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Noise and Random Telegraph Signals in Nanoelectronic
Devices
Zeynep Çelik-Butler
Electrical Engineering Department
University of Texas at Arlington
Arlington, Texas, 76019
celikbutler@ieee.org
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
2
Outline
Motivation: Problems Encountered as the Devices Shrink, Frequencies Increase, and Voltages Reduce
Improved Model for 1/f Noise in MOSFETs Random Telegraph Signals in MOSFETs
Complex RTS Extraction of trapping parameters using RTS
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
3
UTA - Noise Characterization Facilities
6' x 6' x 8' Shielded Room
3 Spectrum and Signal Analyzers,
f=1 Hz - 20 GHz.
3 Cryostats, T= 2 K to 350 K.
Various Lock-ins, Preamps, System Controllers, Battery Operated Sources etc.
Optical Equipment Computer Software for Modeling
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
4
Problems Encountered as the Devices Shrink, Frequencies Increase, and Voltages Reduce
Signal-to-noise ratio decreases.
Noise models based on large number of electrons break down.
Quantum effects become dominant.
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
5
Signal to Noise Ratio Decreases
For a MOSFETStart from W=100m, L=10m, tox=800Å, NSS=4x1010 eV-1cm-
2.Assume scaling factor is K.Assume trap and surface state densities remain the same.
Increase in noise level due to the K1/2 law chosen for tox.Unpredictability of noise level for K>20.NSS is actually a two dimensional Poisson variable.
W W K L L K t t Kox ox , ,
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
6
Large Area Noise Models Break Down
Single electron, single trap effects.
NSS=4x1010 eV-1 cm-2, W=1m, L=0.1m.
EC
EV
EF
SiO2
Si
kT=26 meV
1 trap per channel
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
7
Large Area Noise Models Break Down
Break-down of large-area models for sub-micron channel length.
• A=Nt (cm-3 eV-1)
• B=effNt (cm-1 eV-1)
• C=2eff2Nt (cm eV-1)
• A=B2/(4C)
22
*
*
2
2
2
1)(ln)( LOLO
L
O
ox
effdId NNCNNB
NN
NNA
CfL
IkTqfS
Independent parameters: and Nt
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
8
Large Area Noise Models Break Down
10-14
10-13
10-12
10-11
10-10
0.1 1 10
SV
d (
1H
z) (
V2 /H
z)
Channel length (m)
Vgs-VT= -1 VVds= -50 mV
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
9
Large Area Noise Models Break Down
1015
1016
1017
1018
1019
1020
0.2 0.4 0.6 0.8 1 1.2 1.4
2 channel region modeluniform channel model
Nt (
cm
-3 e
V -
1 )
L (m)
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
10
Large Area Noise Models Break Down
Modified 1/f noise model that takes into account threshold variation along the channel.
• For simplicity assume two regions:– V, L, VT2,, A2, B2, C2
– Vds-V, L-L, VT1, A1, B1, C1
– L<<L, VTVT1
– A1 = A2, since Nt1 = Nt2
– B12/C1 = B2
2/C2 = 4A
– I1 = I2 = Id
– eff1 = eff2,
Independent parameters:Nt, 1, 2, VT2, and V
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
11
Large Area Noise Models Break Down
Modified 1/f noise model that takes into account threshold variation along the channel.
10-22
10-21
10-20
10-19
10-18
10-17
0 0.5 1 1.5 2
L=0.32m
L=0.45m
L=1.0m
SId
(A2 /H
z)
|Vgs
-VT| (V)
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
12
RTS in MOSFETs
Random Telegraph Signals: single electron switching.
-0.0001
-5 10 -5
0
5 10-5
0.0001
0.00015
0.0002
5.2 5.3 5.4 5.5 5.6 5.7
RT
S (
Arb
itra
ry U
nit
s)
Time (sec)
1
0
Id
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
13
RTS in MOSFETs
Random Telegraph Signals (RTS) with a Lorentzian on 1/f spectum.
Time Scale seconds
Time Scale millisecondsFrequency (f)
PSD
22
1010
2
211
4)(
f
IfS
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
14
NMOS,W/L(m)=5/0.23, VDS=175mV, VGS=0.60V
Frequency (Hz)
100 101 102 103 104 105S
v (V
2 /H
z)10-15
10-14
10-13
10-12
10-11
10-10
10-9
Sv = 6.11e-12 / ( 1 + f / 1260 )2
Time (ms)
0 1 2 3 4 5 6 7 8
V (10-4
V)
-10
-8
-6
-4
-2
0
2
2 RTS levels
1 RTS process
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
15
3 RTS levels
2 RTS processes
PMOS T1 W/L=5/0.25 VDS=150mV VGS=0.9V
Frequency (Hz)
10-1 100 101 102 103 104 105
Sv
(V2 /H
z)10-15
10-14
10-13
10-12
10-11
10-10
10-9
Sv = 2.3e-14 / ( 1 + f / 23700)2
Sv = 1.4e-10 / ( 1 + f / 1.8)2
Time (ms)
0 1 2 3
V (10-4
V)
-1
0
1
2
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
16
5 RTS levels
4 RTS processes
Time (ms)
0 1 2 3 4 5 6 7 8
V (10-
4 V
)
-3
-2
-1
0
1
2
3
NMOS ,W/L(m)=5/0.23 ,VDS=150mV,VGS=0.775V
Frequency (Hz)
10-1 100 101 102 103 104 105
Sv
(V2/H
z)
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
Sv = 1.18e-11 / ( 1 + f / 48)2
Sv = 1.11e-10 / ( 1 + f / 3.12 )2
Sv = 2.93e-14 / ( 1 + f / 36 780)2
Sv = 1.08e-12 / ( 1 + f / 1345)2
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
17
COMPLEX RTS
-1.E-03
1.E-03
3.E-03
5.E-03
7.E-03
9.E-03
2 2.02 2.04 2.06 2.08 2.1
Time (s)
Vo
ltag
e (V
)
level 3
(a) level 4
level 2
level 1
Complex random telegraph signals due to multiple traps
trapsN
k kk
kI
f
II
I
fS
122
1010
2
2 211
)(
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
18
RTS in MOSFETs
RTS can be used to characterize trapping sites.
EC
EFp
EFn
qs
qVc
EFg
qVgs
xT
ECox-ET
siliconoxidegate
22
1010
2
211
4)(
f
IfS
RTS modeling.
22
2
2)(
KFf
IAFfS d
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
19
RTS in MOSFETs
RTS can be used to characterize trapping sites.
• Position of the trap along the channel, yT
• Position of the trap in the oxide, xT
• Trap energy, ECox - ET
• Screened scattering coefficient,
NLWN
N
I
I
effeffd
d 11
sFBgs
ox
TscFCTCox
e
c VVT
xqqqVEEEE
kT p
01
ln
LVyV dsc
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
20
10-1
100
101
0.01 0.1 1
c /
e
Drain Voltage (V)
(b)
Trapping Parameters Through RTS in MOSFETs
10-1
100
101
102
0.25 0.3 0.35 0.4 0.45 0.5
ForwardReverse
c /
e
Gate Voltage (V)
(a)
xT=2.7 nm
yT/L=0.6
ECox-ET=3.04 eV
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
21
Trapping Parameters Through RTS in MOSFETs
10-3
10-2
10-1
0.01 0.1 1
Vd
s/ Vd
s
Drain Voltage (V)
10-4
10-3
10-2
10-1
0.04 0.06 0.08 0.1 0.3
N/N
Forward
Reverse
Vd
s/ Vd
s
Vgs
- VT (V)
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
22
Trapping Parameters Through RTS in MOSFETs
1 10-14
2 10-14
3 10-14
4 10-14
5 10-14
6 10-14
0.04 0.06 0.08 0.1
ForwardReverse
Sc
att
eri
ng
Co
eff
icie
nt
(V
-s)
Vgs
-VT (V)
0.2
NKK ln21
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
23
Effects of Quantization
•Increase in effective energy band-gap: change in e and c
• Shift in carrier distribution: change in Cox
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
24
3-D Treatment of RTS
DthnDnc nVDnc 33 )3(
11
Dthn
BTFe nVD
TkEE
3)3(
/)(exp
thnn VDc 3
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
25
2-D Treatment of RTS - c and e
thnn VDc 2
zDthn
zDn
cdz
z
zpnVDdz
z
zpnc 0202
)()2(
1)(
1
zDthn
BTF
ne
dzz
zpnVD
TkEE
e02
)()2(
/)(exp1
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
26
2-D Treatment of RTS
• From Stern - Howard wave-function:
bzzb
zp exp2
)( 23
3/1
02 32
1112
invB
Si
l QQqm
b
bz /3
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
27
2-D Treatment of RTS
• Calculate the inversion carrier concentration assuming they are located primarily at E0:
dzzpnN D )(
11
2
1
002)(/exp
2
zBFCS
tB dzzpTkEEETmk
3/10
3/2
0
3/12
0 )2(28
9
2 FSBBSiSil
VqNq
mE
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
28
2-D Treatment of RTS - c and e
• To first order, the ratio is not affected by quantization.
)5/2()2(
/)(exp2
0
bTmkVD
TkEEE
tBthn
BTCSe
)5/2()2(
/)(exp2
0
bTmkVD
TkEEE
tBthn
BFCSc
sFBgsox
TsFCBTCox
Be
c VVT
zqqEEEE
Tk 01
ln
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
29
RTS Measurements
• MDD n-MOSFETs
• Weff Leff = 1.37 0.17 m2
• Tox = 4 nm
• VT = 0.375 V for VSB = 0 V
• strong inversion, linear region VDS = 100 mV
• VSB = 0 - 0.4 V, VGS = 0.5 - 0.75 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
30
ECox-ET and zT fromc and e
sFBgsox
TsFCBTCox
Be
c VVT
zqqEEEE
Tk 01
ln
0
0.5
1
1.5
2
2.5
3
3.5
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
ln(
c/
e)
VGS
(V)
ln(
c/e)
VSB=0 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
31
ECox-ET and zT fromc and e
sFBgsox
TsFCBTCox
Be
c VVT
zqqEEEE
Tk 01
ln
0
0.5
1
1.5
2
2.5
3
3.5
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
ln(
c/
e)
VGS
(V)
ln(
c/e)
VSB=0.4 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
32
ECox-ET and zT fromc and e
VSB (V) VT (V) zT (Å) ECox-ET (eV)
0 0.375 11.22 3.09
0.1 0.382 11.53 3.08
0.2 0.393 11.37 3.08
0.3 0.401 11.64 3.07
0.4 0.408 11.08 3.08
Tox =4 nm
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
33
Dependence of e on VSB
4 10-4
6 10-4
8 10-4
10-3
2 10-3
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
e(s
)
VSB
(V)
e
(s)
)5/2()2(
/)(exp2
0
bTmkVD
TkEEE
tBthn
BTCSe
VGS=0.75 V
VGS=0.55 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
34
Dependence of c on VSB
)5/2()2(
/)(exp2
0
bTmkVD
TkEEE
tBthn
BFCSc
10-3
10-2
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
c(s
)
VSB
(V)
c
(s)
VGS=0.55 V
VGS=0.75 V
VGS=0.65 V
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
35
cn Extracted from c and e
10-13
10-12
10-11
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
ca
ptu
re c
oe
ffic
ien
t c n
(cm
3/s
)
VGS
(V)
thnn VDc 2
TkE BBn exp0 2/1*/8 nBth mTkV
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
36
2-D Treatment of RTS - Amplitude
• Question: How does quantization affect number and mobility fluctuations?– Number fluctuation through N
– Mobility fluctuations through oxide charge scattering, t.
NLW
NNN
N
NI
I
effefft
ttD
D 1111
tntn N 1111
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
37
Extraction of Scattering Coefficient
• Mobility Fluctuations:– Using Surya’s 2D surface mobility fluctuations model,
zENd
kc
kzdEdz
E
qmt
pav
nt ,
)2
(sin
sin)sin4exp(
82/
02
2
2
3*1
Siak 28.0
*
2
2
*2
exp14
2
nvBsi
nv
mTdk
Nmdqc
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
38
Calculation of Scattering Coefficient
• Considering a single trap:
Nt(E,z) = Nt(E-ET) (z-zT)
tTpav
nt Ndkz
kcE
qm
2/0
2
2
2
3*1 )sin4exp(
)2
(sin
sin
8
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
39
RTS Amplitude
1 10-4
2 10-4
3 10-4
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
VSB
=0V
VSB
=0.1V
VSB
=0.2V
VSB
=0.3V
VSB
=0.4V
VD
S/V
DS
VGS
(V)
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
40
Extraction of Scattering Coefficient
8 10-15
1.2 10-14
1.6 10-14
2 10-14
2.4 10-14
1012 1013
experimental data @VSB
=0V
fitting with zt=0.11nm
fitting with zt=0.12nm
N(cm-2)
(V-s
)
6 10-11
= 2.91x10-13 - 9.93x10-15 ln(N)
Tox =4 nm
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
41
Extraction of Scattering Coefficient
2 10-15
4 10-15
6 10-15
8 10-15
1 10-14
1011 1012 1013
experimental results of Hung et al.8
fitting of Pacelli et al.11
theoretical calculation from 2-D mobility fluctuation model
Sc
att
eri
ng
Co
eff
icie
nt
(V-s
)
N(cm-2)
W L = 1.2 0.35 m2
zT =0.25 nm
Tox =8.6 nm
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
42
Possible Reasons for Discrepancy
• Threshold non-uniformity along the channel is not taken into account.
• Location of the trap along the channel• Variation of the channel voltage from source to drain
is neglected.
• N/Nt 1 is not valid, even in strong inversion, for very thin oxides.
Noise and Reliability Laboratories, Zeynep Celik-Butler, celikbutler@ieee.org
43
ACKNOWLEDGEMENTS
• This work has been supported by NSF, THECB-ATP, SRC, TI, Legerity, Motorola and ST-Microelectronics.
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