[06] Chapter06_Electrical Characteristic of MOSFETs

7/22/2019 [06] Chapter06_Electrical Characteristic of MOSFETs

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Introduction to VLSI Circuits and Systems, NCUT 2007

Chapter 6

Electrical Characteristic of MOSFETs

Introduction to VLSI Circuits and Systems

Dept. of Electronic Engineering

National Chin-Yi University of Technology

Fall 2007


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Outline MOS Physics

nFET Current-Voltage Equations

The FET RC Model

pFET Characteristic

Modeling of Small MOSFETs


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MOS Physics MOSFETs conduct electrical current by using an

applied voltage to move charge from the source to

drain of the device Occur only if a conduction path, or channel, has been

created

The drain current IDn is controlled by voltages applied tothe device

Figure 6.1 nFET current and voltages

IDn = IDn(VGSn, VDSn) (6.1)


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Field-effect Simple MOS structure

Silicon dioxide (SiO2) acts as an insulator

between the gate and substrate

Cox determines the amount of electricalcoupling that exists between the gate electrodeand the p-type silicon region

What isField-effect ?

The electric field induces charge in thesemiconductor and allows us to control the currentflow through the FET by varying the gate voltageVG

Figure 6.2 Structure of the MOS system

Figure 6.3 Surface charge density Qs

ox

oxox

tC

= (C/ cm2) (6.2)

Where, tox is the thickness of the oxide in cm

cmFox /10854.8,9.314

00

==

]/[ 2cmCVCQ Goxs = (6.3)


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Threshold Voltage At the circuit level, Vth is obtained by KVL

The oxide voltage Vox is the difference (VG - )and is the result of a decreasing electric potentialinside the oxide

soxG VV +=

Figure 6.4 Voltages in

the MOS system

(6.4)

Where, Vox is the voltage drop across the oxide layerand is the surface potential that represents thevoltage at the top of the silicon

s

s


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Electric Fields of MOS (1/2)

Figure 6.5 MOS electric fields

Lorentz law: an electric field exerts a force on acharged particle

A depleted MOS structure cannot support theflow of electrical current

EQF particle=

qEFh +=

qEFe =

(6.5)

saSiB NqQ 2=

oxoxB VCQ =

(6.6)

(6.7)

(6.8)

(6.9)

(positively charged holes)

(negatively charged electrons)

Figure 6.6 Bulk (depletion)

charge in the MOS system

(bulk charge)

Where 08.11 Si

(the oxide voltage isrelated to the bulk charge)


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Electric Fields of MOS (2/2)

For VG < VTn, the charge is immobile bulk chargeand QS= QB

For VG > VTn, the charge is mode up of two distinctcomponents such that

If VG

= VTn

, then Qe

= 0

If VG > VTn, then

0


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Outline MOS Physics


The FET RC Model

pFET Characteristic



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nFET The dimensionless quantity (W/L) is the

aspect ratio that is used to specify the

relative size of a transistor with respect toothers

The MOS structure allows one to controlthe creation of the electron charge layer Qeunder the gate oxide by using the gate-

source voltage VGSn

Figure 6.8 Details of the nFET structure

(a) Side view (b) Top view

Figure 6.9 Current and voltages for an nFET

(a) Symbol (b) Structure

LLL = '

WWW = '

(6.19)


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Channel Formation for nFET Cutoff mode as Figure 6.10 (a)

IfVGSn < VTn, then Qe = 0 andIDn = 0

Like an open switch

Active mode as Figure 6.10 (b)

If VGSn > VTn, then Qe 0 andIDn = F(VGSn,VDSn)

Like an closed switch Figure 6.10 Controlling the channel in an nFET

(a) Cutoff (b) Active bias

Figure 6.11 Channel formation in an nFET

(a) Cutoff (b) Active


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nMOS IVCharacteristics (1/2)

Three region for nMOS

According Figure 6.12 (Model I, VDSn = VDD)

Figure 6.12 I-Vcharacteristics

as a function of VGSn

TnGS VV


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nMOS IV Characteristics (2/2)

According Figure 6.13 (Model II, VGSn > VTn)

Figure 6.13 I - Vcharacteristicsas a function of VDSn

[ ]2

)(22 DSnDSnTnGSnn

Dn VVVVI =

0=

DSn

Dn

V

I

[ ] 02)(2)(22

==

DSnTnGSnDSnDSnTnGSnDSn

VVVVVVVV

TnGSncurrentpeakDSnsat VVVV == |

2)(

2

TnGSn

n

Dn VVI =

[ ])(1)(2

2satDSnTnGSn

n

Dn VVVVI +=

2

2 satnDn VI

=

(6.29)

(6.30)

(6.31)

(6.32)

(6.33)

(6.34)

(6.35)

(saturation current)

(active region current)

Figure 6.14 nFET familyof curves

(saturation voltage)

Where (V-1) is channel length modulation parameter


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Body-bias Effect Body-bias effects: occur when a voltage VSBn exists

between the source and bulk terminals

Figure 6.15 Bulk electrode andbody-bias voltage

)22(0 FSBnFnTTn VVV ++=

00 | == SBnVTnnT VV

ox

aSi

C

Nq 2=

(6.45)

(6.46)

(6.47)

Where is the body-bias coefficient with units of V1/2,and is the bulk Fermi potential term1

F2

(zero body-bias threshold voltage)

Where q = 1.6 10-19 C, Si = 11.8 0 is the permittivityof silicon, and Na si the acceptor doping in the p-typesubstrate


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Outline

MOS Physics


The FET RC Model

pFET Characteristic



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Non-linear and Linear

The difference between analysis and design

Since non-linearI-Vcharacteristics issue

Analysis deals with studying a new networkfrom the design, and designers are true problemsolvers

Two approaches to dealing with the problem

of messy transistor equations Let circuit specialists deal with the issues

introduced by the non-linear devices

Create a simplifies linear model since VLSI

design is based on logic and digital architectures

Figure 6.19 RC model of an nFET

(a) nFET symbol

(b) Linear model for nFET


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Drain-Source FET Resistance

Figure 6.20 Determiningthe nFET resistance

In practical, FET are inherently non-linear

Dn

DSn

n I

VR =

DSnTnGSnnDn VVVI )(

)(

1

TnGSnn

nVV

R

])(2[2

DSnTnGSnn

nVVV

R

=

n

nR

1

n

nnL

W

= '

)( TnDDnn

VVR

=

= )( 1 TnDDnn

VVR

(6.64)

(6.65)

(6.66)

(6.67)

(6.68)

(6.69)

(6.70)

(6.71)

(drain-source resistance)

(at a point in Figure 6.20)

(at b point in Figure 6.20)

2)(

2

TnGSnn

DSn

nVV

VR

=

(6.72)

(at c point in Figure 6.20)


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FET Capacitances

The maximum switching speedof a CMOScircuit is determined by the capacitances

When we have C = C(V), the capacitanceis said to be non-linear

Figure 6.21 Gate capacitance in a FET

(a) Circuit perspective (b) Physical origin

GoxG ACC =

'WLCCoxG

=

GDGGS CCC 2

1

Figure 6.22 Gate-source andgate-drain capacitance

(6.76)

(6.77)

(6.78) (ideal model)


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Junction Capacitance (1/2)

Semiconductor physics reveals that a pn junctionautomatically exhibits capacitance due to the opposite

polarity charges involved is called junction or depletioncapacitance

Such that the total capacitance is (CSB and CDB)

Two complications in applying this formula to the nFET First, this capacitance also varies with the voltage (C= C(V))

Second in next slide

Figure 6.23 Junction

capacitance in MOSFET

)(0 FACC pnj= (6.82)

WhereApn is the area of the junction in unitsof cm2, and Cj is determined by the process,and varies with doping levels

Figure 6.24 Junction capacitancevariation with reverse voltage

jm

o

RV

CC

+

=

1

0

= 2ln

i

ado

nNN

qT

(6.83)

(6.84) (built-in potential)


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Junction Capacitance (2/2)

Second, we need to consider in calculating the pnjunction capacitance is the geometry of the pn junctions

Figure 6.25 Calculation of the

FET junction capacitance

(a) Top view

(b) Geometry

XWAbot=

XWCC jbot=

swjjjsw PxxXxWA =+= )(2)(2

)(2 XWPsw +=

faradsPCC swjswsw=

cmFxCC jjjsw /=

)( oLXX +

swjswbotjswbotn PCACCCC +=+=

jswj m

osw

swjsw

m

o

botj

n

V

PC

V

ACC

+

+

+

=

11

(6.85)

(6.86)

(6.87)

(6.88)

(6.89)

(6.90)

(6.91)

(6.92)

(6.93)

(1. bottom section)

(2. sidewall)

(sidewall capacitance per unit perimeter)

(sidewall perimeter)

(non-linear model)

(1 + 2)

(including the overlap section)


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Construction of the Model

Parasitic resistance and capacitance of MOS

It is important to note that the resistance Rn isinversely proportional to the aspect ratio(W/L)n, while the capacitances increase withthe channel width W

Figure 6.25 Calculation of theFET junction capacitance

(b) Linear modelfor nFET

Figure 6.26 Physical visualizationof FET capacitances

(a) nFET

SBGSS CCC +=

DBGDD CCC +=

(6.94)


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Outline

MOS Physics


The FET RC Model

pFET Characteristic


Reference for Further Reading Problems


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pFET Characteristic (1/4)

nFET translates to pFET

Change all n-type regions to p-type regions

Change all p-type regions to n-type regions

Note, both the direction of the electric fieldsand the polarities of the charges will beopposite according equation (6.101)

n-well is tied to the positive power supply

Figure 6.29 Transforming annFET to a pFET

Figure 6.30 Structural detail of a pFET

(a) Side view (b) Top view

ox

ox

oxt

C = (6.101)


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VSGp determines whether the gate is sufficientlynegative with respect to the source to create a layer

of holes under the gate oxide and thus establish apositive hole charge density of Qh C/cm

2

Figure 6.31 Current andvoltages in a pFET

(a) Symbol

(b) Structure

)(0 TpSGph VVforQ

ox

IFBpFpFpdSi

ox

Tp

C

qDVNq

C

V += 2)2(21

=

i

d

Fpn

N

q

kTln22

(6.102)

(6.103)

(6.104)


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Figure 6.33 Gate-controlled pFETcurrent-voltage characteristics

(b) Active bias

Figure 6.32 Conductionmodes of a pFET

(a) Cutoff

2)(2

TpSGp

p

Dp VVI =

p

ppL

Wk

= '

oxpp Ck ='

3~2=p

nr

n

nnL

W

= '

p

ppL

W

= '

(6.105)

(6.106)

(6.107)

(6.108)

(6.109)


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Figure 6.34 pFET I V family of curves

TpSGpsat VVV =

[ ]2)(22

SDpSDpTpSGpp

Dp VVVVI =

2)(2

TpSGp

p

Dp VVI =

(6.110)

(6.111)

(6.112)


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Outline

MOS Physics


The FET RC Model

pFET Characteristic



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Scaling Theory (1/2)

s

LL

s

WW ==

~~

2

~

s

AA=

=

~

~

L

W

L

W

ox

oxox

tC =

s

tt oxox =~

ox

ox

oxox sC

s

tC =

= ~

sL

Ws =

= '~

)(

1

TDD VVR

=

)(1

~

TDD VVsR

=

s

RR=

~

(6.118)

(6.119)

(6.120)

(6.121)

(6.122)

(6.123)

(6.124)

(6.125)

(6.126)

(6.127)


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Scaling Theory (2/2)

s

VV

s

VV TT

DDDD ==

~~

,

RR=~

s

VV

s

VV GSGS

DSDS ==

~~

,

s

I

s

V

s

V

s

V

s

VsI DDSDSTGSD =

=

2

22

2

2

~~~

s

IVIVP DDSDDS ==

(6.128)

(6.129)

(6.130)

(6.132)

(6.133)

[ ]2)(22

DSDSTGSD VVVVI = (6.131)

[06] Chapter06_Electrical Characteristic of MOSFETs

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