學生版本_固態電子元件課程講義_ch5_bipolar transistors

Solid State Electronic Devices (Prof. Edward Yi Chang) p 1

Chapter 5 Bipolar Transistors

1. Higher current and high voltage capability → Power application

2. Faster switching times (fastest transistors ever reported ft > 800 GHz)

Basic Structure

Some facets about bipolar devices

1. The base region is non-uniformly doped, this results in a built- in ε field across the

base which aids the transport of e- from emitter to collector.

2. Parasitic exist in the structure

RB: base resistance from base contact to active base area

RC: collector resistance (predominately through N- layer)

3. The N- collector adjacent to the base reduces CBC, improves BVCB decreases base

width modulation by the collector voltage but adds series resistance to the device.

Basic operation

1. An external voltage is applied across the E-B junction to forward bias it. (≒0.7 V)

2. e- are injected into the base by the emitter

(Holes are also injected into the emitter by the base, but their numbers are much

smaller because relative number of NA, ND)

3. If WB << Ln in the base, most the injected e- get to the collector without combining

a few do recombine, the holes necessary for this are supplied as base current.

4. The e- reaching the collector are collected across the C-B depletion region.


Since most of the injected e- reach the collector and only a few holes are injected into

the emitter, i.e. IB<<IC.

The device has substantial current gain

1B

C

I

I

Internally, the control parameter is VBE (determines the injection level)

Bipolar is considered a current controlled device with IB provided externally

producing IC.

To derive the basic relationship for e- current between E & C, we start by assuming

the device current gain is high ∴ IB=0

diffusion

p

drift

xpp

p

dx

dpqDpqJ

J

0

0base in thecurrent hole

ip)relationsh(Einstein 1

1

dx

dp

pq

kT

dx

dp

p

D

dx

dpDp

p

p

x

pxp

Thus, for uniform doping in the base εx=0 and e- travelling through the base will move

by diffusion only.

In IC transistors, 0 and 0 dx

dpx

The direction of this field aids e- flow E→C and retarded flow C→E.

The e- flow between E & C is given by

diffusion

n

drift

n

nxnn

dx

dnqD

dx

dp

p

nkT

dx

dnqDnqJ


dx

dnp

dx

dpn

p

qDJ n

n

or

dx

pnd

p

qDJ n

n

)(

Neglecting depletion regions, the effective base width XB = metallurgical base width.

BB XX

n

n dxdx

pnd

D

dx

q

pJ

00

)(

Assume no recombination of e- in the base, i.e. constantnJ

)0()(0

pnXpnD

dx

q

pJ B

X

n

n

B

From our diode analysis, we know that the pn product at the edge of the depletion

regions are given by

kT

qV

po

po

enn

pp

kT

qV

iB

kT

qV

i

CB

BE

enXpn

enpn

2

2

)(

)0(

B

BECB

X

n

kT

qV

kT

qV

in

D

pdx

eeqnJ

0

2 )(


region base undepletedin charge total0

BX

BQpdxqA

)( kT

qV

kT

qV

Sn

BECB

eeII

Where

B

niS

Q

DnAqI

222

This is an extremely important result

1. Usually one of two exponential term is important because of the fact that one

junction is typically reverse biased. (If both are forward biased both term must be

included → saturation)

2. The quantity BX

AB dxxN

qA

Q

0

)( is called the base Gummel Number.

It is the total integrated base charge (atoms/cm2)

Since BQ

I1

It is important to minimize QB; IC transistors use low doping levels in the base.

If the base is uniformly doped, 0x

pn np because of relative doping

If the base doping level is constant (NA), then

BAB XqANQ

And we have

1

2

kT

qV

BA

inn

BE

eXN

AnqDI

D

ino

kT

qV

non

A

ipo

kT

qV

pop

N

np

epp

N

nn

enn

BE

BE

2

2


kT

qV

kT

qV

Sn

BECB

eeII

Where

B

niS

Q

DnAqI

222

biased) reverse isjunction BC thebecause negligible is term (The kT

qVCB

e

Alternatively, this may be written as

1

222

kT

qV

B

inn

BE

eQ

nDAqI

This equation predicts an exponential relationship between IC and VBE.

Relationship holds well for IC transistor over many decades of current.

In general, QB is obtained by integration over the base region, QB is well controlled to

1012/cm2 to give high IC for a given VBE.

Current Gain

B

C

I

I

A number of factors can contribute to the current in a BJT (bipolar transistor)


AA.. RReeccoommbbiinnaattiioonn iinn tthhee nneeuuttrraall bbaassee rreeggiioonn

In the general case, some of the e- traversing the base will recombine with majority

carrier hole. (This is usually unimportant)

If we assume the base is uniformly doped, 0x , the the e- current (transport) and

continuity equations are

02

2

n

popp

n

p

nn

nn

dx

dndD

dx

dnqADI

The general solution of the equation is

nn L

x

L

x

pop eKeKnn 2

1

Where

lengthdiffusion nnn DL

The appropriate boundary conditions are

0)(

)0(

poBp

kT

qV

pop

nXxn

enxnBE

n

B

n

B

kT

qV

pop

L

X

L

XX

ennBE

sinh

sinh

1

Substitute into

dx

dnqADI

p

nn

current)(emitter 0X

n

BkT

qV

n

pon

nEL

Xe

L

nqADI

BE

coth1 → current into base

BXX


n

BkT

qV

n

pon

nCL

Xe

L

nqADI

BE

csch1 → current get out base

The ratio of these two currents is defined as the base transport factor

n

B

nE

nCT

L

X

I

Isech

In modern BJT, nB LX

There is little recombination in the neutral base

2

2

2

11

n

BT

L

X , if nB LX

For typical BJT, if μm 30 and μm 1 nB LX

9994.0T

A transport factor that is close to 1 and

16000006.0

9994.0

B

C

I

I

T is not usually a limiting factor in current gain

The base current due to T

T

2

toduecurrent ion recombinat 12

12

BkT

qV

nA

BiE

kT

qV

n

BE

n

EnB

IeN

XnqA

eqXA

AQI

BE

BE

Where n is the e- lifetime in the base.


BB.. HHoollee iinnjjeeccttiioonn iinnttoo tthhee eemmiitttteerr

The dominant mechanism in limiting β in modern BJTs is hole injection into the

emitter from base. Note that this process must occur because VBE decreases the barrier

to e- flow E→B and also the barrier for hole flow B→E.

The injected hole currents in each case come directly from our analysis of long base

and short base diodes.

1

1

2

2

kT

qV

EDE

pE

ipEpEE

kT

qV

pEDE

pE

ipEpEE

BE

BE

eXN

DqAnILX

eLN

DqAnILX

The injection efficiency of the emitter is defined as

tot

nE

pEnE

nE

I

I

II

I

small) is if , (since 1

1

small) is if ,1

coth (since 1

coth1

2

ypN

np

N

ne

X

pqADI

eX

nqAD

yy

yeX

L

L

nqAD

L

Xe

L

nqADI

Eo

DE

EoEo

DE

ikT

qV

E

EopE

pE

kT

qV

B

ponB

kT

qV

B

n

n

ponB

n

BkT

qV

n

ponB

nE

BE

BE

BE

BE


nB

pE

DE

AB

E

B

ABEoDEpo

E

EopE

B

ponB

B

ponB

kT

qV

E

EopEkT

qV

B

ponB

kT

qV

B

ponB

pEnE

nE

D

D

N

N

X

X

NpNn

X

pD

X

nD

X

nD

eX

pqADe

X

nqAD

eX

nqAD

II

I

BEBE

BE

1

1

),(

11

1

If pEnB LXLX or ,

Then the long diode approximations replace XB or XE with Ln and Lp.

We can make close to unity by

A) Making ABDE NN

B) Making XE large or alternatively by preventing hole recombination at the emitter

contact.

C) Making XB small, this is also desirable from the point of view of increasing T

Typically, 0.999 to99.0

nB

pE

DE

AB

E

B

D

D

N

N

X

X

1

1

A current gain of 100~1000 should be achieved.

Such values are typically observed for BJT.


CC.. EE--BB ssppaaccee cchhaarrggee rreeggiioonn rreeccoommbbiinnaattiioonn

Note that both T and are independent of VBE, implying that the ratio of

collector to base current is a constant, independent of VBE, i.e. current level.

In practice, the ratio of the two current (IC/IB) is not independent of IC at low levels,

the dominate reason is recombination in the E-B depletion region.

We saw in our PN junction discussion that some recombination of the carriers moving

through the depletion region will occur, and that

kT

qV

Eic

BE

eWqAn

I 2

0

Re

Where 0 is the lifetime in the depletion region.

(1) kT

qVBE

e 2 dependence is important low current levels

(2) This current flows in the EB circuits and does not directly effect IC, thus as Irec

becomes important, the ratio IC/IB will change.

Summarizing of these together the current gain

regiondepletion at ion recombinat

Re

baseat ion recombinat

emitterat ion recombinat

1

nE

c

nE

nCnE

nE

pE

C

B

I

I

I

II

I

I

I

I

kT

qV

in

EBA

n

B

nED

pBABE

enD

WXN

L

X

DXN

DXN2

0

2

2

22

1

This equation is only valid for larger β.


Note that

(1) kT

qV

C

BE

eI over a wide range of I

(2) kT

qV

B

BE

eI at moderate currents

(3) kT

qV

B

BE

eI 2 at low level due to recombination at depletion region


High level effect

A. High level injection in the base

If injection levels are very high, the assumption n<<NA in the base is no longer valid.

In this case, for the base to remain quasi-neutral.

BX

B

AB

pdxqQ

xnxNx

0

and

)()()(

B. High level injection in the collector

The collector is doped lightly to obtain reasonable B-C breakdown at high level

injection, the assumption of complete depletion in the B-C depletion is no longer

valid.

If the electrons are traveling at the saturation drift velocity, sat , then at any given time,

the density of electrons in the depletion region is satsat

JxNpJ

)(

As a result, there is excess negative charge on the base side of the depletion region

and less positive charge on the collector side, the net result is to maintain charge

neutrality, the depletion region shrinks in the base side and widens in the collectors

side. As a result, the neutral base region widens )region base( , BX


Frequency limitation

A number of time constants inherent to the device may limit its frequency response.

1. Base transit time

In the absence of ε field in the base (NA=constant, love level injection) then the

injected e- concentration varies linearly across the base. The total charge in the base is

EBpB AXqnq2

1

The transit time across the base is simply

n

BB

B

p

n

EBp

B

B

p

nC

C

BB

D

X

X

nqD

AXqn

X

nqDI

I

q

2

2

1

current) (diffusion

2

D: average e- diffusion time in the base

If the base doping is graded, an aiding ε field speeds up the carriers, the B is

reduced by at least 2 times.

B is not usually the dominate frequency limitation.

2. Emitter base capacitance charging time

From the earlier PN diode discussion

EE

BEe

qI

kT

dI

dVr

Cje depends on the doping levels and current level (VBE) in the transistor. A rough

approximation is that

)0(2 BEje CC

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

Junction capacitance

)0(

E

2 BEjeeE CqI

kTCr


3. Collector capacitance charging time

The B-C junction is reversed biased and the junction impedance is very high

CRCC

where

ecapacitancregion depletion C-B:

resistance seriescollector :

C

RC

4. Collector depletion layer transit time

For moderate or high B-C reverse biases, the ε field across the depletion layer is high,

so the electrons can be assumed to move at sat

widthdepletion C-B:

2

DBC

sat

DBCD

X

X

All of time delays we considered add.

We have

DCEBtot

Cutoff frequency of the device is

tot

tf2

1

學生版本_固態電子元件課程講義_ch5_bipolar transistors

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