Lecture #25 OUTLINE • BJT: Deviations from the Ideal – Base-width modulation, Early voltage – Punch-through – Non-ideal effects at low |VEB|, high |VEB| • Gummel.
Download
Report
Transcript Lecture #25 OUTLINE • BJT: Deviations from the Ideal – Base-width modulation, Early voltage – Punch-through – Non-ideal effects at low |VEB|, high |VEB| • Gummel.
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)
pB0 eqVEB / kT 1
IC
(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: g0
VEC VEB VBC
dIC
I
C
dVEC VA
dIC
dIC
so g o
dVEC dVBC
dIC dW
dIC 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
I C qA
DB
LB
pB 0 sinh(W1 / LB ) (e qV EB / kT 1)
DC
LC
nC 0
DB
LB
pB 0
cosh(W / L B )
sinh(W / L B )
qAni2 DB qVEB / kT
IC
e
1
WN B
dIC
qAni2 DB qVEB / kT
IC
2
e
1
dW
W NB
W
C JC
dQdepC
dVBC
d (qNB xnC )
dxnC
qNB
dVBC
dVBC
dxnC
C JC
dVBC qNB
VA
Spring 2007
IC
IC
g 0 dIC dxnC I C
dW dVBC W
IC
qNBW
CJC
CJC
qNB
EE130 Lecture 25, Slide 6
e
qVCB / 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
2
W 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
Spring 2007
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 invertedactivemode operation.Why?
IB
Spring 2007
EE130 Lecture 25, Slide 16