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22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #1

Bipolar Junction Transistors

• Bipolar junction transistors (BJT) are active 3-terminal deviceswith areas of applications:– amplifiers, switch etc.– high-power circuits– high-speed logic circuits for high-speed computers.

• BJT structure:– sandwich of alternating type of Si-layers

♦ npn BJT: sequence of n-p-n♦ pnp BJT: sequence of p-n-p

– npn BJTs are most widely used.

N+ P

E B C

N- N+

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #2

A. IC BJT Structure

a) 2d-cross-section of an npnBJT structure.

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E+21

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Depth (um)

Co

nce

ntr

atio

n (c

m-3

)

N+ Emitter

P Base

N- Collector

N+ Burried layerN+

P−

N-EpiP+ P+N+P N+

Contacts

Active region

NPN

b) 1d-cross-section alongthe intrinsic device.

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #3

B. Basic Features of IC BJT Structures

• The base region is non-uniformly doped. This results in a built-inε field across the base which aids the transport of e− from E → C.

• Parasitic elements exist in a BJT structure such as:– base resistance, RB from base contact to active area– collector resistance, RC (predominantly through n- layer).

• Isolation must be provided between adjacent devices:– reverse biased PN junctions– trench isolation.

• The N- collector region adjacent to the base:– reduces CBC, improves BVCB

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

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #4

C. Basic BJT Operation

• The BJT operation is as follows:– An external voltage is applied across the E-B junction to forward

bias it (≈ 0.7 V)

– e− are injected into the base by the emitter. (Also, holes areinjected into the emitter but their numbers are much smallerbecause of the relative values of NA, ND).

B

E C

≈ 0.7 Vforward bias

XB

e− Mostof the

e−

N+ P N- N+

− + − +

5 Vreverse bias

hole

s

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #5

Basic Operation

– If XB << LN (diffusion length) in the base, most of the injected e-get into the collector without recombining. A few do recombine;the holes necessary for this are supplied as base current.

– The e− reaching the collector are collected across the C-B junctiondepletion region.

Since most of the injected e- reach the collector and only a few holesare injected into the emitter, the required IB << IC.

Therefore, the device has a substantial current gain.

ICIEElectrons flowingemitter to collector

Recombining electronsHoles

into emitter

E B C

IB

ICIB

IE

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #6

Basic Operation - Derivation of Currents

In order to derive the basic relationship for e- current flowingbetween E and C, we assume that the device current gain is high.

∴ IB ≅ 0

∴ Jp ≅ hole current in base = 0

∴ Jp ≅ 0 = qµppεx − qDp(dp/dx) (1)

For uniformly doped base, εx = 0 and the e- travelling through thebase will move by diffusion only.

However, in IC transistors dp/dx ≠ 0 and εx ≠ 0. The direction ofthis field aids e- flow from E → C and retards e- flow from C → E.

dxdp

pqkT

dxdp

pD

p

px

11==

µε (2)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #7

Basic Operation - Derivation of Currents

The e- flow between E and C is given by:

Jn = qµnnεx + qDn(dn/dx) (3)

Using (2) in (3) we get:

We integrate (5) over the quasi-neutral base region of width xB.

+=∴

dxdn

pdxdp

npDq

J nn

dxdn

Dqdxdp

pn

kTJ nnn += µ (4)

( )dxpnd

pDq

J nn = (5)Or,

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #8

Basic Operation - Derivation of Currents

Jn is pulled outside the ∫ assuming no recombination of e- in thebase region, i.e. Jn = constant.

BE C

xB

N+ P N-xd2xd1

x = 0 x = xB

dxx

dxpnd

D

dxx

qp

JBB

ono

n ∫∫

=∴ (6)

( ) ( )0pnxpnD

dxx

qp

J Bno

n

B

−=∴ ∫ (7)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #9

From PN junction analysis, the pn-products at the edge of thedepletion regions are:

Now, the total charge in the un-depleted base region is given by:

Basic Operation - Derivation of Currents

( )( )

∫

−

=∴

=

=

x

Dpdx

eenqJ

enxpn

enpn

B

o n

kTV BEq

kTV CBq

i

n

kTV CBq

iB

kTV BEq

i

2

2

20 (8)

(9)

(10)

∫=x

pdxqAQB

oB (11)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #10

This is an extremely important result. Note that:1 Usually, only one of the two exponential terms is important since

one junction is typically reverse biased. When the device is insaturation, both junctions are forward biased and both terms mustbe included.

2 The quantity, is called the base Gummel number.

It is the total integrated base charge (atoms/cm2). Since I ∝ 1/QB, itis important to minimize QB. Therefore, IC transistors use low basedoping levels.

Basic Operation - Base Gummel Number

−=∴ eeII kT

V BEqkTV CBq

sn (12)

(13)Q

DnAqI

B

nis

222

and, =

∫=x

dxxNqAQ B

o

AB )(

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #11

Since BC junction is reversed biased the eqVBC/kT term is negligibleand we can show from (12) and (13):

IC Vs. VBE

(14) predicts that IC vs. VBE is relatedexponentially. Slope = (kT/q)ln(10)

= 60 mV/decade I (@ 25 oC)

Relationship holds extremely well for ICtransistors over many decades of current.

Generally, QB is obtained by integrationover the base region. Therefore, QB istypically well controlled to ~ 1012 cm-2 togive high IC for a given VBE.

−−=∴ 1

222

eQ

nDAqI kT

V BEq

B

inn (14)

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0.0 0.2 0.4 0.6

VBE (V)

J C (

A/c

m2 )

Expt

Ideal

Decadechangein JC

60mVJS

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #12

D. Current gain

• Let us consider the factors that can contribute to base current in aBJT:– Recombination in the neutral base region– Hole injection into the emitter– Recombination in the E-B space charge region

ICIEElectrons flowingemitter to collector

Recombining electronsHoles

into emitter

E B C

IB

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #13

1. Recombination in the Neutral Base Region

Typically, some of the e- traveling the base will recombine withmajority carrier holes. (This is not important for modern IC BJTs).

If we assume that the base is uniformly doped so that εx = 0, the e-current and continuity equations are:

N+ Nnp

npo

P

QBpn

pno

pno

02

2

=−

−

=

τ n

ppn

pnn

n pn

xdnd

D

dxnd

DqAI

o

(15)

(16)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #14

Recombination in the Neutral Base Region

As we discussed for PN junction, the general solution of theseequations is:

np − npo = K1e−x/Ln + K2ex/Ln (17)

The appropriate boundary conditions are:

np(x = 0) = npoeqVBE/kT

np(x = xB) ≅ 0

Using these boundary conditions we get from (18):

Substituting (18) into (15) we get emitter and collector e− currents.

−

=

LxL

xx

eV

nn

n

B

n

B

kT

q

ppBE

o

sinh

sinh(18)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #15

Base Transport Factor

The ratio of these two currents is defined as the base transportfactor and is given by:

αT ≡ InC/ InE

= sech(xB/Ln) (21)

In modern IC BJTs, XB << Ln and recombination in the neutralbase region is significantly low.

If XB << Ln, (19) reduces to our earlier expression for e- current(14) and the base transport factor αT becomes:

αT ≅ 1 − xB2/2Ln

2

−=

−=

Lxhe

V

L

n pDqAIn

Lx

eV

L

n pDqAIn

n

BkT

q

n

n

C

n

BkT

q

n

n

E

BEo

BEo

csc1

coth1 (19)

(20)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #16

In a typical advanced BJT, XB ≤ 1 µm and Ln ≥ 30 µm ∴αT ≅ 0.9994.

This value of αT would imply a forward current gain:

which is higher than normally observed value of βF in IC BJTswith 1 µm base widths. Thus, αT is NOT usually a limiting factor incurrent gain.

The base current due to αT is:

where τn is e− lifetime in the base.

−= 1

2

2

eN

xnAqI kT

V BEq

nA

BiEBREC τ

(22)

Base Transport Factor

16001

>−

=−

≅≡T

T

nCnE

nET

B

CF II

III

ααα

β

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #17

The dominant mechanism in limiting β in modern BJTs is hole injection intothe E from B. Note that this process must occur because VBE decreases thebarrier to e- flow from E → B and also the barrier for hole flow from B → E.

The injected hole currents in each case come directly from the analysis of longbase and short base diodes (E denotes emitter properties):

2. Hole Injection into the Emitter

−=<<

−=>>

1:

1:

2

2

eV

xND

nqAILx

eV

LND

nqAILx

kT

q

EDE

pEipEpEE

kT

q

pEDE

pEipEpEE

BE

BE

(23)

(24)

E B CxE xB

nppn pn

xE >> LpE

xE

xE << LpE

E B C

nppn pn

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #18

The injection efficiency of the emitter is defined as:

Then from (14) and (24) we get:

(If XB >> Ln or XE >> Lp, then LB diode approximations replace XBand/or XE with Ln or Lp.)

(26) is only approximately correct in IC structures because NA andND are not constant. Note that γ is made close to 1 by: (1) making NDE >> NAB; (2) XB small; (3) XE large (prevent hole recombination at E contact).

Emitter Efficiency

III

III

I

nE

pETOT

nE

pEnE

nE

+==

+=

1

1γ (25)

DNDN

xx

nBDE

pEAB

E

B+=

1

1γ (26)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #19

3. E-B Space Charge Recombination

αT and γ are independent of VBE imply that the ratio of collector tobase current is a constant, independent of VBE i.e. current level.

In practice, the ratio of the two currents is NOT independent of IC.At low levels the dominant reason is recombination in the E-Bdepletion region.

From PN junction theory, we find that some recombination of thecarriers moving through the depletion region will occur, causing arecombination current.

E B Ce−

injection

holeinjection

*recombination

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #20

E-B Space Charge Recombination

where τo is the lifetime in the depletion region.

Note:– This current flows in the EB circuit and does not directly affect IC.

Thus, as IREC becomes important, the ratio of IC/IB will change.

– eqVBE/2kT dependence is important at low current levels.

Summarizing our discussion of current gain:

eWnqA

I kTVq

o

EiREC

A

22τ

= (27)

II

III

II

II

nE

REC

nE

nCnE

nE

pE

C

B +−

+≅≡β1

eV

nDWxN

Lx

DxNDxN

kT

q

oin

EBA

n

B

nED

PBA BE

22

2

221 −++≅

τβ(28)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #21

E. Mode of Operations

BJTs are two back-to-backdiodes.N+ P

E B C

N- N+E C

B

BE C

Four modes ofBJT operations

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #22

Mode of Operations

1) Forward active / normal– BE junction forward biased– BC junction reversed biased

here,,BFC

BC

IIII

β=∴∝

where βF = forward gain

2) Reverse active– BE junction reverse biased and BC junction forward biased

here, reverse gain, βF = IE/IB ≈ 1

3) Saturation region– BE and BC are forward biased

4) Cut-off region– BE and BC are reversed biased

+ VBC

+ VBE

−

−

Saturation

NormalCut-off

Inverse

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #23

F. Basic BJT Model

Basic BJT model can be derived considering two back-to-backdiodes as npn-BJT.

1) B-E junction is forward bias:– forward current, IF flows through E-B diode.

− αFIF flows in the collector

here, αF = forward gain ≅ IC/IE if VBE is +ve

2) B-C junction is reverse bias:– reverse current, IR flows through B-C diode.

− αRIR flows in the emitter

here, αR = reverse gain ≅ IE/IC if VBE is +ve

n p

E B C

n

E C

IE IC

B IB

IF αFIF

aRIR IR

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #24

EM1 BJT Model: Injection Version

• The basic Ebers-Moll model (EM1):

E OIE

O CIC

IB

αRIR αFIF

OB

IF IR

• Terminal currents: IE = − IF + αRIR (29)

IC = αFIF − IR (30)

IB = IF − αRIR − αFIF + IR

= (1 − αF) IF + (1 − αR) IR

∴ IB = (1 − αF) IF + (1 − αR) IR (31)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #25

EM1 BJT Model: Injection Version

• We know from current flow analysis:

Here IES = E-B saturation current; VBE = B-E voltage ICS = C-B saturation current; VBC = B-C voltage

• The terminal currents from (29), (30), (32), (33):

−==

−==

1

1

eIII

eIII

kTV BCq

CSnCR

kTV BEq

ESnEF (32)

(33)

−−

−=

−+

−−=

11

11

eIeII

eIeII

kTV BCq

CSkTV BEq

ESFC

kTV BCq

CSRkTV BEq

ESE

α

α (34)

(35)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #26

EM1 BJT Model: Injection Version

• From reciprocity property: αFIES = αRICS ≡ IS

• Therefore,

• Again, βF = CE forward current gain = αF/(1 − αF) βR = CE reverse current gain = αR/(1 − αR)

• Since IS = f(ni2) = f(T)

−−

−=

−+

−−=

11

11

eI

eII

eIeI

I

kTV BCq

R

SkT

V BEq

SC

kTV BCq

SkTV BEq

F

SE

α

α(36)

(37)

−−

=∴ ref

g

TTkE

refrefSS e

TT

TITI113

)()( (38)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #27

EM1 BJT Model: Injection Version

• Model equations:

Where αF = βF/(1 + βF) αR = βR/(1 + βR)

∴ Total five model parameters: βF, βR, IS, Tref, and Eg can be used todescribe basic BJT device characteristics without parasitics.

−−

−=

−+

−−=

1)(

1)(

1)(1)(

eTI

eTII

eTIeTI

I

kTV BCq

R

SkT

V BEq

SC

kTV BCq

SkTV BEq

F

SE

α

α(36b)

(37b)

−−

= ref

g

TTkE

refrefSS e

TT

TITI113

)()( (38)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #28

EM1 BJT Model: Transport Version

Model equations (36) and (37) can be written as:

Where the reference source currents:

ECR

CCC

ECCCF

E

III

III

−+=

+

−=

α

α

1

1(39)

(40)

−=

−=

1

1

eII

eII

kTV BCq

SEC

kTV BEq

SCC

E OIE

O CIC

IB

IEC ICC

OB

ICC/αF IEC/αR

ECR

CCF

B III

−+

−=∴ 1

11

1αα

(41)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #29

EM1 BJT Model: Nonlinear Hybrid-π

• From transform model (39) and (40), we get:

• Where the reference source current is:

• The diode currents are:

( )

( )R

ECCTEC

RECCCC

CTF

CCECCCCC

FE

IIIIII

II

IIII

βα

βα

−=

−−−=

−−=−−

−=

11

11 (42)

(43)

−−

−=−= 11 eeIIII kT

V BCqkT

V BEq

SECCCCT (44)

−=

−=

1

1

eII

eII

kTV BCq

R

S

R

EC

kTV BEq

F

S

F

CC

ββ

ββ(45)

(46)

22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #30

EM1 BJT Model: Nonlinear Hybrid-π

• The model:

• The terminal currents:

E OIE

O CIC

IB

ICT = ICC - IEC

OB

ICC/βF IEC/βR

+

=

−=

−

−=

R

EC

F

CCB

R

ECCTC

CTF

CCE

III

III

II

I

ββ

β

β(47)

(48)

(49)

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