Lecture #25
OUTLINE
• BJT: Deviations from the Ideal
– Base-width modulation, Early voltage
– Punch-through
– Non-ideal effects at low |VEB|, high |VEB|
• Gummel plot
Reading: Chapter 11.2
Measured BJT
Common-Emitter
Output Characteristics:
Spring 2007
EE130 Lecture 25, Slide 1
Base-Width Modulation
Common-Emitter Configuration, Active Mode Operation
W
IE
P+
N
P
IC
IC
  dc 
IB
1
niE 2 DE N B W
n 2 DB N E LE
iB
2
+
VEB
niB DB N E LE

2
niE DE N BW

DpB(x)

IC

pB 0 e qVEB / kT  1
(VCB=0)
x
0
Spring 2007
VEC
W(VBC)
EE130 Lecture 25, Slide 2
 12
 
W 2
LB
The base-width modulation effect is reduced if we
(a) increase the base width, W, or
(b) increase the base dopant concentration, NB, or
(c) decrease the collector dopant concentration, NC .
Which of the above is the most acceptable action?
Spring 2007
EE130 Lecture 25, Slide 3
Early Voltage, VA
1
Output resistance:
 I C 
VA


r0  


IC
 VEC 
A large VA (i.e. a large ro ) is desirable
IC
IB3
IB2
IB1
VA
Spring 2007
0
EE130 Lecture 25, Slide 4
VEC
Derivation of Formula for VA
Output conductance: g 0 
VEC  VEB  VBC
dI C
I
 C
dVEC VA
dI C
dI C
so g o 

dVEC dVBC
dI C dW
dI C  dxnC 

go 


  
dW dVBC dW  dVBC 
Spring 2007
N
VA 
IC
g0
for fixed VEB
where xnC is the width of the
collector-junction depletion region
on the base side
xnC
P+

P
EE130 Lecture 25, Slide 5

IC  qA
DB
LB

pB 0 sinh(W1 / LB ) (eqVEB / kT  1) 


DC
LC
nC 0 
DB
LB
cosh(W / L

qAni2 DB qVEB / kT
IC 
e
1
WN B


dI C
qAni2 DB qVEB / kT
IC
 2
e
1  
dW
W NB
W
C JC 
dQdepC
dVBC
d (qN B xnC )
dxnC

 qN B
dVBC
dVBC
dxnC C JC


dVBC qN B
VA 
Spring 2007
IC

g 0 dI C
dW
IC

 dxnC   I C
  
  
 dVBC   W
IC
qN BW

C JC
  C JC 

   
  qN B 
EE130 Lecture 25, Slide 6


pB 0 sinh(W / LBB )) eqVCB / kT  1
BJT Breakdown Mechanisms
• In the common-emitter configuration, for high output
voltage VCE, the output current IC will increase rapidly
due to one of two mechanisms:
– punch-through
– avalanche
Spring 2007
EE130 Lecture 25, Slide 7
Punch-Through
E-B and E-B depletion regions in the
base touch, so that W = 0
As |VCB| increases, the potential barrier
to hole injection decreases and therefore
IC increases
Spring 2007
EE130 Lecture 25, Slide 8
Avalanche Multiplication
•
Holes are injected into the base [0], then
collected by the B-C junction
–
•
PNP BJT:
Some holes in the B-C depletion region have
enough energy to generate EHP [1]
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 [0]
 For each EHP created in the C-B depletion region by impact ionization,
(IEp/IEn)+1 > dc additional holes flow into the collector
i.e. carrier multiplication in C-B depletion region is internally amplified
VCE 0 
where VCB0 = reverse breakdown voltage of the C-B junction
VCB 0
(  dc  1)1 / m 2  m  6
Spring 2007
EE130 Lecture 25, Slide 9
Non-Ideal Effects at Low VEB
• In the ideal transistor analysis, thermal R-G currents in
the emitter and collector junctions were neglected.

I Ep
I Ep  I En  I R G
• Under active-mode operation with small VEB, the
thermal recombination current is likely to be a
dominant component of the base current
 low emitter efficiency, hence lower gain
This limits the application of the BJT for amplification
at low voltages.
Spring 2007
EE130 Lecture 25, Slide 10
Non-Ideal Effects at High VEB
• Decrease in F at high IC is caused by:
– high-level injection


qAni2 DB qVEB / kT
IC 
e
1
WN B
– series resistance
– current crowding
Spring 2007
EE130 Lecture 25, Slide 11
Gummel Plot and dc vs. IC
high level
injection in base
10-2
IC
10-4
10-6
dc
IB

10-8
excess base current due to R-G
in depletion region
10-10
10-12
From top to bottom:
VBC = 2V, 1V, 0V
0.2
0.4
0.6
0.8
1.0
1.2
VBE
Spring 2007
EE130 Lecture 25, Slide 12
Gummel Numbers
For a uniformly doped base with negligible band-gap narrowing,
the base Gummel number is
N BW
GB 
DB
(= total integrated “dose” (#/cm2) of majority carriers in the base, divided by DB)



1


qAni2 DB qVEB / kT
qAni2 qVEB / kT
IC 
e
1 
e
1
WN B
GB
Emitter efficiency
1
ni E 2 D N W
E
B
ni B 2 DB N E WE
1

GB
1
GE
GE is the emitter Gummel number
Spring 2007
EE130 Lecture 25, Slide 13
Notice that
 dc 
1
ni E 2 D N W
E
B
ni B 2 DB N E LE

 
1 W 2
2 LB
GE

GB
In real BJTs, NB and NE are not uniform, i.e. they are functions of x
The more general formulas for the Gummel numbers are
W
GB  
0
W
GE  
0
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2
ni N B ( x)
dx
2
ni B DB ( x)
2
ni N E ( x)
dx
2
ni E DE ( x)
EE130 Lecture 25, Slide 14
Summary: BJT Performance Requirements
• High gain (dc >> 1)
 One-sided emitter junction, so emitter efficiency   1
• Emitter doped much more heavily than base (NE >> NB)
 Narrow base, so base transport factor aT  1
• Quasi-neutral base width << minority-carrier diffusion length
(W << LB)
• IC determined only by IB (IC  function of VCE,VCB)
 One-sided collector junction, so quasi-neutral base width W
does not change drastically with changes in VCE (VCB)
• Based doped more heavily than collector (NB > NC)
(W = WB – xnEB – xnCB for PNP BJT)
Spring 2007
EE130 Lecture 25, Slide 15
Review: Modes of Operation
Common-emitter output characteristics
(IC vs. VCE)
IC
βdc 
is lower for inverted active mode operation. Why?
IB
Spring 2007
EE130 Lecture 25, Slide 16