special issue on the nano devices 서울대 나노 협동과정 & 나노 응용시스템...

Special Issue on the nano devices서울대 나노 협동과정 &

나노 응용시스템 연구센터 (NSI_NCRC)

The 2nd lecture: MOS operational principle

Prof. Young June Park

Syllabus (updated)

- 나노 물리소자 특강

부제“ 한글 ; 나노반도체와 분자소자 결합 목요일 오후 1 시 -4 시 교수학습개발센터 1 층 스튜디오 강의실

전기신호를 이용해서 신호 및 에너지를 변환하거나 , 전환하는 소자가 나노 분야에서 사용되고 있다 . 빛 , 화학 , 분자와 전자소자의 interaction 등에 대해서 콜로키움 형태로 특강을 진행한다 .

Syllabus (updated)

1. Introduction: motivation of the lecture 1 주 : 박 영준교수

2. Nano semiconductor Device operational principle 2 주 (3/14): MOSFET operational principle( 박 영준교수 )

3 주 (3/22): 1. IV characteristics of MOSFET( 박 영준교수 ) 2,3: Nanowire MOSFET( 박병국교수 )

4 주 (3/29): Single Electron Transistor and its molecular interaction ( 박 병국 , 박영준교수 )

Syllabus (updated)

3. Lecture from Max Plank(Germany): Dr. S. Roth 5 주 (4/5): Introduction into the physics of low-dimensionsal materials: 6 주 (4/12) Conducting Polymers 7 주 (4/19) Carbon Nanotubes 8 주 (4/26) Graphene Layers 4:30~6:00 교재 : VCH: One dimensional conductor available from

http://www.wiley-vch.de/publish/en/books/ISBN3-527-30749-4/ http://www.amazon.com/One-Dimensional-Metals-Physics-Materials-Science/dp/3527268758

8 주 : review and midterm

Syllabus (updated)

4. 전기화학의 기초 ( 성영은교수 ) 9 주 (5/3): 전기화학의 기초 10 주 (5/10): characterization techniques

(cyclo voltametry) - may be shifted to 9th 11 주 (5/17): Electric double layer structure Faradaic interface Non Faradaic interface

Syllabus (updated)

5. ISFET and molecule-insulator surface 12 주 (5/31) ISFET: Molecular and insulator interface

( 박영준교수 ) 13 주 (6/7): molecule to insulator(electrode) interface( 강헌교

수 ) 6. Others 14 주 (6/14) : 1. Charge transport in Organic device( 이창희교수 )

MOS equation and CV characteristics

- MOS eq:quantum and classical model

- C-V characteristics

- Long channel IV characteristics

Ref : Y.J.Park, B.G.Park, H.C. Shin, H.S.Min, VLSI device with NANOCAD, chapter 2, (Korean) Grove, Chap. 4, Physics and Technology of Semiconductor

Dev., John Wiley & Sons, 1967

MOS Equations(1)

SOXgateFBG VVVV

• describes the voltage across the gate, oxide and semiconductor surface with respect some references

• is when so that is called "the Flat Band Voltage" • : voltage applied in the gate caused by the poly depletion effect : voltage applied across the oxide : Semiconductor surface potential w,r,t some reference voltage (see next page for the reference)

FBG VV 0S FBV

gateV

OXV

S

(1)

MOS Equations(2)

SOXgateFBG VVVV

• Find the relation , with a single variable ,

then we can solve the MOS equations with respec to .

• This can be achieved by using the "semiconductor areal charge density", represented by Vox (so )

gateV

SQ

OXV S

S

From simple D continuity consideration between

interfaces; Gate- oxide and oxide semiconductor interface,

Vox = QG/Cox ( notice that Qs=-QG due to charge conservation)

S

gateFBG VVV OX

S

C

Q

S

Ex) Draw the rho(****) and field relation in the depth direction as you did

in the case of PN junction.

Qs and relationshipsS

There are several models to find Qs and relationships

- classical with MB statistics

- classical with FD statistics

- Quantum mechanical model

S

• Assuming that the surface is not quantized in x direction, and MB statistics is valid, the general relation can be found as,

(2)

where

Then (from the continuity in electric flux, D) (3)

and (4)

relationship: classical model

Sd

tSSS F

L

VQ 2)(

2

1

11

t

SV

po

po

t

SVS V

ep

n

VeF tStS

OX

SOX C

QV

)()( SSgateG QVQ

SSQ

SSQ

Vertical Electric Fields

• Important physical quantities related with vertical fields : Es and Eox, and Eeff • Eox : determines the tunneling current in thin oxide, limiting the minimum thickness of gate oxide. • Eeff : determines the effective vertical field which carriers see in vertical direction.

Ex) relationship

Draw relationship from Eq. (1)

GS V

GS V

FB2

FBV

0gateV

GV

S

)( TT VclassicalV

Classical VT theory

• is value in which is appreciable so that drain current is detectable.

• Eq.(2) states that is exponentially increasing function of whereas is increasing function in the power of 0.5.

• So, as we do approximate I-V of diode such that I=0 when where is around 0.7V even though I flows continuously as increases from 0V, we assume that until becomes a certain value ( ).• Also assume that is fixed to the value and does not increase further.• With this assumptions, classical expression for MOS VT and can be found.

GVTV nQ

nQ S

dQ

onD VV

onV

DV

0NQ

Spf ,2

S

Classical VT theory(2)

• Assume , for , Eq. (1) becomes,

so that

where . For , since is fixed to Eq.(1) becomes,

so after inversion can be written found as, .

0gateV TG VV

pfpfOX

aSFBT C

qNVV ,, 22

2

STG VV

nQ

pf ,2

pfpfFBT VV ,, 22

OX

aS

CqN 2

pfpfOX

nFBG C

QVV ,, 22

TGOXn VVCQ

Subthreshold characteristics

12

12

2

2

2

2

2

2

//2

Fps

Fps

Fps

tstFp

eV

qNQ

eVqNQQQ

eVqN

eeVL

VQ

s

tsAsn

stsAsdsn

tsAs

VV

t

s

d

tss

tFps Vtd eVC /)2(

Subthreshold characteristics(VGS vs. )

ox

sssssFBGS C

QQVV

)()( s

)2()2()(

)2()2()(

2

2

fpss

ssfpsssss

fpss

sfpsss

fps

fps

QQQ

QQQ

)2(nVV

2)2(1Cox/)QQ

(C

)2(Q)2(QVV

fpsTGS

fpfps

2s

ss

s

s

ox

fpssfpsFBGS

fps

s

Subthreshold characteristics

t

tGS

nV

VV

tdGn eVCVQ

)(

ox

Fss

ox

d

ox

ssd

ox

sss

sox

sss

C

qN

C

C

C

CC

C

CC

C

QQn

fps

)2(11

1)(1

2

quantum mechanical model

0

2

*

)()(

0

for )(

ii

ivi

EDED

EEgm

ED

1

/)(2

*

/)(2

*

1In

1

1)()(

iin

TkEEB

E TkEEii

NqQ

eTkm

e

mdEEfEDN

BiF

i BiF

0

2

2

2

*

2

)()(

)(

)()(2

iii

D

iiip

xNxn

Nnpq

ExxVdx

d

m

Eq. For Qn for 2 D gas as function of Ei and Ef.

Schrodinger eq. For Ei and the Poisson equation for Vp

Equation for n(x): n(x) determines Vp => Ei and Ni(Qn)

0 2 4 6 8 100

1x1020

2x1020

3x1020

Gate Material: n+ polysilicontox: 2 nm

Substrate doping: 1018 /cm3

Vg=1.0V

Ele

ctro

n D

en

sity

(/c

m3 )

Distance (nm)

Quantum Semi-Classical

0 2 4 6 8 101012

1013

1014

1015

1016

1017

1018

1019

1020

Gate Material: n+ polysilicontox: 2 nm

Substrate doping: 1018 /cm3

Vg=1.0V

Ele

ctro

n D

ensi

ty (

/cm

3 )Distance (nm)

Quantum Semi-Classical

quantum mechanical model

C-V Characteristics

• One of the most powerful experimental method to know the MOS surface is measurement of gate capacitance CG vs VG.

• Here, DC VG is applied and a small signal is applied with a certain frequency so that the current through the gate is measured and transformed to Capacitance.

• DC VG is scanned so that C-VG can be plotted.

C-V Characteristics(2)

• The applied frequency is so low that the electron concentration can be responded so that Eq. (1) with relation always hold.

• If high frequency is applied so that electron cannot be responded to the applied signal, high frequency characteristics is observed.

SSQ

• Differentiating Eq.(1) with respect to ,

G

S

OXG

gate

G

G

QCQ

V

Q

V

1

S

S

OXG

gate

QCQ

V

1


• Notice that this Eq. can be written as

G

S

OXG

gate

G

G

QCQ

V

Q

V

1

S

S

OXG

gate

QCQ

V

1

SOXgateG CCCC

1111

C-V Characteristics

• Above Fig. shows that approximate Cs behavior. The following feature should be

noticed. and .

• Notice that from , can be found, so the

• Then can be obtained from .

d

SGFBG L

CVV

, min, CCVV GFBG

dNC ,min dL

FBF dS L

ndS CCC


• Let us first consider Cs.

From Eq. (2), Cs can be easily found as,

S

SS d

dQC

S

S

d

tS d

dF

L

V

2

• Fig. 2 shows that approximate Cs behavior. The following feature should be

noticed. and .

• Notice that from , can be found, so be .

Then can be obtained from .

d

SGFBG L

CVV

, min, CCVV GFBG

dNC ,min dL

FBF dS L

Effects of quantum mechanical model on CVFrom C. Richter's, EDL p.35, Jan 2001)

1-1. MOSFET current : General Band diagram

VGS

VBS

VDSVS

x

y

1-2.Classical approximation above threshold

Above threshold, current is mainly due to the drift.

V

CVVC

QVVCyQ

fps

soxsTGSox

sdsTHGSoxn

2

)(

)()()(

soxsFBGSox

dsFBGSoxn

ynnDn

CVVC

yQVVCyQ

EQvQdxyxvyxqnJdxW

I

)(

)()()(

),(),(

Classical approximation above threshold

])2()2[(3

2

22

)(])[(

2/32/3fpfpDS

DSDS

fpFBGSoxnDS

snssFBGSox

V

VV

VVCL

WI

yVVWCI

DSDSTGSoxn

DSDSFFFBGSoxnDS

VVVVCL

W

VVVVCL

WI

2

1

2

122

Classical approximation above threshold (pinch off voltage)

FDSFDSFBT

TGSox

FDSoxDSFFBGSoxn

VVVLV

LVVC

VCVVVCLQ

22)(

)((

2)2()(

GSfpsatDSfpsatDSFB VVVV 22 , ,

The equation for VDS,sat due to pinch off is

1-3. below threshold (Subthreshold characteristics)

)0(2)0( /2d

V

t

s

d

tsn Qee

VL

VQ tsFp

tDSFps

tFpDSs

tDSsFp

VVtd

DSsVV

tDSsAs

sdVV

t

Ds

d

tsn

eVC

VeVVqN

QeeV

V

L

VLQ

/)2(

/)2(

/)(2

2

)(2)(

)1(1

)()0(

//)2(tDStFps VVV

tdn

nnnD

eeVCL

WD

L

LQQWDI

Current in the subthreshold region is assumed to be due to diffusion,

Classical approx. below threshold (Subthreshold characteristics)

Now the relationship between and VGS-VT is,Fps 2

)2(

1 1

1)(

1

)2(

2

ox

Fss

ox

d

ox

ssd

ox

sss

sox

sss

fpsTGS

C

qN

C

C

C

CC

C

CC

C

QQn

nVV

Fs

Classical approx. below threshold (Subthreshold characteristics)

t

tGS

nV

VV

tFdnDS eVCDL

WI

)2(

1-4. Mobility in the inversion layer

S. Takaki et. al, "On the universality of inversion layer mobility in N- and P- channel MOSFET's," IEDM, pp.398-401, 1988.

Mobility enhancement

Enhancement of the MOS mobility is one of the key

Issues to enhance the CMOS circuit performance.

1) Lowering the vertical field

2) Using the strained layer to change the effective mass

3) Stress induced mobility change is used as the molecular sensor.

Mobility enhancement( from Tagaki, IEDM short lecture , 2003)

Using the strained layer to change the effective mass.

[5] J. J. Welser, J. L. Hoyt and J. F. Gibbons, IEDM Tech. Dig., 1000 (1992)

Mobility Enhancement

special issue on the nano devices 서울대 나노 협동과정 & 나노 응용시스템...

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