Ch8 lecture slides Chenming Hu Device for IC

1
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)

2
8.1 Introduction to the BJT
IC is an exponential
function of forward
VBE and independent
of reverse VCB.
-
-
Efn
Efp
VCB
VBE
(b)
(c)
VBEIC
0
VCB
Ec
Ev
NPN BJT:
N+ P N
E C
B
VBE VCB
Emitter Base Collector

3
Common-Emitter Configuration
Question: Why is IB often preferred as a parameter over VBE?

4Modern Semiconductor Devices for Integrated Circuits (C. Hu)
8.2 Collector Current
BBB
B
DL
L
n
dx
nd




22
2
B : base recombination lifetime
DB : base minority carrier (electron)
diffusion constant
Boundary conditions :
)1()0( /
0  kTqV
B
BE
enn
0)1()( 0
/
0  B
kTqV
BB nenWn BC
N+
P N
emitter base collector
x
0 W
depletion layers
B

5
 BB
B
B
kTqV
B
LW
L
xW
enxn BE
/sinh
sinh
)1()( /
0





 

)1( /
2


kTqV
B
iB
B
B
E
BEC
BE
e
N
n
W
D
qA
dx
dn
qDAI
)1( /
 kTqV
SC
BE
eII


B
BE
W
BiB
i
B
kTqV
B
i
EC
dx
D
p
n
n
G
e
G
qn
AI
0
2
2
/
2
)1(
It can be shown
GB (s·cm4) is the base Gummel number
8.2 Collector Current
ni
2
NB
-------e
qVBE kT
1–
n 
n  0
-------------
)0(/)( nxn 
0 1
1
)1()( /
2
 kTqV
B
iB BE
e
N
n
xn
x/x/WB
)/1)(1(
)/1)(0()(
/
2
B
kTqV
B
iB
B
Wxe
N
n
Wxnxn
BE



6
•At low-level injection,
inverse slope is 60 mV/decade
•High-level injection effect :
8.2.1 High Level Injection Effect
0 0.2 0.4 0.6 0.8 1.0
10-12
10-10
10-8
10-6
10-4
10-2
VBE
IC(A)
IkF
60 mV/decadeAt large VBE, BNpn 
pnpn 
kTqV
i
BE
enpn 2/

kTqV
iB
BE
enpG 2/
 kTqV
i
BE
enI 2/
C 
When p > NB , inverse slope is 120mV/decade.
kTqV
i
kTEEq
i
BEFpFn
enennp /2/)(2



7
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 .
pE
' nB'
WE WB
(b)
emitter base collectorcontact
I
E IC
electron flow
–
+
hole flow
I
B
(a) contact

8


E
BE
W
EiE
i
E
kTqV
E
i
EB
dx
D
n
n
n
G
e
G
qn
AI
0
2
2
/
2
)1(
Is a large IB desirable? Why?
8.3 Base Current
emitter base collectorcontact
I
E IC
electron flow
–
+
hole flow
I
B
(a) contact
)1( /
2
 kTqV
EE
iEE
EB
BE
e
NW
nD
qAI
For a uniform emitter,

9
8.4 Current Gain
B
C
F
I
I

How can F be maximized?
Common-emitter current gain, F :
Common-base current gain:
F
F
BC
BC
CB
C
E
C
F
EFC
II
II
II
I
I
I
II











1/1
/
It can be shown that
F
F
F





1
2
2
iEBBE
iBEEB
B
E
F
nNWD
nNWD
G
G


10
EXAMPLE: Current Gain
A BJT has IC = 1 mA and IB = 10 mA. What are IE, F and F?
Solution:
9901.0mA01.1/mA1/
100μA10/mA1/
mA01.1μA10mA1



ECF
BCF
BCE
II
II
III


We can confirm
F
F
F





1 F
F
F





1
and

11
8.4.1 Emitter Bandgap Narrowing
Emitter bandgap narrowing makes it difficult to raise F by
doping the emitter very heavily.
2
2
iE
iB
B
E
n
n
N
N

To raise F, NE is typically very large.
Unfortunately, large NE makes 22
iiE nn 
(heavy doping effect).
kTE
VCi
g
eNNn
/2 
 Since ni is related to Eg , this effect is
also known as band-gap
narrowing.
kTE
iiE
gE
enn
/22 
 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.

12
2
2
iE
iB
B
E
n
n
N
N

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 niE
2 by 30x.
8.4.2 Narrow-Bandgap Base and Heterojuncion BJT

13
Assume DB = 3DE , WE = 3WB , NB = 1018 cm-3, and niB
2 = ni
2. 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,
(b) At NE = 1020 cm-3, EgE  95 meV
(c)
292.12meV26/meV502/22
8.6 iii
kTE
iiE nenenenn gE


13
8.610
109
218
219
2
2




i
i
iEB
iE
BE
EB
F
n
n
nN
nN
WD
WD

22
38 iiE nn  24F
2meV26/meV602/22
10 ii
kTE
iiB nenenn gB


237F
EXAMPLE: Emitter Bandgap Narrowing and SiGe Base

14
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+ poly-
silicon. (A deep diffused emitter junction tends to cause emitter-
collector shorts.)
N-collector
P-base
SiO2
emitter
N+
-poly-Si
8.4.3 Poly-Silicon Emitter

15
Why does one want to operate BJTs at low IC and high IC?
Why is F a function of VBC in the right figure?
F
From top to bottom:
VBC = 2V, 1V, 0V
8.4.4 Gummel Plot and F Fall-off at High and Low Ic
Hint: See Sec. 8.5 and Sec. 8.9.
SCR BE current

16
8.5 Base-Width Modulation by Collector Voltage
Output resistance :
C
A
CE
C
I
V
V
I
r 








1
0
Large VA (large ro )
is desirable for a
large voltage gain
IB3IC
VCE0
VA
VA : Early Voltage
IB2
IB1

17
How can we reduce the base-width modulation effect?
N+
P N
VCE
WB3
WB2
WB1
x
n'
}VCE1
< VCE2
<VCE3
VBE

18
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 .
Which of the above is the most acceptable action?
N+
P N
VCE
WB3
WB2
WB1
x
n'
}VCE1<VCE2<VCE3
VBE

19
8.6 Ebers-Moll Model
The Ebers-Moll model describes both the active
and the saturation regions of BJT operation.
IBIC
0
VCE
saturation
region
active region

20
IC is driven by two two forces, VBE and VBC .
When only VBE is present :
)1(
)1(
/
/


kTqV
F
S
B
kTqV
SC
BE
BE
e
I
I
eII

Now reverse the roles of emitter and collector.
When only VBC is present :
)1)(
1
1(
)1(
)1(
/
/
/



kTqV
R
SBEC
kTqV
R
S
B
kTqV
SE
BC
BC
BC
eIIII
e
I
I
eII


R : reverse current gain
F : forward current gain
IC
VBCVBE
IB
E B C

21
)1()1(
)1)(
1
1()1(
//
//


kTqV
F
SkTqV
F
S
B
kTqV
R
S
kTqV
SC
BCBE
BCBE
e
I
e
I
I
eIeII


In general, both VBE and VBC are present :
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)

22
8.7 Transit Time and Charge Storage
C
F
F
I
Q

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
F determines the high-frequency limit of BJT operation.
F is difficult to be predicted accurately but can be measured.

23
8.7.1 Base Charge Storage and Base Transit Time
Let’s analyze the excess hole charge and transit time in
the base only.
WB
0
n 0 
niB
2
NB
------- e
qVBE kT
1– =
x
p' = n'
)1()0( /
2
 kTqV
B
iB BE
e
N
n
n
pn  B
B
FB
C
FB
BEFB
D
W
I
Q
WnqAQ
2
2/)0(
2




24
What is FB if WB = 70 nm and DB = 10 cm2/s?
Answer:
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.
EXAMPLE: Base Transit Time
ps5.2s105.2
/scm102
)cm107(
2
12
2
262



 

B
B
FB
D
W


25
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.
• Fixed NB , EgB decreases from emitter end to collector end.
dx
dE
q
c1
E
8.7.2 Drift Transistor–Built-in Base Field
-E B C
Ec
Ev
Ef
-E B C
Ec
Ev
Ef

26
8.7.3 Emitter-to-Collector Transit Time and Kirk Effect
Top to bottom :
VCE = 0.5V, 0.8V,
1.5V, 3V.
• 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 .

27
Base Widening at Large Ic
satEC qnvAI 
satE
C
C
C
vA
I
qN
qnqN


s
dx
dE
e /
x
 E
base
N
collector
N+
collector
base
width
depletion
layer
x
 E
base
N N+
collector
“base
width”
depletion
layer
collector

28
8.8 Small-Signal Model
kTqV
SC
BE
eII /

Transconductance:
)//(
)(
/
/
qkTIeI
kT
q
eI
dV
d
dV
dI
g
C
kTqV
S
kTqV
S
BEBE
C
m
BE
BE


At 300 K, for example, gm=IC /26mV.)//( qkTIg Cm 
vbe r gmvbe
C
E
B
E
C
+


29
F
m
BE
C
FBE
B g
dV
dI
dV
dI
r 

11
mFCF
BEBE
F
gI
dV
d
dV
dQ
C  
This is the charge-storage capacitance, better known as the
diffusion capacitance.
Add the depletion-layer capacitance, CdBE :
dBEmF CgC 
8.8 Small-Signal Model
mF gr / 
vbe r gmvbe
C
E
B
E
C
+


30
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)
(b)
(c)
siemens)(milliqkTIg Cm mS39
V
mA
39
mV26
mA1
)//( 
kΩ3.2
mS39
90
/  mF gr 
ad)(femto fargC mF fF19F109.1039.0105 1412
 


31
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.

32
8.9 Cutoff Frequency
The load is a short circuit. The signal source is a current source,
ib , at frequency, f. At what frequency does the current gain
fall to unity?)/( bc ii
CdBEFF
m
b
c
bemc
bb
be
qIkTCjjCjr
g
i
i
vgi
Cjr
ii
v
//1
1
/1
)(
,
/1admittanceinput












)/(2
1
at1
CdBEF
T
qIkTC
f




vbe r gmvbe
C
E
B
E
C
+
-
Signal
source
Load
dBEmF CgC 

33
fT is commonly used to compare the speed of transistors.
• Why does fT increase with increasing IC?
• Why does fT fall at high IC?
fT = 1/2(F + CdBEkT/qIC)
8.9 Cutoff Frequency

34
• 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
BJT Structure for Minimum Parasitics and High Speed

35
•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 ?FFFQ /
FF
F
B
F Q
tI
dt
dQ

 )(
Step 1: Solve it for any given IB(t) to find QF(t).
8.10 Charge Control Model
•For the DC condition,
FF
F
FCB
Q
II

  /
Step 2: Can then find IC(t) through IC(t) = QF(t)/F .
IC(t) = QF(t)/F

36
Visualization of QF(t)
FF
F
B
F Q
tI
dt
dQ

 )(
QF(t)
QF/FF
IB(t) )(tIB
FF
FQ


37
EXAMPLE : Find IC(t) for a Step IB(t)
The solution of is
FF
F
B
F Q
tI
dt
dQ

 )(
)1(/)()(
)1(
/
0
/
0
FF
FF
t
BFFFC
t
BFFF
eItQtI
eIQ








What is ?)()?0(?)(  FFB QQI
IB(t)
IC(t)
IC(t)
t
t
IB
IB0
E B C
n
t
QF

38
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.
)1(1)( ///








 kTqV
F
S
A
CBkTqVkTqV
SC
BCBCBE
e
I
V
V
eeII

C
B
E
QF
CCS
rB
rC
rE
CBE
QR
CBC
IC

39
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
8.11 Model for Large-Signal Circuit Simulation

40
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 .


B
BE
W
BiB
i
B
kTqV
B
i
EC
dx
D
p
n
n
G
e
G
qn
AI
0
2
2
/
2
)1(
• GB is the base Gummel number, which represents all the
subtleties of BJT design that affect IC.

41
• 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 .
B
E
B
C
F
G
G
I
I

• 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.
F
F
E
C
F
I
I





1
• 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).

42
• Due to the forward bias VBE , a BJT stores a certain amount
of excess carrier charge QF which is proportional to IC.
FCF IQ 
F is the forward transit time. If no excess carriers are stored
outside the base, then
• The charge-control model first calculates QF(t) from IB(t)
and then calculates IC(t).
B
B
FBF
D
W
2
2

FF
F
B
F Q
tI
dt
dQ

 )(
FFC tQtI /)()( 
, the base transit time.

43
The small-signal models employ parameters such as
transconductance,
q
kT
I
dV
dI
g C
BE
C
m /
input capacitance,
and input resistance.
mF
BE
F
g
dV
dQ
C  
mF
B
BE
g
dI
dV
r / 

Ch8 lecture slides Chenming Hu Device for IC

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