Noise and Random Telegraph Signals in Nanoelectronic Devices

Noise and Random Telegraph Signals in Nanoelectronic

Devices

Zeynep Çelik-Butler

Electrical Engineering Department

University of Texas at Arlington

Arlington, Texas, 76019

[email protected]

Noise and Reliability Laboratories, Zeynep Celik-Butler, [email protected]

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


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


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.


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 , ,


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


7


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


8


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


9


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)


10


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


11


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)


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


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


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


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


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


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

)(


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


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


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


21


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)


22


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


23

Effects of Quantization

•Increase in effective energy band-gap: change in e and c

• Shift in carrier distribution: change in Cox


24

3-D Treatment of RTS

DthnDnc nVDnc 33 )3(

11

Dthn

BTFe nVD

TkEE

3)3(

/)(exp

thnn VDc 3


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


26


• From Stern - Howard wave-function:

bzzb

zp exp2

)( 23

3/1

02 32

1112

invB

Si

l QQqm

b

bz /3


27


• 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


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


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


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


31


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


32


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


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


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


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


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


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


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


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)


40


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


41


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


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.


43

ACKNOWLEDGEMENTS

• This work has been supported by NSF, THECB-ATP, SRC, TI, Legerity, Motorola and ST-Microelectronics.

Noise and Random Telegraph Signals in Nanoelectronic Devices

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