9-BJT

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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 1

9-BIPOLAR JUNCTION TRANSISTOR (BJT)

Strengths1. Threshold Voltage controlled byEg (only very weak

dependence on doping and process parameters)

2. Very high transconductance (gm) and high nonlinearity

- Lower voltage swing in logic

- Lower sensitivity to parasitics

3. Vertical device (diffusion, ion implantation and epitaxy)

- easier to achieve small dimensions vertically than

laterally (lithography)

4. High current/unit area High drive capability for driving long

off chip lines or for high current devices, such as LEDs or lasers


BIPOLAR JUNCTION TRANSISTOR (BJT)

Weaknesses

1. High Power

- relatively low levels of integration

2. No effective complementary circuit technology

3. Device based upon minority carriers

- charge storage and diffusion rather than drift

4. Difficult compromises for device optimization

- Base resistance: RC time constants and transit time favor

a very thin, highly doped base

- high injection efficiency requiresNE>>NB

- Bandgap shrinkage, lower defect densities and E-Bcapacitance all favor moderate emitter doping

5. Far greater processing complexity, larger number of mask

levels with tight alignment tolerances on high performance

devices.

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I. Basic Structure and Band Diagrams

Basic bipolar transistor structure: Two pn junctions J1 and J2are placed back-to-back a distance Wapart, forming an n-p-n

structure.

The simple, idealized transistor shown below has doping

density of 1018 cm-3 in the emitter and collector and 1016 cm-3

in the base.


C

B

E

Cross section, simplified model and symbol of a double

diffused discrete pnp transistor

Structure and Model of pnp Bipolar Transistor

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C

B

E

Cross section, simplified model and symbol of an integrated

circuit npn bipolar transistor

Structure and Model of npn Bipolar Transistor


The figures on the left show

(i) energy-band diagrams and

(ii) electron-density

for the ideal transistor sketched on

page 1 for the following

conditions:

Equilibrium Cutoff

Saturation Active

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(a) thermal equilibrium (zero bias)

(b) both junctions reverse-biased (cutoff mode)

(c) both junctions forward-biased (saturation mode)

(d) J1 forward-biased and J2 reverse-biased (active mode)


Basic Operation in Forward Active Region

The E-B junction is

forward biased and

the C-B junction isreverse biased

N+ P NE C

B

WB

x

x

x

V

_

Ec

Ev

EF

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Doping profile in a realistic IC npn transistor

Collector is formed by epitaxy

and base and emitter by ion

implantation

N+ P N N+E C

holes for recombinationand injection into emitter

B

~ 0.7 volts

emostof the

e

WB


Notation:

The notation used in these notes is for an npn BJT, which isopposite that used in Pierret. Terms used are defined as follows:

NE= NDE NB= NAB NC = NDC

DE = DP DB= DN DC = DP

E = p B = n C = pLE = LP LB = LN LC = LP

pE0 = pn0 nB0 = np0 pC0 = pn0

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The BJT operates basically as follows:

1. An external voltage is applied to forward bias the B-Ejunction ( 0.7 volts).

2. Electrons are injected from the emitter into the base

(holes are also injected from the base into the emitter, but

their numbers are much smaller becauseNDE> NAB).

3. If WB

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Ec

Ev

EF

0= dx

dpqDpqJ BxBBp

dx

dp

pq

kT

dx

dp

p

D

B

Bx

11=

(1)

To derive the basic relationship for electron current flowing

between the E and C, first assume the device current gain is

high. The hole current in the base is small.

E

E


Thus for uniform doping in the base, Ex 0 and the electrons

traveling through the base will move only by diffusion.In a modern ion implanted base transistor, dp/dx 0, henceEx 0 . The direction of this field aids electron flow from E toC, and retards electron flow from C to E.

The electron flow between E and C is given by

+=

+=

+=

dxdnp

dxdpn

pqD

dx

dnqD

dx

dpn

p

kT

dx

dnqDnqJ

B

BB

BxBBn

E

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where W= the width of the quasi neutral base region

(JBn is pulled outside the integration by assuming no

recombination of electrons in the base, i.e., JBn = constant)

( ) ( )0

)(00

pnWpn

pnddxqD

pJ

dx

pnd

p

qD

WW

B

Bn

B

=

=

=


From diode analysis, the pn products at the edge of the

depletion regions are given bypn x = 0( )= ni

2eqVBE /kT

pn xB( ) = ni2eqVBC/kT

JBn =qni

2e

qVBC / kT eqVBE / kT[ ]p

DBdx

0

W

In = Is eqVBC/kT e

qVBE /kT

AssumingDn is constant in the base

(2)

B

Bis

Q

DAnqI

22

=

(3)

where

(4)

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=W

B dxpqQ

0

(5)

is called the base Gummel number.

(6)

A = E-B cross-sectional area

1. Only one of the two exponential terms is important inforward or reverse active bias region. When the deviceis in saturation, both junctions are forward biased andboth terms must be included.

2. The quantity

which is the total undepleted charge in the base

=W

B

W

B dxNdxp

q

Q

00


( )

( kTqVkTqVB

Bi

kTqVkTqV

B

BiBn

BCBE

BCBE

eeQ

DAnq

eeWN

DqAnI

//

22

//

2

=

=

(7)

QB is the total integrated base charge (atoms/cm2). SinceI

1/QB, it is important to minimize QB, i.e., use low doping levelsin the base (this is a good strategy to achieve maximum dc

current gain, but we will see that this does not work for high

frequencies).

If the base is uniformly doped, E = 0, QB = q NB W

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A. Recombination in the Neutral Base Region

Some of the electrons traversing the base will recombine withmajority carrier holes. (This is usually unimportant in modernIC BJTs).

III. Current Gain

A number of factors can contribute to base current in a BJT. Weconsider them individually.


If we assume that the base is uniformly doped so that Ex = 0,then the electron transport and continuity equations are

02

2

=

=

B

BoBBB

BBn

nn

dx

ndD

dx

dnqADI

NN +

nB

nB0pC0pE

pE0

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As discussed in the case of the P-N junction, the generalsolution to these equations is

whereLB = (DBB)1/2 = diffusion length

The appropriate boundary conditions are

With these boundary conditions, the solution is

BB LxLx

BBeKeKnn

/

2

/

10+=

( )

( ) 0

0/

2

/

0

=

===

Wxn

eN

nenxn

B

kTqV

B

ikTqV

BBBEBE

nB nB0 eqVBE / kT 1( )

sinh Wx( )/ LB[ ]sinh W / LB( )

(8)


Excess Minority Carrier Profiles for Different W/LN

Ratios

Most minority carriers

make it across the base if

WLN. In todays BJTs,

W is typically

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The emitter and collector electron currents are

(9)

(10)

The ratio of these two currents is defined as the base transportfactor.

InE = In x = 0( ) =qADBnB0

LBeqVBE / kT 1( )coth W

LB

InC = In x = W( ) =qADBnB0

LBe

qVBE / kT 1( )csch WLB

(11)

BnE

nC

T

L

W

I

Isech==


(12)

In a typical modern BJT, W 1 m and LB 30 m so that

T 0.9994. T is NOT a limiting factor in current gain.

Using Eq. 9, 11 and 12 the base current due to Tis

(13)

2

2

2

11

B

T

L

W

IBREC= InE InC

= 1T( )In qAni2W

2NBBeqVBE / kT 1( )

In modern IC BJTs,xB

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where B = electron lifetime in base =

B. Hole Injection into the EmitterThe dominant mechanism in limiting in modern BJTs ishole injection from B into E. This process occurs becauseVBEnot only decreases the barrier to electron flow from E toB, but also the barrier for hole flow from B to E.

xE >> LE xE >= for1

/

2

( ) EEkTqVEE

EipE Lxe

xN

DqAnI BE

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If W>>LB or xE>>LE, then WorxE is replaced withLB orLE.

This equation is only approximately correct in IC structuresbecauseNB andNEare not constant. Typically, 0.98 which

implies a current gain 50. Such values are typically observed in

IC BJTs.

is maximized (close to unity) by

1. Making NE >>NB

2. MakingxElarge or alternatively by preventing hole

recombination at the emitter contact.

3. Making Wsmall. This is also desirable for increasingf.


Summarizing our discussion of current gain,

(17)

In modern BJTs Tis nearly 1 and is the main factor

limiting the performance.

(18)

By combining Eq. (12) and (16) and making appropriate

approximations it can be shown that

TpEnE

nE

nE

nC

pEnE

nC

E

CF

III

II

III

II =

+

=

+

==

=IC

IB

=

IC

IE I

C

=

F

1 F

WND

LND

L

W

LND

WND

BE

EEB

BEEB

BE

+=

12

2

1

The main parameter to achieve high gain is the ratio ofNE/NB

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Deviations from the IdealBase Width Modulation

Common Base Configuration

EB o sEB o s

p Collect.

n+ Base

p+ Emit.

onstant ase w t ,independent of V CB

VEB

VCB

IE

Base width

modulation--decrease in W

with bias VCB

n+ Base

p o ect.

p+ Emit.

VEB

More depletion withVCB: smaller x B

IE

VCB


Base Width ModulationCommon Base Configuration

Ideal Experimental

The output characteristics are nearly ideal in spite of the base widthmodulation because the emitter current is controlled or fixed, hence

there is no regenerative feedback and increase in both the collector

and emitter current that is observed in the common emitter

configuration.

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Deviations from the IdealBase Width Modulation

Base width

modulation--

decrease in Wwith bias VCB

EB o s

n+ Base

IC

p o ect.

p+ m t.

VEB

More depletion withVCB: smaller xB

Decreasing W

BL

Wcoth

InE=qADBnB0

LB

eqVBE / kT1( )coth W

LB


BJT Non-idealities

Common Emitter Configuration

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Base Width Modulation: Early

Voltage

The Early Voltage VA is a measure of how independent

the base width, W, is from VCB . Small |VA| means large

base width modulation.


WND

LND

L

W

LND

WND

BE

EEB

BEEB

BE

+=

12

2

1

Base Width Modulation: Early Voltage

As VCincreases, the reverse bias across the B-C increases, the

depletion region widens. Hence the neutral base width W ,

andIC

The Early effect is usually modeled as

IC = IS eqVBE / kT 1( ) 1 +

VCE

VA

(19)

Where

Si

BBA

WqNV

2

is known as the Early voltage

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Breakdown due to Punch-thru

When the base becomes depleted, the base resistance , with

large voltage drop, hence, the base potential no longer controlsthe E-B junction voltage. Carriers are injected from emitter tocollector with exponential dependence on VEC, not VEB. Thisseldom happens in modern BJTs because the base is more heavilydoped than the collector so depletion extends into the collector.

This is an identical process to that

describing extension of the drain

depletion layer thru to the source in a

MOSFET.


Punch-thru Breakdown

n+ Base

IC

p Collect.

p+ Emit.

VEB

VCB

VCB (Volts)

unc t rougbreakdown: base

completely depleted

n+ Base

IC

p Collect.

p+ m t.VEB

VCB

Not as common as avalanche breakdown in modern BJTs

VCE (Volts)

Common Base Common Emitter

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The large shift in the inputIB-VEB characteristic is because, with very

low VEC, the base current is due to injection from the base into the

collector because the built-in voltage of the B-C junction is lower.

The increase in the output characteristic at low VECis due to basewidth modulation and increase in due to an increase in

The sharp reduction in breakdown voltage is due to either punch

through of the collector to the base and reduction of the E-B junction

barrier by the C-B voltage or by amplification ofANYimpact ionized

carriers in the C-B junction which drift back into the base region and

become amplified. This occurs because there is very little

recombination in the base, hence the impact ionized carriers areinjected from the base into the emitter, causing an additional injectionoftimes this number of carriers from the emitter into the base and

these extra injected carriers then make it to the collector, increasing Ic.

dpndx


Preventing Base Width Modulation

(and Punch-Thru)

Base width modulation (and its extreme: punch-through) is

caused by the CB depletion region growing into the base

with applied bias.

To prevent this, collector doping should be much lower than

base doping, so the depletion region extends almost entirely

into the collector rather than into the base.

n+ Base

IC

p co ect.

p+ Emit.

VEB

VCB

n+ Base

IC

p o ect.

p+ Emit.

VEB

VCB

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Avalanche BreakdownCommon Emitter Configuration

Breakdown!


Avalanche Multiplication and Breakdown

P-N-P transistor

Base current is held constant in

the common emitter

configuration, so the only place

that excess electrons in the base

(4) can go is into the emitter.

This produces an internal bias

that causes an injection of holes,

Ip = In, which is regenerative

and leads to a much lower

breakdown voltage

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IC =dc

1dc

IB +1

1dc

ICB0

IC =dc

1 Mdc

IB +1

1 Mdc

ICB0

The common expression for collector current

can be modified to account for the avalanche multiplication andresulting emitter injection by replacing dc by Mdc

Since dc ~ 0.99, M need only be ~1.01 to haveIC.

Recall in PN junction avalanche, M 10-100 beforeI.

Lower voltage for the onset of avalanche breakdown.

Collector doping must be light to prevent avalanche

breakdown. (Also prevents base width modulation.)


IV. Low and High Current Level Effects on Theoretically,Tand are independent ofVBE, implying thatthe ratio of collector current to base current (i.e., current gain) is a constant, independent ofVBEorIC. In practice, theratio of the two currents is NOT independent ofIC.

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A. B-E Depletion Region Recombination

At low current levels, the dominant reason for the reduced isrecombination in the B-E depletion region.


In the P-N junction discussion, it was shown that some

recombination of the carriers moving through the depletion

region will occur, and that (19)

where o = lifetime in the depletion region.

1. This current flows in the B-E circuit and does not directlyaffectIC. Thus asIRECbecomes important, the ratioIC/IBdecreases.

2. dependence important at low current levels.

E B C

einjection

recombination

holeinjection

*

IREC=qAniWE

o

eqVBE/2kT

kT

qVBE

2exp

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High Current Effects

B. High Level Injection in the BaseE B C

einjection

NdNa + n

If injection levels are very high, the assumption of n

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If the electrons are traveling at the saturated drift velocity,vsat, then at any given time, the density of electrons in the

depletion region isJ/qvsat, hence the net charge density is

As a result there is excess negative charge on the base side ofthe depletion region and less positive charge on the collectorside. The net result is that to maintain charge neutrality thedepletion region shrinks in the base side and widens in thecollector side. As a result the neutral base region widens.This phenomenon is first important in the collector sidebecause it is usually the most lightly doped.

andW

= N x( )J

qvsat

While the increase in Wdecreases to some extent, it has a fargreater impact on high frequency performance because the transittime across the C-B depletion region increases significantly.


D. Base Resistance

The effective emitter bias becomes VBE- IBRB

IC = IS exp qVBE IBRB

kT

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Effect of Base Resistance

Base resistance

produces a completely

non-exponentialIC-VBEcharacteristic as

compared with either

ideal injection or G-R in

the E-B depletion

region.


E. Current Crowding

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The previous figure shows a pnp transistor. AsIB andICincrease, the voltage drop acrossRB becomes significant.

This means that the effective VBEacross the active (center)portion of the device is not as great as the externally appliedVBE. The edge of the emitter thus has the highest electroncurrent density (current crowding). This plays a double roleas the bandgap of the material shrinks with increasedtemperature, further increasing the injection around theemitter periphery. The total collector current decreases belowthe ideal exp(qVBE/kT) behavior.

To minimize the impact of this

(1) The emitter should be made narrower. For higher currentcapability multiple emitters can be used in a single base.

(2) In the extrinsic base region a N+ diffusion should be done.


Heterojunction Bipolar Transistor (HBT)

Motivation:

Reduce IEp by making

hole injection into the

emitter more difficult.

Solution: Use differentmaterials with different

bandgaps: Barrier to hole

injection.

e

E mi tt er Ba se

Ec

Ev

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Heterojunction Bipolar Transistor (HBT)Heterojunction E B C

Key feature is that the E-B barrier

for holes is much larger than that

for electrons

If we go back to eqs. (7) and (14) used to calculate the injectionefficiency, but do not cancel out the ni

2 terms since they will be

different when you have an emitter and base with differentEgs,


HBT Current Gain

+

=

2

2

1

1

iB

iE

E

B

EB

E

n

n

N

N

L

W

D

D

the injection ratio becomes

~

1~DB

DE

LE

W

NE

NB

niB

niE

2

and ifis limited by injection efficiency, it becomes

and ifEg = 0.356 eV, then

niB

niE

2

=

10

6

which meansNB can be 100-1000NE and we still have very

high current gain.

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Big Wins for HBTs

1. Eliminates base width modulation because depletionregions are in the more lightly doped emitter and collector

regions

2. Current gain limited only by recombination in the E-B

junction or the base

3. Current crowding and base resistance are both greatly

reduced because of high base doping

4. Completely eliminates Punch-through due to high base

doping

5. Improved high frequency performance from decreased base

resistance and E-B capacitance


VI. High Frequency Limitations

A number of time constants inherent to the device may limit

its frequency response.

A. Base Transit Time

How long does it take from the time a voltage is applied at the

input (E-B) until a voltage appears at the output (CB) ?

E B C

np

~0

W

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In the absence ofEfields in the base (NB = constant, low levelinjection), then the injected electron concentration varies

linearly across the base The total electron charge in the base is

Since

The transit time across the base is simply

qB =1

2qAnBxB

= 12qAnB0 e

qVBE/ kT( )W

IC =qADnnB0

WeqVBE/ kT 1( )

BC

BB

D

W

I

q

2

2

= (21)


If the base doping is graded (typical in IC BJTs), an aiding E

field speeds up the carriers and B is reduced. Also, underhigh level injection, to maintain base neutrality, the holeconcentration in the base and has a gradient similar to theelectron gradient. This sets up an Efield which also speedsup the electron transit. B is usually NOT the dominantfrequency limitation in modern BJTs.

B. Emitter Capacitance Charging Time

E B C

re

Cje

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From the earlier pn diode discussion,

Cje depends upon the doping levels and current levels (VBE) in

the transistor. A rough approximation is that Cje 2 CBE(0)

where CBE(0) is the zero voltage B-E junction depletion

capacitance.

(22)

C. Collector Capacitance Charging Time

re = dVBEdIE

kTqIE

E = reCje kT

qIE2CBE 0( )

Rc

C

E

B


The B-C junction is reverse biased so the junction impedance

is very high.(23)

where

RC = collector series resistance

C = B-C depletion capacitance

D. Collector Depletion Layer Transit Time

For moderate or high B-C reverse biases, the Efield across

the depletion layer is high, so the electrons can be assumed to

move at SAT

C = R CC

SAT

BC

D

W

2 (24)

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All of the time delays we have considered add, so that

(25)

The cutoff frequency of the device is simply

(26)

This is approximately the frequency at which is reduced to 1.Above this frequency, the device is not useful as an amplifier.

TOT

B+

E+

C+

D

fT =1

2TOT

Where WBC = B-C depletion width

The factor of 2 in the denominator is one of the most

erroneously quoted equations in semiconductor device physics.

It arises because the carriers are moving by drift and a current

starts to appear at the output when the carriers just enter the

base side of the B-C depletion region


VII. Ebers-Moll Model

(27)

(28)(29)

R R

E C

E CF F

B

B

F=

ESe kTqVBE

1 R=

CSe kTqVBC

1

IE =IF +RIR

IC=

FIF IR

IB = 1F( )IF + 1R( )IR

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where

F= forward alpha

IC/IE ifVBEis +ve and VBCis -veR = reverse alpha IE/IC ifVBCis +ve and VBEis -ve

IES= emitter reverse saturation current

ICS= collector reverse saturation current

The Ebers-Moll model may be used under all junction bias

conditions (i.e., cut-off, forward active, reverse active and

saturation) to estimate the terminal currents.


VIII. Hybrid ! Equivalent CircuitA useful small signal, AC equivalent circuit for the BJTs inforward active region is shown below.

The parameters are defined as follows

(30)gm = transconductane=dIC

dVBEqIC

kT

B

E

C

Cd + Cje

C

m

g vbe

rb

r

vbe

+

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Cd= Diffusion capacitance of the B-E Junction (due tostored minority carriers)

r = base/emitter resistance=dVBE

dIB

gm

Cje = depletion capacitance of B- E junction

C= depletion capacitance of B- C junction

=

dqB

dVBE=

dqB

dIC

dIC

dVBE= Bgm

(31)

(32)

The DC current gain is 0 =IC

IB= gmr

Considering only the input E-B capacitance, the AC gain is

=0

1+ jrC


The AC gain decreases to 0.7070 when orrC =1

f=

1

2rC

A more widely used measure is when the current gain goes to 1

rC = 0 = gmr and

f =gm

2C

1

2EC

Even if the current gain is less than unity, the transistor can still

produce power gain due to the impedance transformation. The

unity power gain or maximum frequency of oscillation is

fmax =f

8rBCBC

12

This is the performance parameter

which is dramatically improved by

HBTs because of the ability to heavily

dope the base region and lower rB

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IX. Bipolar Transistor Scaling

The intrinsic device is vertical. Scaling of lateral dimensions asconsidered in MOS transistors does not improve the intrinsic

device, but will improve the packing density and reduce the

parasitic capacitances and resistances. Scaling of the intrinsic

device is achieved by reducing the base width WB.

PARAMETER 1980 1985 1990

(1) Emitter Width (m) 3 1.5 0.8

(2) Base Width (m) 0.3 0.15 0.07

(3) fT(GHz) 1 10 30

(4) ECL gate delay (psec) 500 100 30


Bipolar Transistor Evolution

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Polysilicon Emitter

Short emitter or complete

polySi emitter


The emitter injection efficiency is degraded by the carriers

injected from the base into the emitter. The emitter width in amodern BJT is thin, which increases speed and reduces

parasitic resistance. However, a thin emitter increases the

gradient in the minority carrier concentration. The increase in

the gradient increases the B-E back injection current, which in

turn decreases the emitter injection efficiency and decreases the

common emitter current gain. In modern bipolar transistors an

n+ polysilicon emitter is inserted between the metal contact and

the thin n+ single crystal silicon emitter region. As a first

approximation to the analysis, we may treat the polysilicon

portion of the emitter as low-mobility silicon, which means that

the corresponding diffusion coefficient is small.

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Assuming that the neutral widths of both the polysilicon and

single-crystal portions of the emitter are much smaller than

the respective diffusion lengths, then the minority carrier

distribution functions will be linear in each region as shown

in the figure. Both the minority carrier concentration and

diffusion current must be continuous across the

polysilicon/silicon interface.

SinceDEpoly

dpEn+

dx

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9-BJT