IEEE Central NC EDS/MTT/SSC Society Friday, Nov. 5th, 2010 The Nanoscale MOSFET: Physics and Limits Mark Lundstrom 1 Electrical and Computer Engineering

IEEE Central NC EDS/MTT/SSC Society Friday, Nov. 5th, 2010

The Nanoscale MOSFET:Physics and Limits

Mark Lundstrom

1

Electrical and Computer Engineeringand

Network for Computational NanotechnologyBirck Nanotechnology Center

Purdue University, West Lafayette, Indiana USA

2

21st Century: microelectronics nanoelectronics

transistors per cpu chip

Lundstrom

3

nanoscale MOSFETs 2010

source drain

SiO

2

silicon

channel~ 32 nm

gate oxideEOT ~ 1.1 nm

gateelectrode

S G D

VGS

4

MOSFET IV characteristic

(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)

S

D

G

circuitsymbol

VDS

VGS

IDS

gate-voltage controlled

current source

gate-voltage controlledresistor

5

MOSFET IV: low VDS

VG>VT VD0

ID W Qi x x (x)

ID W Cox VGS VT effEx

Ex VDS

L

Q

ix C

oxV

GS V

T

ID W

Leff Cox VGS VT VDS

VGS

gate-voltage controlledresistor

6

MOSFET IV: “pinch-off” at high

VDS

VG VD0

Qi x Cox VGS VT V (x)

V x VGS VT

Qi x 0

7

MOSFET IV: high VDS

VG VD0

ID W Cox VGS VT effE x (0)

ID W

Leff Cox VGS VT 2

2 E x (0)

VGS VT

L

Qi x Cox VGS VT V (x)

V x VGS VT

VGS

gate-voltage controlled

current source

ID W Qi x x (x)W Qi 0 x (0)

8

velocity saturation

electric field V/cm --->

velo

city

cm

/s -

-->

107

104

E

sat

VDS

L

1.0V

30nm3105 V/cm

105

9

MOSFET IV: velocity saturation

VG VD0

ID W Qi x x (x)

ID W Cox VGS VT sat

ID W Coxsat VGS VT

E x 104


10

carrier transport nanoscale MOSFETs

SAT

Lundstrom

Vel

ocity

(cm

/s)

D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.

m

m

11

~1995 - 2000

Lundstrom

1950 1970 1990 2010 2030 20501 nm

10 nm

100 nm

1 m

10 m

100 m

Year

Min

imum

Fea

ture

Siz

e 1

1K

1M

1P

?1G

1T

Moore’s Law? Molecular electronics

http://www.eng.yale.edu/reedlab/

12

objectives

1) Present a simple, physical picture of the nanoscale MOSFET (to complement, not supplement simulations).

2) Discuss ballistic limits, velocity saturation, and quantum limits in nanotransistors.

3) Compare to experimental results for Si and III-V FETs

4) Discuss scattering in nano-MOSFETs

Lundstrom

13

outline

Lundstrom

1) Introduction

2) The nano-MOSFET

3) The ballistic MOSFET

4) Scattering in nano-MOSFETs

5) Summary

14

how transistors work

2007 N-MOSFET

electron energy vs. position

VDS 0.05 V

VGS

EC


VDS 1.0 V

VGS

electron energy vs. position

EC

E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,” RCA Review, 1973

MOSFETs are barrier controlled devices

EC x

x

E

3) Additional increases in VDS drop near the drain and have a small effect on ID

A. Khakifirooz, O. M. Nayfeh, D. A. Antoniadis, IEEE TED, 56, pp. 1674-1680, 2009.

2) region under strong\

control of gateQI 0 CG VG VT 1) “Well-tempered MOSFET”

M. Lundstrom, IEEE EDL, 18, 361, 1997.

15

16

current flows when the Fermi-levels are different

D(E)

2

EF1 EF 2

1f1 E 1

1 e E EF1 kBTf2 E 1

1 e E EF 2 kBT

gate

I 2q

hT E M E f1 f2 dE

N D E

2f1 E f2 E dE

Lundstrom

17

“top of the barrier model”en

ergy

position

contact 1 contact 2

“device”

LDOS

U EC q S

EF1

EF 2

1 x EC x

Lundstrom

18

outline

Lundstrom

1) Introduction

2) The nano-MOSFET



5) Summary

19

ballistic MOSFET: linear region

VDS

IDSVGS VDD

Lundstrom

near-equilibrium f1 f2

IDS GCHVDS

20

linear region with MB statistics

Lundstrom

GCH 2q2

hT E M 2 D E f0

E

dEEC

M

2DE g

VW

2m* E EC

h

T E 1

nS N2 De EF EC kBT

gV

m*

h2 e EF EC kBT

GCH WnS

T

2kBT q

GCH WCox

T

2kBT qVGS VT

nS Cox VGS VT (MOS electrostatics)

✔

f

0E 1 1 e

E EF kBTL

T 2kBTL m* x

Boltzmann statistics:

f0 E f0 kBTL

f0 e EF E kBTL

21

ballistic MOSFET: linear region

VDS

IDVGS VDD

Lundstrom

near-equilibrium f1 f2

IDS GCHVDS

IDS GCHVDS

ID WCox

T

2kBT qVGS VT VDS

22

relation to conventional expression

Lundstrom

IDS WCox

T

2kBT qVGS VT VDS

ballistic MOSFET conventional MOSFET

IDS W

LCoxn VGS VT VDS

IDS W

LCox

T L

2kBT qVGS VT VDS

Dn T0

2n

Dn

kBT q

IDS W

LCoxB VGS VT VDS

B T L

2 kBTL q

n B

23

ballistic MOSFET: on-current

VDS

ID

VGS VDD

Lundstrom

f1 f2

ID 2q

hT E M E f1 f2 dE ID

2q

hT E M E f1 dE

24

saturated region with MB statistics

Lundstrom

IDS 2q2

hT E M 2 D E f1 E dE

EC

M

2DE g

VW

2m* E EC

h

T E 1

Boltzmann statistics: f0 e EC EF kBT

nS N2 D

2e EF EC kBT

gV

m*

2h2 e EF EC kBT

IDS WqnST

T 2kBTL m* x

IDS WCoxT VGS VT ✔

25

under low VDS

x

E

EF1 EF 2

I I nS

T

Lundstrom

I I nS

T

I ; I nS ; nS

nS nS nS

nS ; nS

nS

2

nS Cox VGS VT

26

under high VDS

x

E

EF1

EF 2

I

Lundstrom

I nST I nS

T

I 0 nS 0

nS nS nS

nS

nS Cox VGS VT

27

velocity vs. VDS

x

E

EF1

EF 2

I I

I

qnS

I I

nS

I nST I nS

T

Lundstrom

nS nS nS

nS

nS e qVDS kBTL

T

1 e qVDS kBT 1 e qVDS kBT

28

velocity vs. VDS

x

E

EF1

EF 2

I I

VDS

T

Velocity saturates in a ballistic MOSFET but at the top of the barrier, where E-field = 0.

Lundstrom

VDS

29

velocity saturation in a ballistic MOSFET

VDS 1.0 V

VGS


2007 N-MOSFETvelocity

saturation

sat 1.0107 cm/s

Lundstrom

T 1.2107 cm/s

30

aside: relation to conventional expression

Lundstrom

ION WCoxT VGS VT

ballistic MOSFET conventional MOSFET

IDS WCoxsat VGS VT

sat T

31

the ballistic IV (Boltzmann statistics)

V

G V

T 1

K. Natori, JAP, 76, 4879, 1994.

IDS (on)W T Cox VGS VT

IDS GCHVDS W Cox

T

2kBT q VGS VT VDS

VDS

ID

ballisticchannel resistance

ballisticon-current

Lundstrom

32

comparison with experiment: Silicon

A. Majumdar, Z. B. Ren, S. J. Koester, and W. Haensch, "Undoped-Body Extremely Thin SOI MOSFETs With Back Gates," IEEE Transactions on Electron Devices, 56, pp. 2270-2276, 2009.

Device characterization and simulation: Himadri Pal and Yang Liu, Purdue, 2010.

LG 40 nm

ION Iballistic 0.6

IDlin Iballistic 0.2

• Si MOSFETs deliver > one-half of the ballistic on-current. (Similar for the past 15 years.)

• MOSFETs operate closer to the ballistic limit under high VDS.

33

comparison with experiment: InGaAs HEMTscomparison with experiment: InGaAs HEMTs

Jesus del Alamo group (MIT)

Lundstrom

34

outline

Lundstrom

1) Introduction

2) The nano-MOSFET



5) Summary

35

transmission and carrier scattering

T 0

0 L

0 T 1

R 1 T

1

L

X

X X

λ0 is the mean-free-path for backscattering

IDS TIDS ?

Lundstrom

?

ID T WCox VGS VT T

2kBT q

VDS

36

the quasi-ballistic MOSFET

VDS

IDS

Tlin 0.2

Lundstrom

37

on current and transmission

Lundstrom

ION T

2 T

IBALL

EF1EF 2

ID TI I 1 T I Qi 0 I 1 T I WT

Qi 0 IBALL

WT

I IBALL

2 T

ID WT

T

2 T

Cox VGS VT

ID T WCox VGS VT T

2kBT q

VDS

38

the quasi-ballistic MOSFET

VDS

IDS

Tsat 0.7

Tlin 0.2

Tsat Tlin why?

Lundstrom

39

scattering under high VDS

x

E

EF1

EF 2

Tsat

0

0 l

L

Tlin 0

0 L

L l

Tsat Tlin

Lundstrom

40

connection to traditional model (low VDS)

ID W

LnCox VGS VT VDS

ID W

L 0

nCox VGS VT VDS

ID T WCox VGS VT T

2kBT q

VDS

Lundstrom

T 0

0 L

ID W

LappCox VGS VT VDS

1 app 1 n 1 B

41

connection to traditional model (high VDS)

how do we interpret this result?

ID WCox VGS VT T

T

2 T

ID W

1

T

1

Dn l

1

Cox VGS VT

ID WCoxsat VGS VT

Lundstrom

42

the MOSFET as a BJT

ID W (0) Cox VGS VT

1 x x

E

1

(0)

1

T

1

Dn l

‘bottleneck’“collector”

“base”

Lundstrom

43

outline

Lundstrom

1) Introduction

2) The nano-MOSFET



5) Summary

44

physics of nanoscale MOSFETs

VDS

ID

1) Transistor-like I-V characteristics are a result of electrostatics.

2) The channel resistance has a lower limit - no matter how high the mobility is.

3) The on-current is controlled by the ballistic injection velocity - not the high-field, bulk saturation velocity.

4) Channel velocity saturates near the source, not at the drain end.

Lundstrom

45

limits to barrier control: quantum tunneling

from M. Luisier, ETH Zurich / Purdue

4) 3)

2) 1)

46

21st Century electronics?

Lundstrom

1950 1970 1990 2010 2030 20501 nm

10 nm

100 nm

1 m

10 m

100 m

Year

Min

imum

Fea

ture

Siz

e 1

1K

1M

1P

?1G

1T

Moore’s Law?

47

21st Century electronics

Lundstrom

1) Information processing dominated by “Si CMOS”

2) SOC’s complemented by “CMOS+” technologies

3) and…..

macroelectronics, power electronics, PV, solid-state lighting, thermoelectrics, …

48

for more information

Lundstrom

1) “Physics of Nanoscale MOSFETs,” a series of eight lectures on the subject presented at the 2008 NCN@Purdue Summer School by Mark Lundstrom, 2008.http://nanohub.org/resources/5306

2) “Electronic Transport in Semiconductors,” Lectures 1-7, by Mark Lundstrom, 2009.http://nanohub.org/resources/7281

49

questions

Lundstrom

1) Introduction

2) The nano-MOSFET



5) Summary

Documents

IEEE Central NC EDS/MTT/SSC Society Friday, Nov. 5th, 2010 The Nanoscale MOSFET: Physics and Limits Mark Lundstrom 1 Electrical and Computer Engineering