ElectronicsI-PhysicsofBipolarTransistors

claudio talarico 1

N+ PE

Chapter5

Fall2017

N- C

B

B

CE

TypesofBipolarTransistors

Figure- Asimplifiedstructureofthenpn transistor

Figure- Asimplifiedstructureofthepnp transistor.

n+ p n-

ThinBase

p+ n p-

ThinBase

Figure– Symbolofthenpn transistor

Figure– Symbolofthepnp transistor

2

source:Sedra &Smith

Physicalstructureofannpn BJT

ClaudioTalarico 3

Figure- SimplifiedCross-sectionofannpn BJT.

Figure- npn BJTsymbol

+

-

source:Gray&Meyer

source:Sedra &Smith

NPNBJToperatingin“Forward”ActiveMode

ConceptualView:

4

• Deviceactsasavoltagecontrolledcurrentsource• VBE controlsIC

• TheBEjunctionisforwardbiased(VBE >0)andtheBCjunctionisreversebiased(VBC <0←→ VCB >0)

• Thedeviceisbuiltsuchthat:• TheBASEregionisverythin• TheEMITTERdopingismuchhigherthanthe

BASEdoping(NE(donors)>>NB(acceptors))• TheCOLLECTORdopingismuchlowerthan

theBASEdoping(NB(acceptors)>>NC(donors))

V"#V$

V"#B

E

C

+

-

source:B.Murmann

𝐼& ∝ exp𝑉-.𝑉/

𝐼- ≪ 𝐼&

𝐼. = 𝐼& + 𝐼- ≈ 𝐼&

𝑉&- = 𝑉&. − 𝑉-.

ForwardBiased

ReverseBiased

C

BE

OutlineofdiscussionforNPNBJTinActivemode

• TounderstandtheoperationoftheNPNBJTinactivemode,wewilltolookat:– PropertiesofforwardbiasedPN+ junction(BE)– PropertiesofreversebiasedPN- junction(BC)– TheideaofcombiningthetwojunctionsbyaverythinP-typeregion(B)

5

source:B.Murmann

C

E

BDBC

DBE

ReverseBiased

ForwardBiased

AlthoughthedevicecontainstwoPNjunctionsitcannotbemodeledastwobacktobackdiodes.

ThedopinglevelsanddimensionsofEandCarequitedifferent(NE >>NCandAC >>AE).Thedeviceisnotsymmetric:EandCcannotbeinterchanged

source:Razavi

+

-

Mainidea• MaketheP-region(B)ofthePN+junction(BEjunction)very

thinandforwardbiasit– ThiswaytheelectronsinjectedfromtheN+ side(E)intothe

Pside(B)cannotrecombinemuch

• AttachanN- region(C)to the P-region(B)and reverse biasthe resulting PN- junction (BCjunction)– Thisway most of the electrons injected into the P-region(B)are swept

into the N- region (C)before there is any significant amount ofrecombination occurring

• FinalResult:most of the electrons emitted inEwillmake itthrough Band get collected inC

ClaudioTalarico 6

VoltagepolaritiesforBJTsinactivemode

7Figure– Voltagepolaritiesandcurrentflowinbipolartransistorsbiasedintheactivemode

𝑰𝑬

𝑰𝑪𝑰𝑩

NPNVBE

𝑰𝑪𝑰𝑩

𝑰𝑬NPN

PNP

source:Razavi

𝑉-.³𝑉-.,:;𝑉&.>𝑉&.,<=/

𝑉.-³𝑉.-,:;𝑉.&>𝑉.&,<=/

CurrentsforNPNBJTinactivemode

• Primarycurrentisduetoelectronscapturedbythecollector• Two(undesired)basecurrentcomponents

– Holeinjectionintoemitter(à 0forinfiniteemitterdoping)– Recombinationinbase(à 0forbasewidthapproaching0)

8

+ -

& holes

+ -

& holes

source:Sedra &Smith

source:B.Murmann

ClaudioTalarico 9

CurrentsforNPNBJTinactivemode

source:Razavi

• TherealotofelectronsinjectedintothePregion,notthatmanyholesinjectedinN+region(NE >>NB)

• TheelectronsinjectedinthePregioncausesadiffusioncurrentdecayinginthex”directionduetorecombination(recombinationnecessitateaflowofholestobalanceouttheflowofelectrons)

injectedholes

holes&electronsrecombining

N+

N-

E

C

PB

injectedelectrons

ElectronsdiffusinginPregion

x”

-

E B C

0 WB

CarrierConcentrations

ClaudioTalarico

𝑝?& ≅ 𝑛BC/𝑁&

carrierconcentrationN+ P N-

𝑛?. ≅ 𝑁.

𝑝?. ≅ 𝑛BC/𝑁.

≈ 𝑁-≈ 𝑁&

𝑛?& ≅ 𝑁&

source:Gray&Meyer

BE(PN+)junction• Built-inPotential(PN+junctionatequilibrium:VBE=0)

11

+

+- -

(E)N+ (B)P

𝑛?F ≅ 𝑁.

𝑝?F ≅ 𝑛BC/𝑁.

𝑝GF ≅ 𝑁-

𝑛GF ≅ 𝑛BC/𝑁-

ΦF

𝐸 J 𝑢L

electronswanttodiffuse

holeswanttodiffuse

electrostaticforcepreventse-fromdiffusing

electrostaticforcepreventsh+

fromdiffusing

𝑑𝑟𝑖𝑓𝑡 𝑞𝜇G𝑝𝐸 = 𝑞𝐷G𝑑𝑝𝑑𝑥 (diffusion)

−_ 𝑑𝑉`a(bcd)

a(ebfg)=𝐷G𝜇G_

𝑑𝑝𝑝

Gcd

Gfd

≡ ΦF≡ 𝑉/

𝑝GF𝑝?F

= 𝑒𝑥𝑝ΦF𝑉/

=𝑛?F𝑛GF

ΦF = 𝑉/ J 𝑙𝑛𝑛?F𝑛GF

=𝑉/ J 𝑙𝑛𝑝GF𝑝?F

≈

≈ 𝑉/ J 𝑙𝑛𝑁.𝑁-𝑛BC

xx=0-Xn0 +Xp0 Electrostaticforceanddiffusionbalanceout:

• Thedepletionregionnarrowsanddiffusionprocessesarenolongerbalancedbyelectrostaticforces

ClaudioTalarico 12

BE(PN+)junctionwithforwardbias

+

+- -

(E)N+ (B)P

X”X’0 0

VBE

Φk = ΦF − 𝑉-.

+ -

• WithaforwardbiasappliedsomeelectronscannowdiffusefromtheN+side(wheretheyaremajoritycarriers)tothePside(wheretheybecomeminoritycarriers).Similarly,someholesdiffusefromthePsideintotheN+side

• ThismigrationofcarriersfromonesidetoanotheriscalledINJECTION

• Asaresultofinjectionstheconcentrationofminoritycarriersattheedgesofthedepletionregion(x’=0andx”=0)is“significantly”increased

ClaudioTalarico 13

BE(PN+)junctionwithforwardbias• Sinceoutsidethedepletionregion

theremustbechargeneutrality,theconcentrationsofthemajoritycarriersattheedgesofthedepletionregionmustalsoincreaseofthesameamounttheminoritycarriersincreased

• Howeverifweassumelowlevelofinjectiontheincreaseinmajoritycarriersinnotsignificantandcanbeneglected

• Thecarriersinjectedwouldliketodiffuseintotheneutralregions,butquicklyfallvictimofrecombination

• Thenumberofminoritycarriersdecayexponentiallyanddropsto1/eatthesocalleddiffusionlength(Lp andLn areontheorderofmicrons)

(E)N+ (B)P

X”X’0 0

DepletionRegion

𝑛? ≈ 𝑁. 𝑝G ≈ 𝑁-

𝑝?F

𝑝?(0) 𝑛GF

𝑛G(0)

QNR-1 QNR-2

• Importantresulttoremember– ForwardBiasincreasesthe

concentrationofelectronsatthePside’sedgeofdepletionregionbyafactorexp(VBE/VT)(LawoftheJunction)

𝑛G 0 =𝑛?F

exp ΦF − 𝑉-.𝑉/

=

=𝑛?F

exp ΦF/𝑉/exp

𝑉-.𝑉/

≈

≈ 𝑛GFJ exp𝑉-.𝑉/

≈𝑛BC

𝑁-exp

𝑉-.𝑉/

ReverseBiasedBC(PN-)junction• Reversebiasincreasesthewidthofthedepletionregionand

increasestheelectricfield• DepletionregionextendsmostlyinN- side• Anyelectronthat“somehow”makeitintothedepletion

regionissweptthroughbytheelectricfield,intotheN- region

14

P(B) N- (C)

x

x

𝜌(𝑥)

--

+ +

--

+ +𝑞𝑁&

−𝑞𝑁-𝐸L𝐸

e-

- +

CollectorCurrentforanNPNBJTinactivemode

• Firstorderexpression:– Theelectronsinjectedfromtheemitterintobase

diffusethroughbaseandthengetsweptintocollector:

– Multiplyingbytheemitterareaandchangingthesigntoobtaintheconventionalcurrent

ClaudioTalarico 15

𝐽? = 𝑞𝐷?𝑑𝑛G𝑑𝑥 oF

≅ 𝑞𝐷?Δ𝑛GΔ𝑥 = 𝑞𝐷?

𝑛G 0 − 𝑛GF0 −𝑊-

=

= −𝑞𝐷?𝑊-

𝑛GF 𝑒ars/at − 1 ≈ −𝑞𝐷?𝑊-

𝑛BC

𝑁-𝑒ars/at

source:Razavi

𝐼& ≈ 𝐴.𝑞𝐷?𝑊-

𝑛BC

𝑁-𝑒arsat = 𝐼< J 𝑒

arsat

𝐼<.𝑡𝑜𝑏𝑒𝑝𝑖𝑐𝑘𝑦

Thedeviceoperatesasavoltagecontrolledcurrentsource(itperformsvoltage-currentconversion)

-

E B C

0 WB

x”

𝐼-

𝐼&𝐼.

ElectronsdiffusinginPregion

Relationbetweencollectorcurrentandemitterarea

• Whentwotransistorsareputinparallelandexperiencethesamepotentialacrossallthreeterminals,theycanbethoughtofasasingletransistorwithtwicetheemitterarea.

ClaudioTalarico 16

𝐼& ≅ 2𝐴.×𝑞𝐷?𝑊-

𝑛BC

𝑁-𝑒arsat

source:Razavi

VBE

VCEVBE

VCE

IC IC

Parallelcombinationoftwotransistors

CH4PhysicsofBipolarTransistors 17

CharacteristicsofNPNBJTinactivemode

VBE,ON

source:Razavi

NPNBJTinactivemodebehavesasaconstantcurrentsource

• Ideally,thecollectorcurrentdoesnotdependonthecollectortoemittervoltage.Thispropertyallowsthetransistortobehaveasaconstantcurrentsourcewhenitsbase-emittervoltageisfixed.

18

VBE

VBE

VBE

VBE

𝑉&- = 𝑉&. − 𝑉-. ↔ 𝑉-& = 𝑉-. − 𝑉&.

NOTE:don’tforgettheBC(PN-)junctionmustbereversebiased

soVCE mustnotgobelowVBE

(𝑉-&≤0):

source:Razavi

19

Figure- EffectoftemperatureontheIC-VBE characteristics.AtconstantIC theVBE changesbyabout-2mV/Celsius

EffectoftemperatureonIC vs.VBEcharacteristicsforNPNBJTinactivemode

𝐼&

𝑉-.

source:Sedra andSmith

BasecurrentforNPNBJTinactivemode(1)

20

source:Sedra &Smith • Primarycurrentisduetoelectronscapturedbythecollector

• Two(undesired)basecurrentcomponents– Holeinjectionintoemitter

(à 0forinfiniteemitterdoping)– Recombinationinbase

(à 0forbasewidthapproaching0)

𝐼- = 𝐼-� + 𝐼-C ≈ 𝐼-�

recombinationinbase

holesinjectedinemitter Inmodernnarrow-base

transistorsIB1 >>IB2

np(0)

np0𝐼-C =

𝑄�,-=<.𝜏-=<.

≈12 𝑛G(0)𝑞𝐴.𝑊-

𝜏?≅12𝑞𝐴.𝑊-𝜏?

𝑛BC

𝑁-𝑒ars/atx

WB0Base

Chargeofminoritycarriers(electrons)inBASE

lifetimeelectrons𝑛G 0 − 𝑛GF ≅ 𝑛G 0

+ -

& holes

BasecurrentforNPNBJTinactivemode(2)

21

source:Sedra &Smith • Primarycurrentisduetoelectronscapturedbythecollector

• Two(undesired)basecurrentcomponents– Holeinjectionintoemitter

(à 0forinfiniteemitterdoping)– Recombinationinbase

(à 0forbasewidthapproaching0)

𝐼- = 𝐼-� + 𝐼-C ≈ 𝐼-�

recombinationinbase

holesinjectedinemitter Inmodernnarrow-base

transistorsIB1 >>IB2

=pn0

0x

𝐼-� = −𝑞𝐴.𝐷G𝑑𝑝?(𝑥)𝑑𝑥 o

F≅ −𝑞𝐴.𝐷G

𝑑𝑑𝑥

𝑛BC

𝑁.𝑒arsat 𝑒

eL�c �

F

=

=𝑞𝐴.�c�c

?��

;s𝑒�rs�t

currentduetoholesdiffusinginemitter

+ -

& holes

BasecurrentforNPNBJTinactivemode(3)

22

• Primarycurrentisduetoelectronscapturedbythecollector

• Two(undesired)basecurrentcomponents– Holeinjectionintoemitter

(à 0forinfiniteemitterdoping)– Recombinationinbase

(à 0forbasewidthapproaching0)

𝐼- = 𝐼-� + 𝐼-C ≈ 𝐼-�

recombinationinbase

holesinjectedinemitter Inmodernnarrow-base

transistorsIB1 >>IB2

Importantresult:IB isaconstantfractionofIC (---->bF =IC/IB)

𝐼- = 𝐼-� + 𝐼-C = 𝑞𝐴.�c�c

?��

;s+ �

C�=s�r�f

?��

;r𝑒�rs�t

currentduetoholesdiffusinginemitter

recombinationcurrentinbase

𝐼& ≈ 𝐴.𝑞𝐷?𝑊-

𝑛BC

𝑁-𝑒arsat = 𝐼< J 𝑒

arsat

𝛽� =𝐼&𝐼-=

1𝑊-

C

2𝜏?𝐷?+𝐷G𝐷?

𝑊-𝐿G

𝑁-𝑁.

Asexpected:bF ismaximizedbyminimizingWB andmaximizingNE/NB

Largesignal(DC)modelofNPNBJTinactiveregionsource:GrayandMeyer

IC IC

𝐸 𝐸

IEIE

Figure- Simplifiedmodel;veryusefulforbiaspointcalculations(assuminge.g.VBE(on)=0.8V)

𝐼- =𝐼&𝛽�

=𝐼<𝑒

arsat

𝛽�

𝛽� ∴𝐼&𝐼-

𝛼� ∴𝐼&𝐼.=

𝐼&𝐼- + 𝐼&

=𝛽�

𝛽� + 1

(ideallyinfinite:IB=0)

(ideallyone)

• Thesubscript“F”indicatesthatthedeviceisassumedtooperateintheforwardactiveregion(BEjunctionforwardbiased,BCreversebiased,asassumedsofar)• Moreonotheroperating

regionssoon…

Smallsignal(AC)modelofNPNBJTinactivemode

24

source:Razavi

𝑽𝑩𝑬𝑸

𝑸

𝚫𝑽𝑩𝑬

𝚫𝑰𝑪 ≅ 𝒈𝒎 𝚫𝑽𝑩𝑬𝑰𝑪𝑸

• Thetransconductance gm expressesthe“strengthofthedevice(howwellthecontrollingvoltageisconvertedinacurrent)

𝑔� =𝑑𝐼&𝑑𝑉-.

=𝑑

𝑑𝑉-.𝐼<𝑒

arsat =

𝐼&𝑉/

𝑔� =𝑑𝐼-𝑑𝑉-.

=𝑑 𝐼&/𝛽�𝑑𝑉-.

=𝑔�𝛽�

ib icCommonnotations:Δ𝑉-. ≡ 𝑣�� ≡ 𝑣�Δ𝐼& ≡ 𝑖�Δ𝐼- ≡ 𝑖�

Δ𝑉&. ≡ 𝑣��𝑟� = 1/𝑔� ≡ ℎB�𝛽� ≡ ℎ�� ≅ 𝛽�≡ ℎ�.

ie

Flavorsofb (withBJT inforwardactivemode)

€

ICIB≡ βF ≡ hFE← DC beta

ΔICΔIB

≡ β f ≡ h fe← AC beta

TofirstorderweassumeβDC ≈βAC

25

Inotherwordsweassume bF isconstant(we’llseelaterthatisnotalwaysaccurate) VBE(linearscale)

ln(I)

ln(bF)

Let’sfinallybuildanamplifier!

ClaudioTalarico 26

𝑣B?

𝑉� ¡ = 𝑉� ¡ + 𝑣� ¡𝑣B? 𝑣� ¡

𝑉-. =

𝐼< = 3×10e�£𝐴𝛽 = 100

𝐼& = 𝐼<𝑒arsat ≅ 6.92𝑚𝐴

𝑔� =𝐼&𝑉/

≅ 266𝑚𝑆

𝑟� =𝛽𝑔�

≅ 376Ω

𝐴a =𝑣� ¡𝑣B?

= −𝑔�𝑅�≅ −26.6

ItlookslikebyincreasingRCwecangetwhatevergainwewant.Thissoundstoogoodtobetrue!Theremustbelimitationswearemissing!

source:Razavi

PracticalLimitations• Firstofallforthedevicetobehaveasavoltagecontrolledcurrentsource

wemustoperateinforwardactivemode(BEmustbeforwardbiasedandBCreversebiased)– AsRCincreases,VCEdropsandeventuallyforwardbiasesthecollector-basejunction.This

willforcethetransistoroutofforwardactiveregion.– Therefore,thereexistsamaximumtolerable

collectorresistance

• Second,Iamveryskepticalwecanbuildanythingthatbehaveexactlyasanideal currentsource

ClaudioTalarico 27

𝑉&. = 𝑉&& − 𝑅&𝐼& ≥ 𝑉-.

𝑅& ≤𝑉&& − 𝑉-.

𝐼&∴ 𝑅&,­=b

𝑉-.𝑉-. 𝑉-.

𝑉-.

source:Razavi

𝑽𝑪𝑬(𝑽)

𝟏. 𝟖𝟏. 𝟐

0. 𝟖𝟖𝟕 𝟏𝟒𝟔

EarlyEffect(1)

• TheclaimthatcollectorcurrentdoesnotdependonVCE isnotaccurate

• AsVCEincreases,thedepletionregionbetweenbaseandcollectorincreases.Therefore,theeffectivebasewidthdecreases,whichleadstoanincreaseinthecollectorcurrent.

28

00

WB

0

WB’

n- n-

𝐼& ≈ 𝐴.𝑞𝐷?𝑾𝑩

µ𝑛BC

𝑁-𝑒arsat = 𝐼< J 𝑒

arsat J 1 +

𝑉&.𝑉=

source:Razavi

EarlyEffect(2)

ClaudioTalarico 29

𝑉-.𝑉-.

𝑉&.

𝑉&.

𝑉&.

source:Razavi

Small-signalmodelincludingEarlyeffect

ClaudioTalarico 30

𝑔� =1𝑟�=

𝑑𝐼&𝑑𝑉&.

=𝑑

𝑑𝑉&.𝐼< J 𝑒

arsat J 1 +

𝑉&.𝑉=

= 𝐼< J 𝑒arsat J

1𝑉==

𝐼&1 + 𝑉&.𝑉=

J1𝑉=≅𝐼&𝑉=

𝑔� =𝑑𝐼&𝑑𝑉-.

≅𝐼&𝑉/

𝑔� =𝑑𝐼-𝑑𝑉-.

=𝑑(𝐼&/𝛽�)𝑑𝑉-.

≅𝐼& 𝛽�⁄𝑉/

=𝑔�𝛽�

𝑖𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐𝑔𝑎𝑖𝑛 ∴ 𝑔�𝑟F ≈𝑉=𝑉/

maxgainthedevicecanprovide

𝑉&. ≪ 𝑉=

Δ𝐼&Δ𝐼-

Δ𝐼.

Δ𝑉-. Δ𝑉-.+-Δ𝑉&.

𝑟� = 1/𝑔� ≡ ℎB�𝑔� = 1/𝑟� ≡ ℎ��

𝛽� ≡ ℎ�� ≅ 𝛽�≡ ℎ�.

source:Razavi

BasemodulationandEarlyvoltage

31

Δ𝑉&. ↑⟹ Δ𝐼& ↑⟹ Δ𝑊- ↓

IC =diffusioncurrentofelectronsinbaseµ gradientofelectronsinbase=Dnp(x)/Dx

source:Gray&Meyer

NOTE:theslopechangesverylittle,soitisreasonabletoassumeit» constant)

s𝑙𝑜𝑝𝑒 ↑

𝑉= ∴𝐼&𝜕𝐼&𝜕𝑉&.

=𝑊-

− 𝑑𝑊-𝑑𝑉&.

≈ 𝑐𝑜𝑛𝑠𝑡.

sinceDWB isnegativeweneedaminussignintheequation

DependenceofIC onVCE

ClaudioTalarico 32

InForwardactiveregion: 𝐼& ≈ 𝐴.𝑞𝐷?𝑾𝑩

µ𝑛BC

𝑁-𝑒arsat = 𝐼< J 𝑒

arsat J 1 +

𝑉&.𝑉=

𝐼&

𝐼&

𝑉&.

VA =EarlyVoltage

source:Sedra &Smith

ModelExtensions

• CompletepictureofBJToperatingregions

• DependenceofbF onoperatingconditions

ClaudioTalarico 33

NPNBJToperatingregions

ClaudioTalarico 34

BVCE0 ≈½BVCB0BVEB0<<BVCB0

βR <<BF

Discussedsofar:BE=forwardbiasedBC=reversebiased

BE=reversebiased,BC=forwardbiasedthecollectorinjectselectronsinbaseandtheemitter collectthem

source:Gray&Meyer

DependenceofbF onoperatingconditions(andtemperature)

ClaudioTalarico 35

AtypicaltemperaturecoefficientforbF isabout+7000ppm/℃

source:Gray&Meyer

Gummel Plot(IC andIB vs.VBE)

ClaudioTalarico 36

source:Gray&Meyer

excessofundesiredrecombinationinbase

Highlevelofelectronsinjectedinbase(neartoThedopinglevelofthebase:NB)

bF staysaboutconst.

L=lowcurrentdensityM=mediumcurrentdensityH=highcurrentdensity

bF fall-off

• RegionII (mediumcurrentdensity)bF isaboutconstant(asdesired)

• RegionI (lowcurrentdensity)thereisanexcessofundesiredrecombinationinbase

• RegionIII (highcurrentdensity)thelevelofelectronsinjectedinbaseisextremelyhighnearthelevelofdopingofthebase(NB).Itcanbeshownthatforthiscase:

ClaudioTalarico 37

source:B.Murmann

𝐼& ≈ 𝐼<𝑒�C×arsat

NPNBJTinsaturationmode

• InactivemodeIC isalmostindependentofVCE (andVCB«VCB = VCE – VBE(on)@ VCE – 0.8)

• InsaturationnotonlytheBEjunctionisforwardbiased,butalsotheBCjunctionisforwardbiased– Asaresult,IC mustalsostronglydependsonVCB (andVCE« VBC =VBE(on)– VCE =0.8– VCE

ClaudioTalarico 38

saturationmode:

𝑉-.³𝑉-.,:;𝑉&. £ 𝑉&.,<=/

VCE,SAT

Theterm“saturation”isusedbecauseincreasingthebasecurrentinthisregionofoperationleadstolittlechangeincollectorcurrent(thereisasignificantdropinb comparedtoactivemode)

source:Razavi

NPNBJTinSaturationmode

ClaudioTalarico 39

Insaturationthecollectorcurrentisreduced byISC×exp(VBC/VT):

whilethebasecurrentisincreased byISC×exp(VBC/VT):

𝐼& = 𝐼<.𝑒arsat − 𝐼<&𝑒

ar½at

𝐼- =𝐼<.

𝛽¾�¡B¿�𝑒arsat + 𝐼<&𝑒

ar½at

ISC =saturationcurrentoftheBC(PN−)diode

ISE º IS =saturationcurrentoftheBE(PN+)diode

TheBCjunctionareaislargerthantheBEjunctionareathereforetheONvoltageoftheBCdiodeissmallerthantheONvoltageoftheBEdiode(typicallyVBC,on <VBE,on by0.4V)AE <AC « ISC >ISE

ISC exp(VBC/VT)

ISE exp(VBE/VT)

ICIB

AddtheBCforwarddiodetothepreviousmodel

IE 𝐼. = 𝐼- − 𝐼<&𝑒�r½�t +𝐼<.𝑒

�rs�t =

= 𝐼- + 𝐼&

source:Razavi

NPNBJTinSaturationmode

• SinceinsaturationIC decreasesandIB increasesthebetaofthetransistordecreasessignificantly:

• ByadjustingVBC (i.e.VCE)thebetaofatransistorinsaturation(βforced)canbesettoanyvaluelowerthanβactive€

βsat ≡ β forced =ICIB sat

≤ β ≡ βactive

ClaudioTalarico

VCE,SAT

IB=IB1

IB=IB3IB=IB2

source:Razavi

“Soft”Saturation• ForVCE=VBE,theBCjunctionsustainazerovoltagedifference

(VBC=VBE-VCE=0),anditsdepletionregionstillabsorbsmostoftheelectronsinjectedbytheemitterintothebase– Weconsiderthisconditionastheedgebetweenactivemodeandsaturationmode

• WhathappensifVCE <VBE ,i.e.VBC >0?NotmuchuntilVBC ³ VBC,ON.UptoVBC,ON thecurrentcarriedbytheBCforwardbiaseddiodeisstillextremelysmall,soassumethebehaviorofthedevicestillacceptable:– Asaruleofthumbwepermit“soft”saturation:

VBC <400mV« VCB >-400mV(VCB=VCE – VBE>– 400mV«« VCE >VBE – 400mV« VCE >400mV)

41

Typicallyassume:VCE(edge)=800mVVCE,SAT(soft)=VCB,ON +VBE,ON@ 400mVVCE,SAT(deep)º VCE,SAT@ 200mV

edgebetweenactiveregionandsaturationregion:VCB =0« VCE =VBE

VCB

IC

forIB= IB1

edge

soft

source:Sedra &Smith

source:Razavi

“Deep”Saturation• IndeepsaturationtheBCdiodecarriesasignificantamountofcurrent,so

thetransistorbearnolongeranyresemblancetoacontrolledcurrentsource.

• Thecollector-emittervoltageapproachesaconstantvaluecalledVCE,SATandthetransistorcanbemodeledasfollows:

ClaudioTalarico 42

almostashort

source:Razavi

NPNBJTinSaturationmode

• InsaturationtheIC vs.VCE curvesarerathersteepindicatingthatthesaturatedBJTexhibitsalowresistance(RCE,SAT rangesfromafewohmstoafewtensofohms).ThisresultwastobeexpectedfromthefactthatbetweenCandEwehavetwoforwardbiaseddiodes

ClaudioTalarico 43

IB=IB1

IB=IB3IB=IB2

VCE,SAT

largeb (=bactive)

smallb (=bsat)

slope=1/RCE,SAT

source:Razavi

source:Sedra &Smith

Example

ClaudioTalarico 44

bactive=50

FindVBB tosetthetransistorin:(a) ActivemodewithVCE =5V(b) Edgeofsaturation(c) Deepinsaturationwith

βforced =10

𝑉&.=𝑉&& − 𝑅&𝐼& → 𝐼& =a½½ea½s

Á½= 5𝑚𝐴 → 𝐼-=

ýÄÅÆÇ�ÈÉ

= 100𝜇𝐴 → 𝑉--=𝑉-. + 𝑅-𝐼- = 0.8 + 10𝑘×100𝜇 = 1.8𝑉

𝐼& =a½½ea½s(�ËÌ�)

Á½= �FeF.Í

�FFF= 9.2𝑚𝐴 → 𝐼-=

ýÄÅÆÇ�ÈÉ

= 184𝜇𝐴 → 𝑉--=𝑉-. + 𝑅-𝐼- = 0.8 + 10𝐾×184𝜇 ≈ 2.64𝑉

𝐼& =a½½ea½s(Ë��G)

Á½= �FeF.C

�FFF= 9.8𝑚𝐴 → 𝐼-=

ýÄÐgÑÆÉÒ

= 980𝜇𝐴 → 𝑉--=𝑉-. + 𝑅-𝐼- = 0.8 + 10𝐾×980𝜇 ≈ 10.6𝑉

a)

b)

c)

source:Sedra &Smith

PNPtransistor

• AlltheprinciplesthatappliedtoNPNalsoapplytoPNP,withtheexceptionthatemitterisatahigherpotentialthanbaseandbaseatahigherpotentialthancollector.

ClaudioTalarico 45

𝐼.

𝐼-

𝐼&E B C

P-P+ N0 WB

𝐼&𝐼.

𝐼-

source:Razavi

NOTE:UsethecurrentsdirectionsshowninfigureandVEBandVECtogetallpositivevalues

PNPtransistor

• EquationsforPNPinactivemode

• AcomparisonbetweenNPN(a)andPNP(b)

ClaudioTalarico 46

÷ø

öçè

æ+÷

ø

öçè

æ=

+=

=

=

A

EC

T

EBSC

T

EBSE

T

EBSB

T

EBSC

VV

VVII

VVII

VVII

VVII

1exp

exp1

exp

exp

bbb

𝐼.

𝐼-

𝐼&

source:Razavi

PNPBJTinactivemode:largesignal(DC)model

ClaudioTalarico 47

source:Razavi

PNPBJTinactivemode:smallsignal(AC)model

• ThesmallsignalmodelforthePNPtransistorisexactlyIDENTICALtothatoftheNPN.Thisisnotamistake!

ClaudioTalarico 48

source:Razavi

PNPBJTisdeepsaturation

ClaudioTalarico 49

source:Gray&Meyer

800mV 200mV - 800mV - 200mV

ICIB

IE

IE

IB IC

SummaryofoperatingregionsNPN BipolarTransistor

Region VBE VBC

CutoffForwardActiveReverseActiveSaturation

<VBE(on)³ VBE(on)<VBE(on)³ VBE(on)

<VBC(on)<VBC(on)³ VBC(on)³ VBC(on)

ClaudioTalarico 50

PNP BipolarTransistorRegion VEB VCB

CutoffForwardActiveReverseActiveSaturation

<VEB(on)³ VEB(on)<VEB(on)³ VEB(on)

<VCB(on)<VCB(on)³ VCB(on)³ VCB(on)