1

Analysis of Strained-Si Device including Quantum Effect

Fujitsu Laboratories Ltd.

Ryo Tanabe Takahiro Yamasaki Yoshio　 Ashizawa Hideki　Oka

E-mail : tanabe.ryou@jp.fujitsu.com

IWCE-10October 24-27, 2004, Indiana USA

2

Si Substrate

SiGe buffer layer

Gate

Source DrainStrained Si

tensile strain

x

y

z

tens

ile st

rain

compressive strain

Background

Strained Si is studied and used aggressively as one of “Technology Booster”

Is the merit of strain kept with scaling ?

・ Quantum Effect・ Ballistic Transport

The necessity of Strained-Si Monte Carlo simulation including quantum effect.

3

The Implementation of Strained Band

ky

kx

kz

We linked the first principle band calculation program to the FUJITSU ensemble full band Monte Carlo simulator FALCON directly

Full band Monte Carlo simulator :FALCON

The first principle band calculation program :PHASE

Full band structure of Strained Si

Monte Carlo Analysis

Band structure of conduction band near X point with 50% expansion of ky, kz direction.

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1k

En

erg

y (

eV

)

ky,kz direction

kx direction

4

Evaluated Structure・We calculated below Lg=50nm.

・We used Double Gate structure.

Source DrainTSOI

Tox

L

P- type：1× 1010(/ cm3)N- type：1× 1020(/ cm3)

P- type N- typeN- type

Top Gate

Back Gate

x：Lengthy：Depth

(0,0)

Lg=40nmTsoi=10nmTox=1nm

Phonon, Impurity and Surface Roughness scattering

5

Id-Vg@Vd=0.05V

1.0E-05

1.0E-04

1.0E-03

0 0.2 0.4 0.6 0.8 1Gate Voltage (V)

Dra

in C

urre

nt (A/u

m)

50%30%20%10%0%

・ Vd=0.05V・ Drain current is saturated at Ge=20%

6

Id-Vg@Vd=0.8V・ Vd=0.8V・ Drain current is not saturated.

1.0E-05

1.0E-04

1.0E-03

1.0E-02

0 0.2 0.4 0.6 0.8 1Gate Voltage (V)

Dra

in C

urre

nt (A/u

m)

50%30%20%10%0%

7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2fold 4fold① 4fold② 2fold 4fold① 4fold②

0% 30%

Vd=0.05VVd=0.2VVd=0.4VVd=0.6VVd=0.8VVd=1.0V

Valley Distribution

2fold

4fold①

4fold②

8

The Introduction of Quantum Effect

2**2

,

2* )(

1

2

1)(

4)()( rV

TkrV

TrkmrVrV

BByx

Tk

rVrn

B

)(exp)(

*

)(1 * rV

dt

dkr

・・・(1)・・・ (2)

n

n

mrVrV

yx

2

,

2*

2)()(

t < tmax

Scattering

V(r)

V *(r)

E(r)

Eq. (1)

Eq. (2)

V(r) ： PotentialV*(r) ： Quantum Corrected PotentialE(r) ： Electric Field

・We implemented quantum effect by Bohm Potential method

9

The Comparison with Schrödinger-Poisson

Gate OxideL=40nmVg=0.8V, Vd=0V

0

2E+19

4E+19

6E+19

8E+19

1E+20

-5 0 5 10 15Position along the depth (nm)

Elec

tron

Den

sity

(/c

m3) Tsoi=2nm SP

Tsoi=5nm SPTsoi=10nm SPTsoi=2nm FALCONTsoi=5nm FALCONTsoi=10nm FALCON

10

Id-Vd@Vg=0.8V

0

0.001

0.002

0.003

0 0.2 0.4 0.6 0.8Drain Voltage (V)

Dra

in C

urre

nt (A/u

m)

x=0.3 (Classical)x=0.3 (Quantum)x=0 (Classical)x=0 (Quantum)

Lg=40nmVg=0.8V

11

The Comparison of Scattering

0% 10% 20% 30% 50%

phonon

Impurity

surface roughness0

2

4

6

8

Sca

tter

ing

Even

ts (tim

es)

Ge Content

Including quantum effect

ClassicalQuantum

phonon

Impurity

surface roughness0

2

4

6

8

Sca

tter

ing

Even

ts (tim

es)

L=40nmVd=Vg=0.8V

Strain Effect Quantum Effect

12

Ballistic Rate and Ion Improvement

0

20

40

60

80

0 10 20 30 40 50Gate Length (nm)

Bal

listic

Rat

e (%

) x=0.5x=0.3x=0

1

1.2

1.4

1.6

1.8

2

0 10 20 30 40 50Gate Length (nm)

Ion(

stra

ined

)/Io

n(un

stra

ined

)

x=0.3 (Quantum)x=0.3 (Classical)x=0.1 (Quantum)x=0.1(Classical)

・ Ballistic particles exceed 50% at L=10nm.

・ Both ballistic rate and Ion improvement with quantum effect are larger than with classical.

13

The Comparison of Electron Velocity

Source region

x=0.3 x=0

L=40nm

L=20nm

L=10nm

L=5nm

Vg=Vd=0.8 V

0.0E+00

2.0E+07

4.0E+07

6.0E+07

-30 -20 -10 0 10 20 30Position along the channel (nm)

Ele

ctr

on

Velo

cit

y (

cm

/sec)

14

Summary

•We linked the first principle band calculation program to full-band MC simulator directly.

•We implemented Bohm Potential Quantum correction model and analyzed Strained-Si device including quantum effect.

•As gate length is scaled down, Ion improvement by strain effect will decrease, but In the regime that ballistic transport is dominant (about below 10nm), strain effect will increase again due to increasing injection velocity from source region.