EE143 F2010 Lecture 22 Electrical Characteristics of MOS ...ee143/fa10/lectures/Lec_22.pdf ·...

Professor N Cheung, U.C. Berkeley

Lecture 22EE143 F2010

1

Electrical Characteristics of MOS Devices

• The MOS Capacitor

– Voltage components

– Accumulation, Depletion, Inversion Modes

– Effect of channel bias and substrate bias

– Effect of gate oxide charges

– Threshold-voltage adjustment by implantation

– Capacitance vs. voltage characteristics

• MOS Field-Effect Transistor

– I-V characteristics

– Parameter extraction

“metal”

oxide

semiconductor

VG

+

xox

“metal”

oxide

semiconductor

VG

+

xox



2

2) Visit the Device Visualization Website

http://jas.eng.buffalo.edu/

and run the visualization experiments of

1) Charge carriers and Fermi level,

2) pn junctions

3) MOS capacitors

4) MOSFETs

1) Reading Assignment

Streetman: Section of Streetman Chap 8 on MOS



3

Work Function of Materials

Eo

EV

ECq

SEMICONDUCTOR

Ef

Eo

Ef

METAL

Work function

= q

Vacuum

energy level

qM is determined

by the metal material

qS is determined

by the semiconductor material,

the dopant type,

and doping concentration



4

Work Function (qM) of MOS Gate Materials

Eo = vacuum energy level Ef = Fermi level

EC = bottom of conduction band EV = top of conduction

band

Ef

Examples:

Al = 4.1 eV

TiSi2 = 4.6 eV

Ef

Eo

qM

Eo

qM

Ei

EC

EV

0.56eV

q = 4.15eV

0.56eV

q = 4.15eV (electron affinity)

Eo

Ei

EC

EV

0.56eV

q = 4.15eV

0.56eV

Ef

n+ poly-Si

(Ef = EC)p+ poly-Si

(Ef = EV)

qM



5

Work Function of doped Si substrate

q = 4.15eV

Ef

Eo

qs

Ei

EC

EV

|qF|

0.56eV

0.56eV

* Depends on substrate concentration NB

Ef

Eo

qs

Ei

EC

EV

|qF|

0.56eV

0.56eV

q = 4.15eV

n-type Si p-type Si

s (volts) = 4.15 +0.56 - |F| s (volts) = 4.15 +0.56 + |F|

i

BF

n

N

q

kTln



6

The MOS Capacitor

SioxFBG VVVV

ox

oxox

xC

[in Farads /cm2]

+_ VFB

Vox (depends on VG)

Vsi (depends on VG)

+

_

+

_

“metal”

oxide

semiconductor

VG

+

xox

Oxide capacitance/unit area



7

Flat Band Voltage

• VFB is the “built-in” voltage of the MOS:

• Gate work function M:

Al: 4.1 V; n+ poly-Si: 4.15 V; p+ poly-Si: 5.27 V

• Semiconductor work function S :

• Vox = voltage drop across oxide (depends on VG)

• VSi = voltage drop in the silicon (depends on VG)

SMFBV

s (volts) = 4.15 +0.56 - |F| for n-Si

s (volts) = 4.15 +0.56 + |F| for p-Si



8

A) Accumulation: VG < VFB for p-type substrate

VSi 0, so Vox = VG - VFB

QSi’ = charge/unit area in Si

=Cox (VG - VFB )

MOS Operation Modes

M O Si (p-Si)

Thickness of accumulation layer ~0

holes

Charge Distribution



9

MOS Operation Modes

• B) Flatband Condition : VG = VFB

No charge in Si (and hence no charge in metal gate)

• VSi = Vox = 0

M O S (p-Si)

Charge Distribution



10

C) Depletion: VG > VFB

MOS Operation Modes (cont.)

M O S (p-Si)

qNB

xd

s

2

dB

ox

dBFBG

2

xqN

C

xqNVV

(For given VG, can solve for xd)

B

SiSid

qN

V2x

VoxVSi

Depletion layer

Charge Distribution

Depletion

Layer

thickness

Note: NBxd is the total

charge in Si /unit area



11

x

x=0

Q'

Metal

(x)

Oxide

x=xo

x

xd

x=0

Q'

Metal Semiconductor

(x)

Oxide

x=xo

x=xo+

Q'-

x

xd

x=0

Q'

Metal Semiconductor

(x)

Oxide

x=xo

x=xo+

Semiconductor

Depletion Mode :Charge and Electric Field Distributions

by Superposition Principle of Electrostatics

x

xd

x=0

Metal SemiconductorE(x)

Oxide

x=xo

x=xo+

x

xd

x=0

Metal Semiconductor

E(x)

Oxide

x=xo

x=xo+

x

xd

x=0

Metal Semiconductor

E(x)

Oxide

x=xo

x=xo+

=+



12

D) Threshold of Inversion: VG = VT

nsurface = NB (for p-type substrate)

=> VSi = 2|F|


M O S (p-Si)

qNB

xdmax

F

ox

BFs

FBTGC

qNVVV

2

22 )(

Q’n

This is a definition

for onset of

strong inversion



13

E) Strong Inversion: VG > VT


M O S (p-Si)

qNa

xdmax

)(

max

TGoxn

ox

ndB

ox

VVCQ

C

QxqNV

B

FSi

dqN

x

4

max

Q’n

electrons

xdmax is approximately unchanged

when VG> VT



14



15



16

p-Si



17

Accumulation

Depletion

Inversion

Vox = Qa/Cox

VSi ~ 0

Vox =qNaxd/Cox

VSi = qNaxd2/(2s)

Vox = [qNaxdmax+Qn]/Cox

VSi = qNaxdmax2/(2s)

= 2|F|

Voltage drop = area under E-field curve

* For simplicity, dielectric constants assumed to be same for oxide and Si in E-field sketches



18

Most derivations for MOS shown in lecture notes

are done with p-type substrate (NMOS)

as example.

Repeat the derivations yourself for n-type substrate

(PMOS) to test your understanding of MOS.

Suggested Exercise



19

VG

(more

positive)VFB VT

Accumulation

(holes) depletionstrong inversion

(electrons)

p-Si substrate (NMOS)

n-Si substrate (PMOS)

VG

(more

negative)VFBVT

Accumulation

(electrons)depletionStrong inversion

(holes)



20



21



22



23



24



25

C-V Characteristic

C/Cox

VT

1

VG

p-type

substrate

a

c

d

b

e

C/Cox

VT

1

VG

n-type

substrate

a

c

d

b

e

a) accumulation: Cox

b) flatband: ~Cox (actually a bit less)

c) depletion: Cox in series with the Cdepl

d) threshold: Cox in series with the minimum Cdepl

e) inversion: Cox (with some time delay!)



26

Accumulation

Depletion

Inversion

Q

Q

Q

Q

Q

Q

Low frequency High frequency

Q

Q

All frequencies

All frequencies

C = Cox

C = Cox 1/C = 1/Cox + xdmax/s

1/C = 1/Cox + xd/s

Small signal charge response Q due to VG



27

SioxFBBG VVVVV

net bias across MOS

M

O

p-Si

V

VG

C

inversion

electrons

depletion

region

VB

n+n+

Effect of Substrate Bias VB and Channel Bias VC



28

s

da

OX

daFBBG

BCpSi

XqN

C

XqNVVV

VVV

max2

max

2

1

2

M O SiEi

Efs

q(VC-VB)

Efn

pq

pq

s

daSi

XqNV

max2

2

1

At the onset of strong inversion, where VG is defined

as the threshold voltage



29

At threshold: VG – VB = VFB+Vox+VSi

But VSi = 2|p| + (VC - VB ) =>

xdmax is different from no-bias case

B

SiSid

qN

Vx

2max

VT -VB = VFB + 2sqNB(2|F| + VC-VB)

Cox + 2|F| + VC - VB

VoxVSi



30

Flat Band Voltage with Oxide charges

VFB is the Gate voltage required to create no charge in the Si

dxx

xx

CC

QV

oxx

ox

ox

oxox

f

SMFB 0

)(1

x = 0 x = xox

M O S

ox (x)Qf

ox (x) due to alkaline

contaminants or trapped

chargeQf due to broken bonds

at

Si-SiO interface



31

VT Tailoring with Ion Implantation

Nsub

Shallow implanted

dopant profile at Si-SiO2

interface (approximated as

a delta function)

• Acceptor implant gives positive shift (+ VT)

• Donor implant gives negative shift - VT

Algebraic sign of VT shift is independent of n or p substrate !

OX

iT

C

QV

Qi = q implant dose in Si



32

p-Si

implanted acceptors

Na

SiO2

Doping Profile After Implantation

SiO2

xdmax

Q

Qd

d

Qn

p-Si

(due to implanted acceptors)

Charge Distribution for V G > VT

* Valid if thickness of implanted dopants << xdmax

The VT shift can be viewed as the extra gate voltage needed to

deplete the implanted dopants ~ Qi/Cox

The delta-function approximation of implanted profile



33

Summary : Parameters Affecting VT

6

7

n+

Na

VB

5

1

2

4

3

Dopant implant near Si/SiO2 interface

fOX Q& M

xox

VCQn n+



34

+ Qf or Qox

B threshold implant

As or P threshold implant

Xox increases

Xox increases

M increases

M decreases

|VCB| increases

|VCB| increases



35

Summary of MOS Threshold Voltage (NMOS, p-substrate)

• Threshold voltage of MOS capacitor:

• Threshold voltage of MOS transistor:

Note 1: At the onset of strong inversion, inversion charge is negligible

and is often ignored in the VT expression

Note 2: VT of a MOSFET is taken as the VT value at source ( i.e., VC =VS)

Note 3 : Qi = (q implant dose ) is the charge due to the ionized donors

or acceptors implanted at the Si surface. Qi is negative for acceptors

and is positive for donors

VT = VFB + 2sqNB(2|F|)

Cox + 2|F| -

Qi

Cox

VT = VFB + 2sqNB(2|F| + |VC-VB|)

Cox + 2|F| + VC -

Qi

Cox



36

Summary of MOS Threshold Voltage (PMOS, n-substrate)

• Threshold voltage of MOS capacitor:

• Threshold voltage of MOS transistor:

* Yes, + sign for VC term but VC (<0) is a negative bias for PMOS because the

inversion holes have to be negatively biased with respect to the n-substrate

to create a reverse biased pn junction.

VT = VFB - 2sqNB(2|F|)

Cox - 2|F| -

Qi

Cox

VT = VFB - 2sqNB(2|F| + |VC-VB|)

Cox - 2|F| + VC -

Qi

Cox

EE143 F2010 Lecture 22 Electrical Characteristics of MOS ...ee143/fa10/lectures/Lec_22.pdf ·...

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