Chapter 8 Bipolar Junction Transistors
• Since 1970, the high density and low-power advantage of
the MOS technology steadily eroded the BJT’s early dominance.
• BJTs are still preferred in some high-frequency and analog
applications because of their high speed and high power output.
Question: What is the meaning of “bipolar” ?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-1
Ec
Efn
8.1 Introduction
to the EBJT
(b)
v
-
Efp
VB E
-
VCB
NPN BJT:
B
E
N+
Emitter
VBE
C
P
Base
N
VB E
IC
Collector
(c)
VCB
VCB
0
IC is an exponential
function of forward
VBE and independent
of reverse VCB.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-2
Common-Emitter Configuration
Question: Why is IB often preferred as a parameter over VBE?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-3
8.2 Collector Current
depletion layers
N+
emitter
d 2 n n
 2
2
dx
LB
N
P
base
collector
x
0
WB
B : base recombination lifetime
LB   B DB
DB : base minority carrier (electron)
diffusion constant
Boundary conditions :
n(0)  nB 0 (e qVBE / kT  1)
qVBC / kT

n (WB )  nB 0 (e
 1)  nB 0  0
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-4
n( x )  nB 0 (e qVBE / kT
n
------------n( x )n/n0 (0) 2
1
 WB  x 

sinh 
 LB 
 1)
sinh WB / LB 
ni qV BE  kTn 2

iB
-------e
– 1 qVBE / kT

(
x
)

(e
Nn
B
NB
8.2 Collector Current
dn
I C  AE qDB
dx
DB niB2 qVBE / kT
 AE q
(e
 1)
WB N B
 1)
I C  I S (e qVBE / kT  1)
It can be shown
0
x/ B
x/W
n( x )  n(0)(1  x / WB )
1
qni2 qVBE / kT
I C  AE
(e
 1)
GB
WB
ni2 p
GB   2
dx
n DB
0 iB
niB2 qVBE / kT

(e
 1)(1  x / WB )
NB
GB (s·cm4) is the base Gummel number
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-5
8.2.1 High Level Injection Effect
•At low-level injection,
inverse slope is 60 mV/decade
10-2
IkF
10-4
IC (A)
•High-level injection effect :
At large VBE, n  p  N B
n  p  n  p
10-6
60 mV/decade
10-8
10-10
2 q ( EFn  EFp ) / kT
np  ni e
 ni eqVBE / kT
2
10-12
0
0.2
0.4
 n  p  ni e qVBE / 2 kT
GB  p  ni e qVBE / 2 kT
0.6
0.8
1.0
VBE
I C  ni e
qVBE / 2 kT
When p > NB , inverse slope is 120mV/decade.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-6
8.3 Base Current
Some holes are injected from the P-type base into the N+ emitter.
The holes are provided by the base current, IB .
(a)
contact emitter
I
E
+
base
electron flow
collector contact
–
hole flow
I
B
IC
pE' nB'
(b)
WE
WB
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-7
8.3 Base Current
(a)
contact emitter
collector contact
base
electron flow
I
E
+
–
hole flow
IC
I
B
qni2 qVBE / kT
I B  AE
(e
 1)
GE
WE
2
i
2
iE
n n
GE  
dx
n DE
0
For a uniform emitter,
DE niE2 qVBE / kT
I B  AE q
(e
 1)
WE N E
Is a large IB desirable? Why?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-8
8.4 Current Gain
Common-emitter current gain, F :
Common-base current gain:
IC   F I E
IC
F 
IB
IC
IC
IC / I B
F
F  


I E I B  IC 1  IC / I B 1   F
It can be shown that  F 
GE DBWE N E niB2
F 

GB DEWB N B niE2
F
1F
How can F be maximized?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-9
EXAMPLE: Current Gain
A BJT has IC = 1 mA and IB = 10 mA. What are IE, F and F?
Solution:
I E  I C  I B  1 mA  10 μA  1.01 mA
 F  I C / I B  1 mA / 10 μA  100
 F  I C / I E  1 mA / 1.01 mA  0.9901
We can confirm
F
F
F 
and  F 
1 F
1F
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-10
8.4.1 Emitter Bandgap Narrowing
To raise F, NE is typically very large.
Unfortunately, large NE makes niE2  ni2
(heavy doping effect).
N E niB2

N B niE2
ni2  NC NV e
niE2  ni2e
 Eg / kT
EgE / kT
Since ni is related to Eg , this effect is
also known as band-gap
narrowing.
EgE is negligible for NE < 1018 cm-3,
is 50 meV at 1019cm-3, 95 meV at 1020cm-3,
and 140 meV at 1021 cm-3.
Emitter bandgap narrowing makes it difficult to raise F by
doping the emitter very heavily.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-11
8.4.2 Narrow-Bandgap Base and Heterojuncion BJT
N E niB2

N B niE2
To further elevate F , we can raise niB by
using an epitaxial Si1-hGeh base.
With h = 0.2, EgB is reduced by 0.1eV and niE2 by 30x.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-12
EXAMPLE: Emitter Bandgap Narrowing and SiGe Base
Assume DB = 3DE , WE = 3WB , NB = 1018 cm-3, and niB2 = ni2. What is
F for (a) NE = 1019 cm-3, (b) NE = 1020 cm-3, and (c) NE = 1020 cm-3
and a SiGe base with EgB = 60 meV ?
(a) At NE = 1019 cm-3, EgE  50 meV,
niE2  ni2e
EgE / kT
 ni2e50 meV / 26 meV  ni2e1.92  6.8ni2
DBWE N E ni2 9 1019  ni2
F 

 18
 13
2
2
DEWB N B niE 10  6.8ni
(b) At NE = 1020 cm-3, EgE  95 meV
niE2  38ni2
 F  24
(c) niB2  ni2eEgB / kT  ni2e60 meV / 26 meV  10ni2
 F  237
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-13
8.4.3 Poly-Silicon Emitter
A high-performance BJT typically has a layer of As-doped N+
poly-silicon film in the emitter.
F is larger due to the large WE , mostly made of the N+ polysilicon. (A deep diffused emitter junction tends to cause emittercollector shorts.)
N+-poly-Si
emitter
SiO2
P-base
N-collector
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-14
F
8.4.4 Gummel Plot and F Fall-off at High and Low Ic
SCR BE current
From top to bottom:
VBC = 2V, 1V, 0V
Why does one want to operate BJTs at low IC and high IC?
Why is F a function of VBC in the right figure?
Hint: See Sec. 8.5 and Sec. 8.9.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-15
8.5 Base-Width Modulation by Collector Voltage
Output resistance :
 I C
r0  
 VCE

VA
 
IC

IB3
IC
IB2
VA : Early Voltage
VA
1
IB1
0
Large VA (large ro )
is desirable for a
large voltage gain
VCE
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-16
8.5 Base-Width Modulation by Collector Voltage
V BE
N+
N
P
emitter
base
WB3
WB2
WB1
collector
VCE
}
VCE 1 < VCE 2 <VCE 3
n'
x
How can we reduce the base-width modulation effect?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-17
8.5 Base-Width Modulation by Collector Voltage
VBE
The base-width modulation
effect is reduced if we
(A) Increase the base width,
(B) Increase the base doping
concentration, NB , or
(C) Decrease the collector doping
concentration, NC .
N+
emitter
N
P
base
WB3
WB2
WB1
n'
collector
VCE
}
VCE1< VCE2<VCE3
x
Which of the above is the most acceptable action?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-18
8.6 Ebers-Moll Model
IB
IC
active region
saturation
region
0
VCE
The Ebers-Moll model describes both the active
and the saturation regions of BJT operation.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-19
8.6 Ebers-Moll Model
IC is driven by two two forces, VBE and VBC .
VB E
When only VBE is present :
I C  I S (e
IB 
IS
qVBE / kT
VB C
IB
 1)
(e qVBE / kT  1)
E
F
Now reverse the roles of emitter and collector.
When only VBC is present :
I E  I S (e qVBC / kT  1)
IB 
IS
R
C
IC
R : reverse current gain
F : forward current gain
(e qVBC / kT  1)
I C   I E  I B   I S (1 
B
1
R
)(e qVBC / kT  1)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-20
8.6 Ebers-Moll Model
In general, both VBE and VBC are present :
I C  I S (e
IB 
IS
F
qVBE / kT
(e
 1)  I S (1 
qVBE / kT
 1) 
IS
F
1
R
)(e qVBC / kT  1)
(e qVBC / kT  1)
In saturation, the BC junction becomes forward-biased, too.
VBC causes a lot of holes to be injected
into the collector. This uses up much
of IB. As a result, IC drops.
VCE (V)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-21
8.7 Transit Time and Charge Storage
When the BE junction is forward-biased, excess holes are stored
in the emitter, the base, and even in the depletion layers.
QF is all the stored excess hole charge
QF
F 
IC
F is difficult to be predicted accurately but can be measured.
F determines the high-frequency limit of BJT operation.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-22
8.7.1 Base Charge Storage and Base Transit Time
Let’s analyze the excess hole charge and transit time in
the base only.
QFB  qAE n(0)WB / 2
np' = n'p
0
QFB
WB2
  FB 
IC
2 DB
niB22iB qV
 kT
qVBEBE/ kT

n
(
0
)

(
e
 1–)1 




n 0 = ------- e
N BB
x
WB
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-23
EXAMPLE: Base Transit Time
What is FB if WB = 70 nm and DB = 10 cm2/s?
Answer:
 FB
WB2 (7 106 cm) 2
12



2
.
5

10
s  2.5 ps
2
2 DB
2 10 cm /s
2.5 ps is a very short time. Since light speed is
3108 m/s, light travels only 1.5 mm in 5 ps.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-24
8.7.2 Drift Transistor–Built-in Base Field
The base transit time can be reduced by building into the base
a drift field that aids the flow of electrons. Two methods:
• Fixed EgB , NB decreases from emitter end to collector end.
E
B
-
C
Ec
Ef
Ev
• Fixed NB , EgB decreases from emitter end to collector end.
E
Ec
-
B
C
Ef
1 dEc
E
q dx
Ev
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-25
8.7.3 Emitter-to-Collector Transit Time and Kirk Effect
• To reduce the total transit time, emitter and depletion layers must be thin, too.
• Kirk effect or base widening: At high IC the base widens into the collector. Wider
base means larger F .
Top to bottom :
VCE = 0.5V, 0.8V,
1.5V, 3V.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-26
Base Widening at Large Ic
E
I C  AE qnvsat
base
N
collector
N+
collector
  qN C  qn
IC
 qN C 
AE vsat
dE
dx
x
base
width
depletion
layer
E
N
  /es
base collector
N+
collector
x
“base depletion
width”
layer
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-27
8.8 Small-Signal Model
C
B
I C  I S e qVBE / kT
+
C
vbe
r
gm vbe

Transconductance:
E
E
gm 
dI C
d

( I S e qVBE / kT )
dVBE dVBE
q

I S e qVBE / kT  I C /( kT / q)
kT
g m  I C /( kT / q)
At 300 K, for example, gm=IC /26mV.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-28
8.8 Small-Signal Model
C
B
g
1
dI B
1 dI C


 m
r dVBE  F dVBE  F
r   F / g m
+
C
vbe
r
gm vbe

E
E
dQF
d
C 

 F IC   F gm
dVBE dVBE
This is the charge-storage capacitance, better known as the
diffusion capacitance.
Add the depletion-layer capacitance, CdBE :
C   F g m  CdBE
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-29
EXAMPLE: Small-Signal Model Parameters
A BJT is biased at IC = 1 mA and VCE = 3 V. F=90, F=5 ps,
and T = 300 K. Find (a) gm , (b) r , (c) C .
Solution:
(a) g m  I C /( kT / q) 
1 mA
mA
 39
 39 mS (milli siemens)
26 mV
V
90
 2.3 kΩ
(b) r   F / g m 
39 mS
(c) C   F g m  5 1012  0.039  1.9 1014 F  19 fF (femto farad)
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-30
Once the model parameters are determined, one can analyze
circuits with arbitrary source and load impedances.
The parameters are routinely
determined through comprehensive
measurement of the BJT AC
and DC characteristics.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-31
8.9 Cutoff Frequency
B
C
+
Signal
C
source 
vbe
r
gm vbe
Load
E
  1 at fT 
E
1
2 ( F  CdBE kT / qI C )
The load is a short circuit. The signal source is a current source,
ib , at frequency, f. At what frequency does the current gain
 ( ic / ib ) fall to unity?
ib
ib
vbe 

input admittance 1 / r  jC
,
C   F g m  CdBE
ic  g m vbe
ic
gm
1
 ( )  

ib 1 / r  jC
1 /  F  j F  jCdBE kT / qI C
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-32
8.9 Cutoff Frequency
fT = 1/2(F + CdBEkT/qIC)
fT is commonly used to compare the speed of transistors.
• Why does fT increase with increasing IC?
• Why does fT fall at high IC?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-33
BJT Structure for Minimum Parasitics and High Speed
• Poly-Si emitter
• Thin base
• Self-aligned poly-Si base contact
• Narrow emitter opening
• Lightly-doped collector
• Heavily-doped epitaxial subcollector
• Shallow trench and deep trench for electrical isolation
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-34
8.10 Charge Control Model
•For the DC condition, IC(t) = QF(t)/F
I B  IC /  F 
QF
 F F
•In order to sustain an excess hole charge in the transistor,
holes must be supplied through IB to susbtain recombination at
the above rate.
•What if IB is larger than QF /  F  F ?
dQF
QF
 I B (t ) 
dt
 F F
Step 1: Solve it for any given IB(t) to find QF(t).
Step 2: Can then find IC(t) through IC(t) = QF(t)/F .
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-35
Visualization of QF(t)
II B( t)(t )
B
dQF
QF
 I B (t ) 
dt
 F F
Q F (t)
QF
 F F
Q F / F  F
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-36
EXAMPLE : Find IC(t) for a Step IB(t)
IB
IC (t)
I B0
t
I B(t)
IC (t)
t
The solution of
dQF
QF
 I B (t ) 
dt
 F F
is
QF   F  F I B 0 (1  e t / F  F )
I C (t )  QF (t ) /  F   F I B 0 (1  e
n
E
t /  F  F
B
C
t
)
What is I B () ? QF (0)? QF () ?
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
QF
Slide 8-37
8.11 Model for Large-Signal Circuit Simulation
• Compact (SPICE) model contains dozens of parameters,
mostly determined from measured BJT data.
• Circuits containing tens of thousands of transistors can
be simulated.
• Compact model is a “contract” between
device/manufacturing engineers and
circuit designers.
QR
B
rB
I C  I S (e
qVBE / kT
e
qVBC / kT
CCS
rC
CB C
QF

C
IC
CB E
 VCB  I S qVBC / kT
 
)1 
(e
 1)
 VA   F
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
rE
E
Slide 8-38
8.11 Model for Large-Signal Circuit Simulation
A commonly used BJT compact model is the Gummel-Poon
model, consisting of
•Ebers-Moll model
•Current-dependent beta
•Early effect
•Transit times
•Kirk effect
• Voltage-dependent capacitances
• Parasitic resistances
•Other effects
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-39
8.12 Chapter Summary
• The base-emitter junction is usually forward-biased while
the base-collector is reverse-biased. VBE determines the
collector current, IC .
qni2 qVBE / kT
I C  AE
(e
 1)
GB
WB
ni2 p
GB   2
dx
n DB
0 iB
• GB is the base Gummel number, which represents all the
subtleties of BJT design that affect IC.
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-40
8.12 Chapter Summary
• The base (input) current, IB , is related to IC by the
common-emitter current gain, F . This can be related to
the common-base current gain, F .
I C GE
F 

I B GB
IC
F
F 

IE 1 F
• The Gummel plot shows that F falls off in the high IC
region due to high-level injection in the base. It also falls
off in the low IC region due to excess base current.
• Base-width modulation by VCB results in a significant slope
of the IC vs. VCE curve in the active region (known as the
Early effect).
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-41
8.12 Chapter Summary
• Due to the forward bias VBE , a BJT stores a certain amount
of excess carrier charge QF which is proportional to IC.
QF  I C F
F is the forward transit time. If no excess carriers are stored
outside the base, then
 F   FB
WB2

, the base transit time.
2 DB
• The charge-control model first calculates QF(t) from IB(t)
and then calculates IC(t).
dQF
Q
 I B (t )  F
dt
 F F
I C (t )  QF (t ) /  F
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-42
8.12 Chapter Summary
The small-signal models employ parameters such as
transconductance,
dI C
kT
gm 
 IC /
dVBE
q
input capacitance,
dQF
C 
  F gm
dVBE
and input resistance.
dVBE
r 
  F / gm
dI B
Modern Semiconductor Devices for Integrated Circuits (C. Hu)
Slide 8-43