# EE 612 Lecture 19 Device Variability Mark Lundstrom Electrical and Computer Engineering Purdue University

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```					              EE-612:
Lecture 19:
Device Variability
Mark Lundstrom
Electrical and Computer Engineering
Purdue University
West Lafayette, IN USA
Fall 2008

NCN
www.nanohub.org
Lundstrom EE-612 F08       1
outline

1) Sources of variability
2) Random dopant fluctuations (RDF)
3) Line edge roughness (LER)
4) Impact on design

Lundstrom EE-612 F08       2
sources of variability

1) Intrinsic device variability
-random dopant fluctuations (RDF)
-line-edge roughness (LER)
-oxide thickness fluctuations

2) Extrinsic process variability
-lot to lot
-wafer to wafer
-across wafer
-across chip

3) Reliability
-negative bias temperature instability (NBTI)
-hot electron injection
-electromigration
Lundstrom EE-612 F08          3
50 nm MOSFET

(a) Randomly placed dopants in a 50-
(a)          nm channel-length MOSFET. Blue
dots are donors creating the source
and drain. Red dots are acceptors,
primarily in the channel. The gate is
not shown, but would cover the
channel region between source (S)
and drain (D).
(b)
(b) Top view.

IBM J. Res. and Dev., 50, p. 433, 2006
K. Bernstein, et al,Lundstrom EE-612 F08                         4
discrete doping effects

V = W × L × W DM
example:
L=     50 nm
W = 100 nm
N+                 N+                 WDM =     50 nm
NA = 1018 cm-3
NTOT = 250
P (NA cm-3)

Number of dopants in the critical volume is a statistical quantity
Lundstrom EE-612 F08                 5
discrete doping trends

S. Borkar, IEEE Explore, p. 10, Nov./Dec. 2005

Lundstrom EE-612 F08               6
VT variation

number of dopants in the channel depletion region:

N TOT = N AWLWDM

standard deviation:

σN   TOT
= N AWLWDM

threshold voltage:

q    N AWDM
σV       =                  eqn. (4.64) Yuan and Taur
T
Cox    3WL

Lundstrom EE-612 F08              7
discrete doping effects (ii)

source           drain                    Effects:

1) σVT (10’s of mV)

2) lower avg. VT (10’s of mV)

3) asymmetry in ID
4) increased off-current

(see Wong and Taur, IEDM, 1993, p. 705)
Lundstrom EE-612 F08                   8
variation in VT

90 nm NMOS
1
σV T
∝
WL

IBM J. Res. and Dev., 50, p. 433, 2006
K. Bernstein, et al,Lundstrom EE-612 F08                      9
effect on off-current

ρ (VT ) =
1           − (VT −VT 0 ) 2 σ VT
2     2
e
2πσ VT

+∞

I OFF =    ∫ ρ (V )I (V )dV
−∞
T   OFF         T        T

⎡ σV   2
⎤
I OFF   = I OFF,nom exp ⎢       T
2 ⎥ > I OFF,nom
⎢ 2 (mkBT ) ⎥
⎣            ⎦

al., Proc. IEEE, 89,
D.J. Frank, etLundstrom EE-612 F08 259, 2001   10
solutions

2) undoped SOI
3) circuit design
4) new doping technologies

Takahiro Shinada, et al., Nature, 437,1128, 2005

Lundstrom EE-612 F08   11
LER
Line edge roughness

discrete
dopants

From A. Asenov, Univ. of Glasgow
Lundstrom EE-612 F08              12
LER

1) second most significant contributor to variability

2) arises from statistical variations in lithography (photons)
absorption, chemical reactivity, molecular structure of resist

3) Leads to variation of Leff along the width

al, IBM EE-612 and
Source: K. Bernstein, et LundstromJ. Res.F08 Dev., 50, p. 433, 2006   13
variability is becoming a major issue

G. Declerck, Keynote talk, VLSI Technol. Symp. 2005
Lundstrom EE-612 F08                    14
sources of variability

1) Intrinsic device variability
-random dopant fluctuations (RDF)
-line-edge roughness (LER)
-oxide thickness fluctuations

2) Extrinsic process variability
-lot to lot
-wafer to wafer
-across wafer
-across chip

3) Reliability
-negative bias temperature instability (NBTI)
-hot electron injection
-electromigration
Lundstrom EE-612 F08          15

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