EEE 531: Semiconductor Device Theory I
Instructor: Dragica Vasileska
Department of Electrical Engineering
Arizona State University
Bipolar Junction Transistor
EEE 531: Semiconductor Device Theory I
Outline
1.
2.
3.
4.
Introduction
IV Characteristics of a BJT
Breakdown in BJT
Geometry Effects in BJT
EEE 531: Semiconductor Device Theory I
1. Introduction
Original
point-contact
transistor
(1947)
Inventors of the transistor:
William Shockley, John Bardeen
and Walter Brattain
First grown transistor (1950)
EEE 531: Semiconductor Device Theory I
(A) Terminology and symbols
PNP - transistor
NPN - transistor
C
E
B
B
E
+
p+
n
VEB
C
E
p
C
+
E
VCB
B
n+
VBE
p
+ +
B
n
C
VBC
• 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.
EEE 531: Semiconductor Device Theory I
• There are four regions of operation of a BJT transistor
(example for a pnp BJT):
VEB
Forward active region
Saturation region
(emitter-base FB, collector-base RB) (both junctions forward biased)
VCB
Inverted active region
Cutoff region
(both junctions reverse biased) (emitter-base RB, collector-base FB)
• Since it has three leads, there are three possible amplifier
types:
C
B
E
p+
n
p
VEB
B
(a) Common-base
C
VCB
VEB
p
n
p+
B
VEC
VCB
E
(b) Common-emitter
EEE 531: Semiconductor Device Theory I
p+
n
p
E
VEC
C
(c) Common-collector
(B) Qualitative description of transistor operation
p+
n
p
IEp {
ICp
IEn
ICn
IB1
IB3
IB2
Icn
IEn
EC
• Emitter doping is much larger than
base doping
• Base doping larger than collector
doping
• Current components:
I E  I Ep  I En
I C  I Cp  I Cn
I B  I E  I C  I B1  I B 2  I B 3
EF
EV
IEp
ICp
• IB1 = current from electrons being
back injected into the forward-biased
emiter-base junction
• IB2 = current due to electrons that
replace the recombined electrons in
the base
• IB3 = collector current due to
thermally-generated electrons in the
collector that go in the base
EEE 531: Semiconductor Device Theory I
(C) Circuit definitions
Base transport factor T:
T  I Cp / I Ep
Ideally it would be equal to unity
(recombination in the base reduces its value)
Emitter injection efficiency :

I Ep
I Cp  I Ep

I Ep
IE
Approaches unity if emitter doping is
much larger than base doping
Alpha-dc:
 dc
I Cp
I C I Cp  I Cn



 T 
I E I Ep  I En I Ep  I En
Beta-dc:
 dc
IC
IC
 dc



I B I E  I C 1   dc
Current gain is large when dc
approaches unity
EEE 531: Semiconductor Device Theory I
Collector-reverse saturation current:
I BC 0  I Cn  I C  I Cp  I Cn   dc I E  I BC 0
Collector current in common-emitter configuration:
I C   dc I C  I B   I BC 0
 dc
I BC 0
 IC 
IB 
1   dc
1   dc
 I C   dc I B  I EC 0
 I EC 0  1   dc I BC 0
Large current gain capability:
Small base current IB forces the E-B junction to be forward
biased and inject large number of holes which travel through
the base to the collector.
EEE 531: Semiconductor Device Theory I
(D) Types of transistors
• Discrete (double-diffused)
p+np transistor
Emitter Base
5 m
200 m
• Integrated-circuit
n+pn transistor
6 m
200 m
EEE 531: Semiconductor Device Theory I
Collector
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:
p+
NAE = NE
Ln = LE
Dn = DE
np0 = nE0
n = E
n
NDB = NB
Lp = LB
Dp = DB
pn0 = pB0
p = B
EEE 531: Semiconductor Device Theory I
p
NAC = NC
Ln = LC
Dn = DC
np0 = nC0
n = C
• The carrier concentration variation for various regions of operation is
shown below:
E-B
C-B
pB(0)
saturation
nC(0’)
nE(0”)
pB(W)
Forward
active p
nE(x”)
nC(x’)
pB(x)
nC0
B0
nE0
pB(W)
x”
x’
0”
0
Cut-off
W
0’
• Assuming long emitter and collector regions, the solutions of the
minority electrons continuity equation in the emitter and collector are
of the form:

e
VEB / VT
n E ( x" )  n E 0 e
nC ( x ' )  nC 0
VCB / VT

 1e
1 e
EEE 531: Semiconductor Device Theory I
 x" / LE
 x ' / LC
• For the base region, the steady-state solution of the continuity equation
for minority holes, of the form:
2
d p B
dx
2

p B
2
LB
0
using the boundary conditions:

VEB / VT
p B (0)  p B 0 e


VCB / VT
 1 , p B (W )  p B 0 e

1
is given by:
sinh(W  x ) / LB  VEB / VT
p B ( x )  p B 0
e
1
sinhW / LB 


sinh x / LB  VCB / VT
 pB0
e
1
sinhW / LB 


Note: The presence of the sinh() terms means that recombination in
the base quasi-neutral region is allowed.
EEE 531: Semiconductor Device Theory I
• Once we have the variation of nE(x”), pB(x) and nC(x’), we can
calculate the corresponding diffusion current components:
E-B
IE=InE(0”)+IpB(0)
C-B
IC=InC(0’)+IpB(W)
IpB(0)
IpB(W)
InE(x”)
InE(0”)
IpB(x)
InC(0’)
InC(x’)
IB2=IpB(0)-IpB(W)
x”
x’
0”
0
W
0’
Base recombination current
• Expressions for various diffusion current components:
dnC
d n E
I nE (0" )   AqDE
, I nC (0' )  AqDC
dx" x"0"
dx '
d p B
I pB (0)   AqDB
dx
dp B
, I pB (W )   AqDB
dx
x 0
EEE 531: Semiconductor Device Theory I
x '  0'
x W
• Final results for the emitter, base and collector currents:
IE 

IC 

IB 

2
Aqni 
 VEB / VT
DE
DB

coth(W / LB )  e
1
 LE N E LB N B



Aqni2
DB
1
V /V
e CB T  1
LB N B sinh(W / LB )
2
Aqni
DB
1
V /V
e EB T  1
LB N B sinh(W / LB )



2
Aqni 

 VCB / VT
DC
DB

coth(W / LB )  e
1
 LC N C LB N B

2
Aqni 
DE
DB

 LE N E LB N B



  VEB / VT
1
1
coth(W / LB )  sinh(W / L )   e

B 
2
Aqni 


DC
  VCB / VT
DB 
1

coth(W / LB ) 
1
e


sinh(W / LB )  
 LC N C LB N B 
EEE 531: Semiconductor Device Theory I


• For short-base diodes, for which W/LB<<1, we have:
x2
x
1

cosh( x )  1  ; sinh( x )  x; coth( x ) 
2
sinh( x ) 2
• Therefore, for short-base diodes, the base current simplifies to:
IB2
IB1

IB 

2
Aqni 

DE
DB
W  VEB / VT


1
e
 LE N E LB N B 2 LB 

2
Aqni 

DC
DB
W  VCB / VT


1
e
 LC N C LB N B 2 LB 


-IB3


IB2
• As W/LB0 (or B ), the recombination base current IB2 0 .
EEE 531: Semiconductor Device Theory I
(B) Current expressions for different biasing regimes
Forward-active region:
• E-B junction is forward biased, C-B junction is reversebiased:
IE 
2
Aqni 
IC 
Aqni2
IB 
2
Aqni 

 VEB / VT
DE
DB
coth(W / LB ) e

 I En  I Ep
 LE N E LB N B

DB
1
VEB / VT
e
 I Cp
LB N B sinh(W / LB )
DE
DB  cosh(W / LB )  1  VEB / VT

e


 LE N E LB N B  sinh(W / LB )  
2
Aqni 
DC
DB  cosh(W / LB )  1 




 LC N C LB N B  sinh(W / LB )  
EEE 531: Semiconductor Device Theory I
These terms vanish if
there is no recombination in the base
• Graphical description of various current components:
p+
n
p
IE
IEp
{
}I
IEn
{
ICn
IB1
IB3
Cp
IC
Recombination in the base
is ignored in this diagram.
IB
• The emitter injection efficiency is given by:

I Ep
I Ep  I En
LE N E DB
LE N E DB
coth(W / LB )
LB N B DE
WN B DE


short
LE N E DB
LE N E DB
1
coth(W / LB ) base 1 
LB N B DE
WN B DE
EEE 531: Semiconductor Device Theory I
• The base transport factor is given by:
T 
I Cp
I Ep
2
1
W

1  2
cosh(W / L B ) short
2 LB
base
• Common-emitter current gain:
LE N E DB
coth(W / LB )
LB N B DE
LE N E DB
dc 

short WN D
LE N E DB
2
B E
1 2
coth(W / LB ) sinh (W / 2LB ) base
LB N B DE
GB = WNB (Gummel number)
• For a more general case of a non-uniform doping in the base, the
Gummel number is given by:
W
G B   N B ( x )dx
Typical values of GB:
0
EEE 531: Semiconductor Device Theory I
Saturation region:
• E-B and C-B junctions are both forward biased:
IE 

 VEB / VT
DE
DB


coth(W / LB ) e
 LE N E LB N B

2
Aqni
IC 

2
Aqni 
DB
V /V
coth(W / LB )e CB T  I En  I Ep - I Ep'
LB N B
2
Aqni
DB
1
V /V
e EB T
LB N B sinh(W / LB )
2
Aqni 
 VCB / VT
DC
DB

coth(W / LB ) e
 I Cp  I Cn  I Cp '
 LC N C LB N B

I B  I E  IC

Base current much larger
than in forward-active regime
I Cn   I B 3
EEE 531: Semiconductor Device Theory I
• Graphical description of various current components:
p+
n
p
IE
IEp
{
}I
} ICp’
IEp’ {
IEn
Cp
IC
ICn
{
IB3
IB1
Recombination in the base
is ignored in this diagram.
IB
• Important note:
 As VCB 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.
EEE 531: Semiconductor Device Theory I
Cutoff region:
• E-B and C-B junctions are both reverse biased. For shortbase diode with no recombination in the base, this leads to:
IE 
 Aqni2
DE
2 DC
  I En , I C  Aqni
 I Cn
LE N E
LC N C
I B  I E  IC 
2
 Aqni 
DC 
DE
2 DC

  Aqni

LC N C
 LE N E LC N C 
p+
IE
n
p
IC
IEn
ICn
IB1
IB
IB3
EEE 531: Semiconductor Device Theory I
Recombination in the base
is ignored in this diagram.
(C) Form of the input and output characteristics
Common-base configuration:
IE
IC
Forward active
saturation
VCB<-3VT
IE0
VCB=0
IBC0
VEB
cutoff
IE=0
VBC
Common-emitter configuration:
IC
IB
VCB= 0
Forward active
saturation
VEC= 0
IB0
VEC > 3VT
VEB
IEC0
cutoff
EEE 531: Semiconductor Device Theory I
IB=0
VEC
• Note on the collector-base reverse saturation current:
C
E
ICn
VBC>0
B
IB=IBC0
VBC
EEE 531: Semiconductor Device Theory I
Minority electrons in
the collector that are
within LC from the C-B
junction are collected
by the high electric
field into the base.
• Why is IEC0 much larger than IBC0?
E
IEn
ICn
IEp
ICp
C
VEC > 0
B IB=0
IE = IEC0
I EC 0  I Cn  I Cp  I BC 0  I Ep   dc  1I BC 0 ,  dc 
I Ep
I Cn
 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 IEC0 >> IBC0 .
EEE 531: Semiconductor Device Theory I
(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:
IF
IR
IE
RIR

e
VEB / VT
IC I F  I F 0 e
I R  I R0
FIF
VCB / VT

 1
1
IB
• Using the results for IE and IC, we can calculate various coefficient:

VEB / VT
IE  IF0 e


e
 1   R I R0 e
VEB / VT
IC  F I F 0 e

VCB / VT

 1  I R0
VCB / VT

 1
1
• The reciprocity relation for a two-port network requires that:
 F I F 0   R I R0
EEE 531: Semiconductor Device Theory I
(E) Early effect
• In deriving the IV-characteristics of a BJT, we have assumed that dc,
dc, IBC0 and IEC0 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 Weff
to decrease:
Weff  W (metallurgical)  xdeb  xdcb
• The common-emitter current gain, taking into account the effective
width of the base quasi-neutral region (assuming =1) is then given by:
 dc
1
 T  1  Weff LB
2

2
• The common-emitter current gain can be approximated with:
 dc
 LB
 dc

 2
W
1   dc
 eff
EEE 531: Semiconductor Device Theory I




2
• Graphical illustration of the Early (base-width modulation) effect:
Weff’
Weff
E
C
B
• If we approximate the collector current with the hole current:
I C  I Cp 
2
Aqni W
B
DB
VEB / VT
e

2
Aqni
 N B ( x )dx
DB
VEB / VT
e
GB (WB )
o
we find:
I C
IC
n(WB ) WB
  IC

VBC
G B VBC V A
Early voltage
• Since WB/ VBC <0, we have that IC/ VBC > 0, i.e. IC increases.
EEE 531: Semiconductor Device Theory I
• Empirically, it is found that a linear interpolation of the collector
current dependence on VEC is adequate in most cases:
I C   dc I B  I EC 0 1  VEC / V A    dc I B  I EC 0 1  VEC / V A 
qGBWB
where the Early voltage is given by: V A  k A
k s 0
• Graphical illustration of the Early effect:
IC
VEC
-|VA|
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).
EEE 531: Semiconductor Device Theory I
(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 pnjunctions)
EEE 531: Semiconductor Device Theory I
• 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 VBC ,
i.e. small increase in VBC is needed for large increase in IC .
VBC increasing
p+
n
p
Note: Punch-through voltage is
usually much larger than the
avalanche breakdown voltage.
• The mechanism of avalanche breakdown in BJT’s depend
on the circuit configuration (common-emitter or commonbase configuration).
EEE 531: Semiconductor Device Theory I
• For a common-base configuration, the avalanche breakdown
in the C-B junction (open emitter) BVBC is obtained via the
maximum (breakdown) electric field FBR (~300 kV/cm for
Si and 400 kV/cm for GaAs):
BVBC 
2
k s  0 FBR
2q
2
k s  0 FBR
 1
1 

 

2 qN C
 N B NC 
• The increase in current for voltages higher than BVBC is
reflected via the multiplication factor in the current expression. 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:
1
M CB
mb 
  V

BC
 
 1  
  BVBC  
EEE 531: Semiconductor Device Theory I
• For a common-emitter configuration, the collector-emitter
breakdown voltage BVEC is related to BVBC :
I E  IC
Open base configuration
M BC I BC 0
I C  M BC  dc I E  I BC 0   I C 
 M EC I EC 0
1   dc M BC
Multiplication factor
M EC
50
40
M BC (1   dc )

 BVEC  BVBC 1   dc 1 / mb
1   dc M BC
MEC
MBC
Much smaller than BVBC
due to transistor action.
30
20
10
20
40
Reverse voltage
EEE 531: Semiconductor Device Theory I
IC
IC
VEC
BVBC0
Common-base output
characteristics
VBC
BVEC0
Common-emitter output
characteristics
EEE 531: Semiconductor Device Theory I
4. Geometry effects
• The geometry effects include:
(1) Bulk and contact resistance effects
(2) Current crowding effect
B
E
p+
p
n+
B
Base contacts
p+
n
n+
collector
Emitter contacts
• Base current flows in the direction parallel to the E-B
junction, which gives rise to base spreading resistance.
• When VBB’ is much larger than VT, most of the emitter
current is concentrated near the edges of the E-B junction.
EEE 531: Semiconductor Device Theory I
Generation-recombination in the depletion region
Current crowding, high-level
injection series resistence
ln(IC)
ln(IB)
IC
dc
IB
• Reverse-biased C-B junction
adds a generation current to IC.
• Forward-biased E-B junction
has recombination current. IC is
g-r current
not affected by the recombinaVEB tion in the E-B junction.
dc
Current
dc modification:
crowding or rC
• Low-current levels 
recombination current
• large current levels 
g-r
high-level injection and
series resistance
ln(IC)
EEE 531: Semiconductor Device Theory I