ece594a notes set 1, device models and device characteristics

ECE145A /218CA notes, M. Rodwell, copyrighted

ECE145a / 218a: Notes Set 5 device models & device characteristics:

Mark Rodwell

University of California, Santa Barbara

[email protected] 805-893-3244, 805-893-3262 fax


Content:

s.frequencie Cutoff

models (JFET) HEMT

Models MOSFET

Models TransistorBipolar


Active Devices:

Bipolar Transistors


HBT Physical Structure


Increasing total emitter area

current. specified someat bandwidth peak reach toselectedgenerally areaEmitter

current. maximum theincreases fingers) multipleor , g(increasin areaemitter theIncreasing EL

area)emitter total/(EE IJ


0

5

10

15

20

0 1 2 3 4V

ce

mA

/m

2

Bipolar Transistor: DC characteristics: common-emitter

Vce,sat

Vbr,ceo

bc II

10-12

10-10

10-8

10-6

10-4

10-2

0 0.25 0.5 0.75 1

I c ,

I b (

A)

Vbe

(V)

Ic

Ib

densitiescurrent higher at fail and

e,approximat are ipsrelationsh These

/ and

:elyApproximat

/ cb

nkTqV

sc IIeII be


HBT hybrid-Pi equivalent-circuit model

cbf Ccbi

Ccbx

Rbe

RbbB C

E

Rex

Rc

Vbe

CjeCbe,diff =gm f

gmVbee-jc

mbe gR /

0.8)~ (typically 10 cj

mom egg

collectorbasef

)/( qnkT

I

V

Ig C

BE

Cmo

circuits. somein t significan becan neglected,often though , termThe cje

resitances parasitic :,,

collector and basein sansit timecarrier tr :,

ecapacitancdiffusion :

escapacitancdepletion :,,

cb

,

ceb

diffbe

cbxcbije

RRR

C

CCC


Bipolar Transistor T-model

)(1

1

1

1

1

1

exp1

1)(

0

0

0

cb

cb

c

b

j

jj

jj

The approximations above, if taken to first order in , produce the hybrid pi model.

The T model is more convenient for common-base amplifier analysis.


How model varies as emitter area is increased

Ccbi

Ccbx

Rbe

RbbB C

E

Rex

Rc

Vbe

CjeCbe,diff =gm f

gmVbee-jc

pages. previous on the formulas by thegiven are and ,

N.:1 decrease sresistance all 1,:N increase escapacitanc All

parallel.in HBTs N wiringas same 1:Nby areaemitter theIncreasing

mbebe gRC


Active Devices:

Silicon MOSFETs


Planar Bulk MOSFET

N+ source N+ drain

source contact (silicide) drain contact (silicide)

N+ polygate

gate metal(silicide) dielectric

sidewall

gate oxide

P substrate

S D S D S D S

G

G

Wg

Cross-Section Layout (multi-finger)

P substrate

gatedielectric

N+polysilicongate

inversionlayer


MOSFET DC Characteristics

ID

VDS

increasingVGS

gthgsgoxD LVVWcI 2/)(

current limitedmobility

2

,

)(

current limitedvelocity

, thgssatgoxvD VVvWcI

1

Expression dGeneralize

,

2

,

D

D

vD

D

I

I

I

I

Id

VgsVth

mobility-limited

velocity-limited

: voltageknee thenlarger tha voltagesdrainFor


Knee Voltage: Mobility-Limited Case

VGD

=Vth

regionscurrent -constant and Ohmic the

betweenboundary thedefines voltageknee TheID

VDS

increasingVGS

Oh

mic

constant-current

thgsdsdg VVVV

whenoccurs curve in knee the

regime, limited-mobility theIn

IDR

D

VGD

=Vth

IDR

S

s.resistance drain & source parasitic theacross drops

by voltage increasedfurther is Voltage KneeThe


Knee Voltage: Velocity-Limited Case

/ whenoccurs

curve in knee theregime, limitedvelocity theIn

gsatds LvV

s.resistance drain & source

parasitic theacross drops by voltage

increasedfurther is Voltage Knee theAgain,

VDS

=vsat

Lg/

IDR

D

VDS

=vsat

Lg/

IDR

S


DC Characteristics---Far Above Threshold

/ where

1/)(for )(

gsat

thgsthgssatgoxD

LvV

VVVVVVvWcI

Id

VgsVth

V


MOSFET Transconductance

gthgsgox

GS

Dm

gthgsgoxD

LVVWcV

Ig

LVVWcI

/)(

2/)(

limitedmobility

2

,

satgox

GS

Dm

thgssatgoxvD

vWcV

Ig

VVvWcI

)(

limitedvelocity

,

Id

VgsVth

V

gm

VgsVth

V

mobility-limited

velocity-limited


Linear vs. Square-Law Characteristics: 90 nm


90 nm MOSFET DC Characteristics

3V~1/ V 6.0||

mm/S 7.0μm/mS 7.0/

channel-P

3V~1/ V 6.0

mm/S 4.1μm/mS 4.1/

channel-N

th

satoxgm

th

satoxgm

V

vcWg

V

vcWg


Device Structure and Model: multi-finger device

mi

gds

gogg

eq

gs

o

gogd

thgsg

eq

geff

eq

m

gR

NWG

WkNWLT

C

k

WkC

VVNWT

NWvT

g

/1~

mfF/)5.03.0(

or

gdb

gsb

gs

gd

endg

g

sg

NWC

NWC

NWR

NWR

N

R

N

W

LR

/1

/1

212~

CgdRg

Ri

Cgs Vg’s’

gmVg’s’ Gds

Rs

RdG

D

S

Csb

Cdb

CgdRg

Ri

Cgs Vg’s’

gmVg’s’ Gds

Rs

G

D

S

Csb

Cdb

S D S D S D S

G

G

Wg

contacts substrate ample -

fingers gateshort -

using Increase maxf


Cgd

Rin

Cgsx Vg’s’

gmxVg’s’ GdsxG

D

S

Cdb

Csb

Oversimplified Model

igsin

sm

dsdsx

sm

gs

gsx

sm

mmx

RRRR

Rg

GG

Rg

CC

Rg

gg

~

1

~

1~

1~

etc analysis, hand roughFor CgdRg

Ri

Cgs Vg’s’

gmVg’s’ Gds

Rs

G

D

S

Csb

Cdb

gdgdsigs

gddsmgdmgs

CRGRRR

ff

CRRgCgCf

2)(2~

)(//~2/1

sfrequencie cutoff eApproximat

max


Active Devices:

III-V

Field-Effect Transistors


FET with Heterojunction for Gate Barrier→ HEMT

gate. and channel betweenbarrier for

tionheterojunctor semiconduc withFET

:HEMT

Source Drain

Gate

drawing: K. Shinohara, HRL

N+ InGaAs contact layer

InAlAs gate barrier layer

undoped InGaAs channel

Brar. B.:drawing


HEMTs: Typical interdigitated structure

gate

drain

source

Note multiple gate fingers.


HEMT: approximate equivalent circuit model

Idss. Cgs, Cgd, gm, Gds all scale proportionally with gate periphery

Ri, Rs scale proportionally with (1/ gate periphery)

Rg scales proportionally to (gate finger length)/(number fingers)


HEMT DC-IV characteristics

V 0.6 c.a. thanpositive more for current draw willgate

channel; and gate between diodeSchottky

gsV

Scientific Teledyne Shinohara, K. :Data


Figures of Merit


Transistor figures of Merit

Transistor small-signal bandwidth is typically stated in terms of

the figures of merit f and fmax

In order to understand these figures of merit, we must introduce

device power gain.

These power gains will be studied in more detail

later in the course.


Definition of short-circuit current gain

Ri

Cgs Vg's

gmVg's Rds

S

G

D

D

S

G example: FET

small-signal model

Ri

Cgs Vg's

gmVg's RdsIin

Iout

short-circuit current gain:

drive input with AC current,

short output, measure

Iout/Iin

jf

f

Cj

g

I

Vg

I

ICjIV

gs

m

in

gsm

in

outgsings /


Variation of H21 with frequency: Bipolar Transistors

0

10

20

30

40

50

1 10 102

Ga

ins (

dB

)

Frequency (GHz)

h21

U

VCE

= 1 V, JC = 1.5 mA/um

2

fMAX

= 295 GHz

f = 295 GHz

fF9.6cbxC

fF2.3cbiC 48bbR

7.4exR

ebmVg 'ebV '

E

B C

diffC

fF172

jeC

fF34

R433

7000cbr

500cer

)exp( cmom jgg

fmodiff gC

R mg

H21 is plotted in dB.

because H21 is a

current gain:

)(log*20)( 211021 HHdB

jfffH

gm

//1

1)(

:/R ofeffect of Because

21


Current-gain cutoff frequency: Bipolar Transistors

collex

E

bc

E

jecollectorbase RRqI

kTC

qI

kTC

f

2

1

nbbase DT 22 satccollector vT 2

base

BC grade

collector

N+ sub collector

semi-insulating InP substrate

emitter

emittercontact

base contact

cT

b,contW

eW

ebW

underW

N- drift collector

base contact

collector contact

bT

cW

EB grade

Ccbi

Ccbx

Rbe

RbbB C

E

Rex

Rc

Vbe

CjeCbe,diff =gm f

gmVbee-jc


Current-gain cutoff frequency: Field-Effect Transistors

N+ source N+ drain

source contact (silicide) drain contact (silicide)

N+ polygate

gate metal(silicide) dielectric

sidewall

gate oxide

P substrate

)(2 gdgs

m

CC

gf

CgdRg

Ri

Cgs Vg’s’

gmVg’s’ Gds

Rs

G

D

S

Csb

Cdb


Maximum Power Transfer Theorem

gen

RMSgen

avg

genloadgenload

R

VP

RRXX

4

ispower generator available thecalled delivered,power The

***matching impedance conjugate*** called is this

and

if load togenerator from ed transferrispower Maximum

2

)(,

generator load

Vgen

RgenXgenXload Rload


Impedance Matching

Maximum power transfer can be obtained by adding a

***lossless*** (no resistances) impedance matching network

between the generator and the load:

generator load

Vgen

RgenXgenXload Rload

match

loadZ*

loadZgenZ *

genZ


Maximum Available Power Gain (if it exists)

Ri

Cgs Vg's

gmVg's Rds

generator

losslessmatchingnetwork

Rgen

Vgen


RL

load

The transistor or amplifier is connected to generator and load via lossless

matching networks. If it is possible to match at both input and output, then the

power gain is called the *maximum available gain* (MAG)

Detailed microwave circuit theory (see later notes) indicates that this

procedure often produces an oscillator (if the device is “potentially unstable”) .

In that case we must define Maximum stable gain


Maximum Stable Power Gain (if MAG does not exist)

If the device is potentially unstable (usually due to strong feedback through

Cgd as indicated), addition of a minimum amount of series/shunt resistance to

the device input/output will prevent oscillation, and the device can then be

matched. The resulting power gain is called the

Maximum stable power gain.

Ri

Cgs Vg's

gmVg's

Rds

generator


Rgen

Vgen


RL

load

resistiveloss

(stabiliz-ation)


Unilateral power gain

Ri

Cgs Vg's

gmVg's Rds

generator


Rgen

Vgen


RL

load

seriesfeedback

shuntfeedback

If the device is potentially unstable (due to strong feedback ), addition of

lossless reactive feedback as indicated can cancel the feedback and prevent

oscillation. The device can then be matched. The resulting power gain is called

Mason’s invariant power gain **or** the Unilateral power gain , U.


Power-Gain Cutoff Frequency (Fmax)

This is the frequency at which the device Unilateral power gain reaches

unity.

The maximum available gain (either in the forward or reverse direction)

also reaches unity at the same frequency

cbibbcbibbcebb

ce

dggdsgsi

CR

f

CRfRR

ff

R

CRfGRRR

ff

82/2

:large) being ( sTransistorr For Bipola

2)(2

:sTransistor Effect-For Field

max

max

CgdRg

Ri

Cgs Vg’s’

gmVg’s’ Gds

Rs

G

D

S

Csb

Cdb

Ccbi

Ccbx

Rbe

RbbB C

E

Rex

Rc

Vbe

CjeCbe,diff =gm f

gmVbee-jc


Power gains of a typical transistor

0

5

10

15

20

25

30

35

40

1 10 100

Ga

ins, d

B

Frequency, GHz

MAG/MSG

common base

U: all 3

MAG/MSG

common collector

MAG/MSG

common emitter

The inflection in the curves is the break between unstable (MSG) at lower frequencies

and stable (MAG) at higher frequencies.

MAG/MSG is directly relevant for RF/microwave/mm-wave IC design.

Because U has -20 dB/decade slope, it is used to extrapolate measurements to determine fmax

fmax


End


Appendix

(optional)


Bipolar Transistor

Operation


Bipolar Transistor ~ MOSFET Below Threshold

ceV

voltagecollector with little varies

it through pass base reaching electrons allAlmost

)/exp(

al)(exponenti thermalison distributienergy emitter Because

c

bec

I

kTqVI


Bipolar Transistor ~ MOSFET Below Threshold

cI

beV ceV

voltagecollector with little varies

it through pass base reaching electrons allAlmost

)/exp(

al)(exponenti thermalison distributienergy emitter Because

c

bec

I

kTqVI


HBT Equivalent

Circuit Model


Physical structure, symbolic

base

BC grade

collector

N+ sub collector

semi-insulating InP substrate

emitter

emittercontact

base contact

cT

b,contW

eW

ebW

underW

N- drift collector

base contact

collector contact

bT

cW

EB grade

drawing lar toperpendicu

LengthStripe Device EL


Bipolar Transistor DC-IV Characteristics


Bipolar Transistor: Carrier Transit Times


Base resistance & collector-base capacitance

2008 Feb.IEEE Proc.2001, Nov. EDLIEEE Rodwell(see class of scope beyond Details

and into of splitting ddistribute are and

12

1

6

1

2

emitterunder spreading contact under spreading rmcontact te

torsemiconduc

__

,

,

cbicbxcbcb bb

c

eccb

sheetbase

E

Esheetbase

E

contactb

contbE

contactbb

bb

CCCCR

T

LWC

L

W

L

W

WLR

R

drawing lar toperpendicu

LengthStripe Device EL


HBT RC Parasitics

base contact width

< 2 transfer lengths

→ simple analysis

Limiting case of

Pulfrey / Vaidyanathan

fmax model.


HBT RC Parasitics

emitteremittercontactex AR /,

Eesspread LWR 12/ ELlength emitter

Egapsgap LWR 4/

Ebcscontactspread LWR 6/,

contactsbasebcbasecontactcontact AWR _, /

cemitterecb TAC /,

cgapgapcb TAC /,

ccontactsbasecontactcb TAC /_,


Base-Collector Time Constant & Fmax.

where8

max

cbibbCR

ff

)(

)2/(

,,

,,

,

spreadgapcontactspreadcontactecb

gapcontactspreadcontactgapcb

contactcontactcbcbibbcb

RRRRC

RRRC

RCCR


Relationship to HBT Equivalent Circuit Model

contactspreadcontactgapspreadbb RRRRR ,

contactcbgapcbecbcbicbx CCCCC ,,,

)(

)2/(

,,

,,,

spreadgapcontactspreadcontactecb

gapcontactspreadcontactgapcbcontactcontactcbcbibb

RRRRC

RRRCRCCR


Field-Effect Transistor

Operation (Approximate)


Field-Effect Transistor Operation

source drain

gate

Positive Gate Voltage

→ reduced energy barrier

→ increased drain current


FETs: Basic Operation

chdC

/ where/ electrongd vLQI

/~ DACgs

/ and / where chdgdgsmdsdsgsmd CGCgVGVgI

dschdgsgs VCVCQ


FET Characteristics

chdC /~ DACgs

dsdsgsmd VGVgI

ID

VDS

increasingVGS

electrongchdgdgsm vLCGCg / / /


FET Parasitic Capacitances (Estimate)

oxgm TvWg /~/

oxgggs TLWC /~/

~/, gfgs WC

subcgsb TLWC /~/

~/ ggd WC

ece594a notes set 1, device models and device characteristics

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