Bipolar Junction Transistor

EEE 531: Semiconductor Device Theory I

Instructor: Dragica Vasileska

Department of Electrical Engineering

Arizona State University

Outline

1. Introduction

2. IV Characteristics of a BJT

3. Breakdown in BJT

1. Introduction

Inventors of the transistor:

William Shockley, John Bardeen

and Walter Brattain Original

point-contact transistor

(1947)

(A) Terminology and symbols

•

Both,

pnp

and

npn

transistors can be thought as two very

closely spaced

pn

-junctions.

•

The base must be small to allow interaction between the two

pn

-junctions.

p+ n p E C B + + V_{EB VCB} n+ p n E C B + + V_{BE VBC} PNP - transistor E B C NPN - transistor E B C

•

There are four regions of operation of a BJT transistor

(example for a

pnp

BJT):

•

Since it has three leads, there are three possible amplifier

types:

V_EB

V_CB

Saturation region

(both junctions forward biased)

Cutoff region

(both junctions reverse biased)

Forward active region

(emitter-base FB, collector-base RB)

Inverted active region

(emitter-base RB, collector-base FB) B p+ n p E C V_{EB V} CB p p+ n C E B V_EB V_EC p+ p n E C B V_CB V_EC

(B) Qualitative description of transistor operation

p+ n p

• Emitter doping is much larger than base doping

• Base doping larger than collector doping

• Current components:

• I_B1 = current from electrons being back injected into the forward-biased emiter-base junction

• I_B2 = current due to electrons that replace the recombined electrons in the base

• I_B3 = collector current due to

thermally-generated electrons in the collector that go in the base

I_Ep I_En I_Cp I_cn I_B1 I_En I_Cn I_B3

{

I_{Ep I} Cp I_B2 3 2 1 B B B C E B Cn Cp C En Ep E I I I I I I I I I I I I          E_C E_F E_V

(C) Circuit definitions

Base transport factor



_T

:

Emitter injection efficiency



:

Alpha-dc:

Beta-dc:

Ep Cp

T



I

/

I



_{Ideally it would be equal to unity}

(recombination in the base reduces its value)

E Ep Ep Cp Ep

I

I

I

I

I









Approaches unity if emitter doping is much larger than base doping





















_T En Ep Cp En Ep Cn Cp E C dc

I

I

I

I

I

I

I

I

I

dc dc C E C B C dc

I

I

I

I

I

















1

Current gain is large when dc

Collector-reverse saturation current:

Collector current in common-emitter configuration:

Large current gain capability:

Small base current

I

_B

forces the

E

-

B

junction to be forward

biased and inject large number of holes which travel through

the base to the collector.

0 0 Cn C Cp Cn dc E BC BC

I

I

I

I

I

I

I



















dc BC B dc dc C BC B C dc C

I

I

I

I

I

I

I

























1

1

0 0 0 EC B dc C

I

I

I













₀ 0

1

dc BC EC

I

I









(D) Types of transistors

• Discrete (double-diffused) p+np transistor Emitter Base Collector 5 m 200 m • Integrated-circuit n+pn transistor 6 m 200 m

2. IV-Characteristics of a BJT

(A) General Considerations

• Approximations made for derivation of the ideal IV-characteristics of a BJT:

(1) no recombination in the base quasi-neutral region (2) no generation-recombination in the E-B and C-B

depletion regions

(3) one-dimensional current flow (4) no external sources • Notation: N_AE = N_E L_n = L_E D_n = D_E n_p0 = n_E0 _n = _E N_DB = N_B L_p = L_B D_p = D_B p_n0 = p_B0 _p = _B N_AC = N_C L_n = L_C D_n = D_C n_p0 = n_C0 _n = _C p+ n p

• The carrier concentration variation for various regions of operation is shown below:

• Assuming long emitter and collector regions, the solutions of the

minority electrons continuity equation in the emitter and collector are of the form: n_E0 n_E(0”) x” 0” 0 W 0’ x’ n_C(0’) n_C0 E-B _C-B p_B(0) p_B(W) saturation Forward active p_B0 Cut-off n_E(x”) p_B(x) p_B(W) n_C(x’)







CB T



C E T EB L x V V C C L x V V E E

e

e

n

x

n

e

e

n

x

n

/ ' / 0 / " / 0

1

)

'

(

1

)

"

(

 













• For the base region, the steady-state solution of the continuity equation for minority holes, of the form:

using the boundary conditions:

is given by:

Note: The presence of the sinh() terms means that recombination in the base quasi-neutral region is allowed.

0

2 2 2









B B B

L

p

dx

p

d



1



,

(

)



1



)

0

(



₀ /







₀ /





p

_B

p

_B

e

VEB VT

p

_B

W

p

_B

e

VCB VT



















/





1



sinh

/

sinh

1

/

sinh

/

)

(

sinh

)

(

/ 0 / 0













T CB T EB V V B B B V V B B B B

e

L

W

L

x

p

e

L

W

L

x

W

p

x

p

• Once we have the variation of n_E(x”), p_B(x) and n_C(x’), we can calculate the corresponding diffusion current components:

• Expressions for various diffusion current components: x” 0” 0 W 0’ x’ E-B _C-B I_nE(0”) I_pB(0) I_pB(W) I_nC(0’) I_nE(x”) I_nC(x’) I_pB(x) I_B2=I_pB(0)-I_pB(W) I_E=I_nE(0”)+I_pB(0) I_C=I_nC(0’)+I_pB(W)

Base recombination current

W x B B pB x B B pB x C C nC x E E nE dx p d AqD W I dx p d AqD I dx n d AqD I dx n d AqD I                ) ( , ) 0 ( ' ) ' 0 ( , " ) " 0 ( 0 ' 0 ' " 0 "

• Final results for the emitter, base and collector currents:























1



) / sinh( 1 ) / coth( 1 ) / sinh( 1 ) / coth( 1 ) / coth( 1 ) / sinh( 1 1 ) / sinh( 1 1 ) / coth( / 2 / 2 / 2 / 2 / 2 / 2                                                       T CB T EB T CB T EB T CB T EB V V B B B B B C C C i V V B B B B B E E E i B V V B B B B C C C i V V B B B B i C V V B B B B i V V B B B B E E E i E e L W L W N L D N L D Aqn e L W L W N L D N L D Aqn I e L W N L D N L D Aqn e L W N L D Aqn I e L W N L D Aqn e L W N L D N L D Aqn I

• For short-base diodes, for which W/L_B<<1, we have:

• Therefore, for short-base diodes, the base current simplifies to:

• As W/L_B0 (or _B ), the recombination base current I_B2 0 .

2

)

sinh(

1

)

coth(

;

)

sinh(

;

2

1

)

cosh(

2

x

x

x

x

x

x

x



















1

2

1

2

/ 2 / 2









































T CB T EB V V B B B B C C C i V V B B B B E E E i B

e

L

W

N

L

D

N

L

D

Aqn

e

L

W

N

L

D

N

L

D

Aqn

I

  I_B1



I_B2 -I_B3



I_B2

(B) Current expressions for different biasing regimes

Forward-active region:

•

E-B junction is forward biased, C-B junction is

reverse-biased:

                                          ) / sinh( 1 ) / cosh( ) / sinh( 1 ) / cosh( ) / sinh( 1 ) / coth( 2 / 2 / 2 / 2 B B B B B C C C i V V B B B B B E E E i B Cp V V B B B B i C Ep En V V B B B B E E E i E L W L W N L D N L D Aqn e L W L W N L D N L D Aqn I I e L W N L D Aqn I I I e L W N L D N L D Aqn I T EB T EB T EB

These terms vanish if there is no

recombi-• Graphical description of various current components:

• The emitter injection efficiency is given by:

p+ n p

{

I_Ep

{

I_En

}

I_Cp I_Cn I_B1 I_B3

I

_E

I

C

I

_B

Recombination in the base is ignored in this diagram.

E B B E E E B B E E base short B E B B B E E B E B B B E E En Ep Ep

D

WN

D

N

L

D

WN

D

N

L

L

W

D

N

L

D

N

L

L

W

D

N

L

D

N

L

I

I

I





 













1

)

/

coth(

1

)

/

coth(

• The base transport factor is given by:

• Common-emitter current gain:

• For a more general case of a non-uniform doping in the base, the Gummel number is given by:

2 2

2

1

)

/

cosh(

1

B base short B Ep Cp T

L

W

L

W

I

I





 









E B B E E base short B B E B B B E E B E B B B E E dc

D

WN

D

N

L

L

W

L

W

D

N

L

D

N

L

L

W

D

N

L

D

N

L



 









)

2

/

(

sinh

)

/

coth(

2

1

)

/

coth(

2 G_B = WN_B (Gummel number)





W B B

N

x

dx

G

0

)

(

Typical values of G_B:

Saturation region:

•

E-B and C-B junctions are both forward biased:

                           C E B Cp Cn Cp V V B B B B C C C i V V B B B B i C Ep' Ep En V V B B B B i V V B B B B E E E i E I I I I I I e L W N L D N L D Aqn e L W N L D Aqn I I -I I e L W N L D Aqn e L W N L D N L D Aqn I T CB T EB T CB T EB ' / 2 / 2 / 2 / 2 ) / coth( ) / sinh( 1 ) / coth( ) / coth( 3 B Cn

I

I





Base current much larger

• Graphical description of various current components:

• Important note:

 _{As V}

CB becomes more positive, the number of holes injected from

the collector into the base and afterwards in the emitter increases.

 _{The collector hole flux is opposite to the flux of holes arriving from}

the emitter, and the two currents subtract, which leads to a reduction of the emitter as well as the collector currents.

p+ n p

{

I_Ep

{

I_En

}

I_Cp I_Cn I_B1 IB3

I

_E

I

C

I

_B

Recombination in the base is ignored in this diagram.

}

_I

Cp’

Cutoff region:

•

E-B and C-B junctions are both reverse biased. For

short-base diode with no recombination in the short-base, this leads to:

C C C i C C C E E E i C E B Cn C C C i C En E E E i E N L D Aqn N L D N L D Aqn I I I I N L D Aqn I I N L D Aqn I 2 2 2 2 ,                    p+ n p I_B1 I_B3

I

_E

I

C

I

_B

Recombination in the base is ignored in this diagram.

I_En

(C) Form of the input and output characteristics

Common-base configuration:

Common-emitter configuration:

I_E V_EB V_CB=0 V_CB<-3V_T I_C V_BC I_E0 I_E=0 saturation Forward active cutoff I_BC0 I_B V_EB V_EC > 3V_T V_EC= 0 V_EC I_B0 I_B=0 saturation Forward active cutoff I_EC0 I_C VCB= 0

•

Note on the collector-base reverse saturation current:

I_Cn V_BC>0 I_B=I_BC0 C B E V_BC Minority electrons in the collector that are within L_C from the C-B junction are collected by the high electric field into the base.

•

Why is I

_EC0

much larger than I

_BC0

?

I_Cn V_EC > 0 I_E = I_EC0 C B E I_B=0 I_En I_Ep I_Cp





Cn Ep dc BC dc Ep BC Cp Cn EC

I

I

I

I

I

I

I

I

₀







₀









1

₀

,





 _{The electrons injected from the collector into the base and}

then into the emitter forward bias the E-B junction .

 _{This leads to large hole injection from the emitter into the base and} then into the collector.

 _{In summary, relatively small number of electrons into the emitter}

forces injection of large number of holes into the base (transistor action) which gives I_EC0 >> I_BC0 .

(D) Ebers-Moll equations

• The simplest large-signal equivalent circuit of an ideal (intrinsic) BJT consists of two diodes and two current-controlled current sources:

• Using the results for I_E and I_C, we can calculate various coefficient:

• The reciprocity relation for a two-port network requires that:

I_{F I} R _RI_R _FI_F I_E I_C I_B







1



1

/ 0 / 0









T CB T EB V V R R V V F F

e

I

I

e

I

I











1





1



1

1

/ 0 / 0 / 0 / 0





















T CB T EB T CB T EB V V R V V F F C V V R R V V F E

e

I

e

I

I

e

I

e

I

I

0 0 R R F F

I





I



(E) Early effect

• In deriving the IV-characteristics of a BJT, we have assumed that _dc,

_dc, I_BC0 and I_EC0 to be constant and independent of the applied voltage.

• If we consider a BJT in the forward active mode, when the reverse bias of the C-B junction increases, the width of the C-B depletion region

increases, which makes the width of the base quasi-neutral region W_eff to decrease:

• The common-emitter current gain, taking into account the effective width of the base quasi-neutral region (assuming =1) is then given by:

• The common-emitter current gain can be approximated with:

dcb deb eff

W

x

x

W



(metallurg

ical)









2

2

1

1

_{eff B} T dc









W

L



2

2

1





























eff B dc dc dc

W

L

• Graphical illustration of the Early (base-width modulation) effect:

• If we approximate the collector current with the hole current:

we find:

• Since W_B/ V_BC <0, we have that I_C/ V_BC > 0, i.e. I_C increases.

E _C B W_eff W_eff’ T EB T EB B V V B B B i V V W o B B i Cp C

e

W

G

D

Aqn

e

dx

x

N

D

Aqn

I

I

2 / 2 /

)

(

)

(









A C BC B B B C BC C

V

I

V

W

G

W

n

I

V

I















(

)

Early voltage

• Empirically, it is found that a linear interpolation of the collector current dependence on V_EC is adequate in most cases:

where the Early voltage is given by:

• Graphical illustration of the Early effect:



_{dc B EC}



_{EC A}

 

_{dc B EC}





_{EC A}



C

I

I

V

V

I

I

V

V

I







₀

1



/







₀

1



/

0





s B B A A

k

W

qG

k

V

V_EC I_C -|V_A|

Another effect contributing

to the slope is due to generation currents in the C-B junction:

 _{Generated holes drift to the}

collector.

 _{Generated electrons drift into} the base and then the emitter, thus forcing much larger hole injection (transistor action).

(F) Deviations from the ideal model:

There are several factors that lead to deviation from the ideal

model predictions:



_{Breakdown effects}



_{Geometry effects}



_{Generation-recombination in the depletion regions}

3. Breakdown in BJT’s

•

There are two important mechanisms for breakdown in

BJT

’

s:

(1) punch-through breakdown

(2) avalanche breakdown (similar to the one in

pn

-junctions)

•

The

punch-through breakdown

occurs when the reverse-bias

C-B voltage is so large that the C-B and the E-B depletion

regions merge.

•

The emitter-base barrier height for holes is affected by

V

_BC

,

i.e. small increase in

V

_BC

is needed for large increase in

I

_C

.

•

The

mechanism of avalanche breakdown

in BJT

’

s depend

on the circuit configuration (emitter or

common-base configuration).

p

+

n

p

V_BC increasing

Note:

Punch-through voltage is

usually much larger than the

avalanche breakdown voltage.

•

For a

common-base

configuration, the avalanche breakdown

in the C-B junction (open emitter)

BV

_BC

is obtained via the

maximum (breakdown) electric field

F

_BR

(~300 kV/cm for

Si and 400 kV/cm for GaAs):

•

The increase in current for voltages higher than

BV

_BC

is

reflected via the

multiplication factor

in the current

expres-sion. It equals one under normal operating conditions, and

exceeds unity when avalanche breakdown occurs.

•

When the emitter is open, the

multiplication factor for the

C-B junction

is:

C BR s C B BR s BC

qN

F

k

N

N

q

F

k

BV

2

1

1

2

2 0 2 0



























1

1







































b m BC BC CB

BV

V

M

•

For a

common-emitter

configuration, the collector-emitter

breakdown voltage

BV

_EC

is related to

BV

_BC

:









mb dc BC EC BC dc dc BC EC EC EC BC dc BC BC C BC E dc BC C C E

BV

BV

M

M

M

I

M

M

I

M

I

I

I

M

I

I

I

/ 1 0 0 0

1

1

)

1

(

1





































_{Open base configuration}

Much smaller than

BV

_BC

due to transistor action.

M u lt ip li c a ti o n f a c to r Reverse voltage 10 20 30 40 50 20 40 M_EC M_BC

V_EC I_C BV_EC0 Common-emitter output characteristics I_C V_BC BV_BC0 Common-base output characteristics

4. Geometry effects

•

The geometry effects include:

(1) Bulk and contact resistance effects

(2) Current crowding effect

•

Base current flows in the direction parallel to the E-B

junction, which gives rise to base spreading resistance.

•

When V

_BB’

is much larger than V

_T

, most of the emitter

current is concentrated near the edges of the E-B junction.

p+ n+ p+ p n n+ collector B E B Emitter contacts Base contacts

Generation-recombination in the depletion region

V_EB

ln(I_C)

ln(I_B)

•

Reverse-biased C-B junction

adds a generation current to I

_C

.

•

Forward-biased E-B junction

has recombination current. I

_C

is

not affected

by the

recombina-tion in the E-B juncrecombina-tion.

I_C

I_B

_dc

g-r current

Current crowding, high-level injection series resistence

ln(I

)



_dc g-r Current crowding or r_C



_dc

modification:

•

Low-current levels



recombination current

•

large current levels



high-level injection and

series resistance