c0
10
cm
cm/Vs
-3
eV
-1


EOT=1.46nm
=
HK
=-0.455 eV
-1
HK
6
=-4.67x10 cm
-1
t0HK
=-3.53x10 cm
10
-1
10
= =-0.947
eV
=1.75x10
cm/Vs
 =1.75x10 cm/Vs c0HK
HK

5 10
(1.31x10
18
-0.2
EC
Fermi energy sweep range
0
19
~ 1.34x10
19
-3
)cm eV
0.2 0.4 0.6 0.8
1
EV
(3.37x10
-0.2
E (eV)
g
10
19
6
=-3.53x10 cm
0
18
-1
HK
18
-3
-1
1
2 10
1.2 1.4
~ 3.54x10 )cm eV
0.2 0.4 0.6 0.8
As the excursion range is
comparatively small, the
calculated trap density outside the highlighted region
may not correctly represent
actual device
characteristics.
EC
Fermi energy sweep range
-1
1.2
-1
c0
HK
EOT=1.66nm
EV
19
18
-3
-1
18
-3
-1
NN
=6.0x10 -1 cm eV
N =6.0x10 cm eV
=
tHK0=-0.947 eV
t0
6
The active trap densities as
probed by the quasi-Fermi
energy and it’s excursion is
shown for devices with
different IL thicknesses.
18
At 300K, the active trap
density was observed to be
IL dependent. The thinnest
gate oxide devices showed
highest active trap density.
UTA Noise and Reliability Laboratory
39
Results I





The temperature dependence of extracted trap density is
inconsistent with the core model assumption.
Multi-Stack Unified Noise (MSUN) model is proposed to predict
noise in high-k/interfacial layer MOSFETs.
It is scalable with respect to HK/IL thicknesses, temperature and
applied bias.
It accounts for the material properties of constituent dielectric
materials and the non-uniform dielectric trap density profile with
respect to energy and location in dielectric.
Four model parameters




Mid-gap trap density at the IL/high-k interface
Parameter for the energy distribution of traps in the high-k dielectric layer
Spatial trap distribution parameter for the high-k layer
Mobility fluctuation coefficient
UTA Noise and Reliability Laboratory
40
Results II
• The model is in excellent agreement with the experimental
data down to cryogenic temperatures.
Metal-Gated HfO2/SiO2 NMOSFETs – different interfacial layer
processing

Poly-Gated HfSiON/SiON NMOSFETs – variable interfacial layer
thickness
• Metal-Gated HfSiON/SiON MOSFETs – different nitridation techniques

UTA Noise and Reliability Laboratory
41
Acknowledgements
 Thanks to
Luigi Colombo, Texas Instruments
Keith Green, Texas Instruments
Ajit Shanware, Texas Instruments
Hsing-Huang Tseng, Freescale
Ania Zlotnicka, Freescale
Manuel Quevedo-Lopez, Texas Instruments / SEMATECH
UTA Noise and Reliability Laboratory
42