Semiconductor Device Physics
Lecture 9
BJT Fundamentals
and
BJT Static Characteristics
Dr. Gaurav Trivedi,
EEE Department,
IIT Guwahati
Bipolar Junction Transistors (BJTs)
 Over the past decades, the higher layout density and low-power advantage of CMOS
(Complementary Metal–Oxide–Semiconductor) has eroded away the BJT’s dominance in
integrated-circuit products.
 Higher circuit density  better system performance
 BJTs are still preferred in some digital-circuit and analog-circuit applications because of their
high speed and superior gain
 Faster circuit speed (+)
 Larger power dissipation (–)
• Transistor: current flowing between two
terminals is controlled by a third terminal
Introduction
Circuit Configurations
Modes of Operation
 Common-Emitter Output Characteristics
Mode
E-B Junction
C-B Junction
Saturation
forward bias
forward bias
Active/Forward
forward bias
reverse bias
Inverted
reverse bias
forward bias
Cutoff
reverse bias
reverse bias
BJT Electrostatics
 Under equilibrium and normal operating conditions, the BJT may be viewed electrostatically
as two independent pn junctions.
NAE  NDB  NAC
WCB  WEB
W  WB  xnEB  xnCB
W : quasineutral
base width
BJT Electrostatics
 Electrostatic potential, V(x)
 Electric field, E(x)
 Charge density, ρ(x)
BJT Design
 Important features of a good transistor:
 Injected minority carriers do not recombine in the neutral base region  short base,
W << Lp for pnp transistor
 Emitter current is comprised almost entirely of carriers injected into the base rather
than carriers injected into the emitter  the emitter must be doped heavier than the
base
pnp BJT, active mode
Base Current (Active Bias)
 The base current consists of majority carriers (electrons) supplied for:
1. Recombination of injected minority carriers in the base
2. Injection of carriers into the emitter
3. Reverse saturation current in collector junction
4. Recombination in the base-emitter depletion region
EMITTER
COLLECTOR
BASE
1
iCB0
4
p-type
2
n-type
3
p-type
BJT Performance Parameters (pnp)
Collector Current (Active Bias)
 The collector current is comprised of:
 Holes injected from emitter, which do not recombine in the base 2
 Reverse saturation current of collector junction 3
I C  αdc I E  ICB0
ICB0 :collector current when IE = 0
IC  αdc ( IC  I B )  ICB0
αdc
I CB0
IC 
IB 
1  αdc
1  αdc
I C  βdc I B  ICE0
Common emitter dc current gain:
 dc
IC
dc 

1   dc I B
Notation (pnp BJT)
Minority
carrier
constants
N E  N AE
DE  DN
E  n
LE  LN
nE0  np0
 ni2 N E
N B  N DB
DB  DP
B  p
LB  LP
pB0  pn0
 ni2 N B
N C  N AC
DC  DN
C  n
LC  LN
nC0  np0
 ni2 N C
Emitter Region
 Diffusion equation:
d 2 nE nE
0  DE

2
dx
E
 Boundary conditions:
nE ( x  )  0
nE ( x  0)  nE0 (eqVEB
kT
 1)
Base Region
 Diffusion equation:
d 2 pB pB
0  DB

2
dx
B
 Boundary conditions:
pB (0)  pB0 (eqVEB kT  1)
pB (W )  pB0 (eqVCB kT  1)
Collector Region
 Diffusion equation:
d 2 nC nC
0  DC

2
dx
C
 Boundary conditions:
nC ( x '  )  0
nC ( x '  0)  nC0 (eqVCB
kT
 1)
Ideal Transistor Analysis
 Solve the minority-carrier diffusion equation in each quasi-neutral region to obtain excess
minority-carrier profiles
 Each region has different set of boundary conditions
nE ( x),
 Evaluate minority-carrier diffusion currents at edges of depletion regions
p ( x),
B
nC ( x)
I En
I Cn
d nE
 qADE
dx x0
d nC
 qADC
dx x0
I Ep
I Cp
d pB
 qADB
dx
d pB
 qADB
dx
x 0
x W
 Add hole and electron components together  terminal currents is obtained
IC
IE
IB
I E  I Ep  I En
I C  I Cp  I Cn
IB  IE  IC
Emitter Region Solution
 Diffusion equation:
 General solution:
 Boundary conditions:
d 2 nE nE
0  DE

2
dx
E
 x LE
x LE

nE ( x )  Ae
 A2e
1
nE ( x  )  0
nE ( x  0)  nE0 (eqVEB kT  1)
nE ( x)  nE0 (eqVEB kT 1)e x LE
 Solution
I En
d nE
 qADE
dx
DE
 qA
nE0 (eqVEB
LE
x0
kT
 1)
Collector Region Solution
 Diffusion equation:
 General solution:
 Boundary conditions:
d 2 nC nC
0  DC

2
dx
C
 x LC
x LC

nC ( x )  Ae
 A2e
1
nC ( x  )  0
nC ( x  0)  nC0 (eqVCB kT  1)
nC ( x)  nC0 (eqVCB
 Solution
I Cn
kT
1)ex LC
DC
d nC
 qA
nC0 (eqVCB
 qADC
LC
dx x0
kT
 1)
Base Region Solution
d 2 nB pB
0  DB

2
dx
B
 Diffusion equation:
 General solution:
 x LB
x LB
pB ( x)  Ae

A
e
1
2
 Boundary conditions:
pB (0)  pB0 (eqVEB kT  1)
pB (W )  pB0 (eqVCB kT  1)
 Solution
(W  x ) LB
 (W  x ) LB


e

e
qVEB kT
pB ( x)  pB0 (e
 1) 

W LB
W LB
e
 e

x LB
 x LB


e

e
qVCB kT
 pB0 (e
 1)  W LB W LB 
e
e

Base Region Solution
 Since
e  e
sinh( ) 
2
(W  x ) LB
 (W  x ) LB


e

e
qVEB kT
pB ( x)  pB0 (e
 1) 

W LB
W LB
e
 e

x LB
 x LB


e

e
qVCB kT
 pB0 (e
 1)  W LB W LB 
e
e

 We can write
as
pB ( x)  pB0 (e
qVEB kT
 pB0 (eqVCB
 1)
kT
sinh  (W  x) LB 
sinh(W LB )
sinh( x LB )
 1)
sinh(W LB )
Base Region Solution
 Since
I Ep
I Cp
d
d  e  e
sinh( ) 

d
d  2
 e  e
 cosh( )

2

d pB
 qADB
dx x 0
 cosh(W LB ) qVEB
DB
 qA
pB0 
(e
LB
 sinh(W LB )
d pB
 qADB
dx x W

DB
1
 qA
pB0 
(eqVEB
LB
 sinh(W LB )
kT
kT
1
 1) 
(eqVCB
sinh(W LB )
cosh(W LB ) qVCB
 1) 
(e
sinh(W LB )
kT
kT

 1) 


 1) 

Terminal Currents
 Since
 Then
I E  I En  I Ep , IC  ICn  ICp
 DE
DB
cosh(W LB )  qVEB
 I E  qA 
nE0 
pB0
 (e
LB
sinh(W LB ) 
 LE

 DB
 qVCB kT
1

pB0
 1) 
 (e
sinh(W LB ) 
 LB

 D
 qVEB kT
1
B
 I C  qA 
p
(e
 1)
 L B0 sinh W L  
 B
B 
 DC
DB
cosh(W LB )  qVCB

nC0 
pB0
 (e
LB
sinh(W LB ) 
 LC
 I B  I E  IC
kT
kT
 1)

 1) 

Simplified Relationships
 To achieve high current gain, a typical BJT will be constructed so that W << LB.
 Using the limit value
lim sinh( )  
 0
lim cosh( )  1 
 0
2
2
Due to VEB
 We will have
x

pB ( x)  pB0 (e
 1) 1  
 W
 x
qVCB / kT
 pB0 (e
 1)  
W 
qVEB / kT
x
pB ( x)  pB (0)   pB0 (W )  pB (0) 
W
Due to VCB
Performance Parameters
 For specific condition of
 “Active Mode”: emitter junction is forward biased and collector junction is reverse
biased
 W << LB, nE0/pB0  NB/NE
1

DE N B W
1
DB N E LE
 dc 
T 
1
DE N B W 1  W 
1
  
DB N E LE 2  LB 
2
,  dc 
1
1W 
1  
2  LB 
2
1
DE N B W 1  W 
  
DB N E LE 2  LB 
2
Ebers-Moll Model
 The Ebers-Moll model is a large-signal equivalent circuit
which describes both the active and saturation regions of BJT
operation.
 This model is to be used to calculate IC, IE for given VBE, VBC.
D
cosh W LB   qVEB
D
I E  qA   E nE0  B pB0
 (e
L
L
sinh
W
L
 B 
  E
B


 qVCB kT
1
IFO   DB pB0
(
e

1)


L
sinh
W
L



B 
 B
kT
 1)
 D
 qVEB kT
1
IRO
I C  qA  B pB0
 1)
 (e
L
sinh
W
L
 B
 B

D
cosh W LB   qVCB kT
D
  C nC0  B pB0
(
e

1)


L
L
sinh
W
L



B
B 
 C
If only VEB is applied (VCB = 0):
If only VCB is applied (VEB = 0):
I E  I F0 (eqVEB kT  1)
I C   F I F0 (eqVEB kT  1)
I B  (1   F ) I F0 (eqVEB kT  1)
I C   I R0 (eqVCB kT  1)
I E   R I R0 (eqVCB kT  1)
I B  I R0 (1   R )(eqVCB kT  1)
Ebers-Moll Model
 Reciprocity relationship:
 F I F0   R I R0
pB0
DB
 qA
LB sinh(W LB )
R : reverse common
base gain
F : forward common
base gain
 In the general case, when VEB
and VCB are non-zero:
I C   F I F0 (e qVEB
kT
 1)  I R0 (e qVCB
fraction of E-B diode
current that makes it
to the C-B junction
I E  I F0 (e qVEB
kT
E-B diode
current
kT
 1)
C-B diode
current
 1)   R I R0 (e qVCB
kT
 1)
fraction of C-B diode
current that makes it
to the E-B junction
Deviations from the Ideal
 Common base
Deviations, due to
model limitations
 Common emitter
Base-Width Modulation
 Common-Emitter Configuration
Active Mode Operation
 Recalling two formulas,
W
IE
P+
N
IC
P
+ 
VEB
I C  βdc I B  ICE0
1
 dc 
2
DE N B W 1  W 
  
DB N E LE 2  LB 
D N L
 B E E
DE N BW
pB(x)
qVEB kT
pB0 (e
1)
(VCB=0)
Increasing –
VCB
x
0
W
If –VCB increases
→ W decreases
→ dc increases
→ IC increases
Punch-Through
 Punch-Through: E-B and
C-B depletion regions in the base touch
each other, so that W = 0.
WB  xnEB  xnCB
 As –VCB increases beyond the punchthrough point, the E-B potential hill
decreases and therefore increases the
carrier injections and IC.
Breakdown Mechanisms
 In the common-emitter configuration, for high output voltage VCE, the output current IC will
increase rapidly due to the two mechanisms: punch-through and avalanche.
Punch-through
Avalanche
VEC =VEB  VCB
Increasing reverse bias
of C-B junction
Avalanche Multiplication
 Holes [0] are injected into the base [1],
then collected by the C-B junction.
 Some holes in the C-B depletion region
have enough energy do impact ionization
[2].
 The generated electrons are swept into
the base [3], then injected into the
emitter [4].
 Each injected electron results in the
injection of IEp/IEn holes from the emitter
into the base [5].
 For each pair created in the C-B
depletion region by impact ionization,
(IEp/IEn) +1> dc additional holes flow into
the collector.
 This means that carrier multiplication in
C-B depletion region is internally
amplified.
pnp BJT
Mαdc
I CB0
IC 
IB 
1  Mαdc
1  Mαdc
M : multiplication factor
Geometrical Effects
 Emitter area is not equal to collector area.
 Current does not flow in one direction
only.
 Series resistance.
 Voltage drop occurs not only across the
junction.
 Current crowding.
 Due to lateral flow, current is larger around
emitter periphery than the collector
periphery.
Graded Base
 Dopants are injected through diffusion.
 More or less falling exponential distribution with
distance into beneath of the semiconductor.
 The doping within the base is not constant as
assumed in ideal analysis.
 A function of position, having maximum at E-B
junction and minimum at C-B junction.
 Creating a built-in electric field.
 The electric field enhances the transport of minority
carrier across the quasineutral width of the base.
 Increase of IE and IC.
kT q
E
xdiff
xdiff : exponential
decay constant
Figures of Merit
Due to recombination in
emitter depletion region
Gummel Plot
Due to high level injection in
base, base series resistance, and
current crowding
Polysilicon Emitter BJT
 dc is larger for a poly-Si emitter BJT as
compared with an all-crystalline emitter BJT.
 This is due to reduced dpE(x)/dx at the edge of
the emitter depletion region.
Lower p
 Continuity of hole current in emitter
d pE1
d pE2
qDE1
 qDE2
dx
dx
d pE1 DE2 d pE2 E2 d pE2


dx
DE1 dx
E1 dx
(1  polysilicon; 2  Si)
Shallower slope
 less JP
 higher , 
Summary on BJT Performance
 High gain (dc >> 1)
 One-sided emitter junction, so that emitter efficiency   1
 Emitter doped much more heavily than base (NE >> NB).
 Narrow base, so base transport factor T  1.
 Quasi-neutral base width << minority-carrier diffusion length
(W << LB).
 IC determined only by IB (IC  function of VCE or VCB)
 One-sided collector junction, so that quasineutral base width W does not change
drastically with changes in VCE or VCB.
 Base doped more heavily than collector (NB > NC),
W = WB – xnEB – xnCB for pnp BJT.