Lecture 18
PNP Bipolar Junction Transistors (BJTs)
In this lecture you will learn:
• The operation of bipolar junction transistors
• Forward and reverse active operations, saturation, cutoff
• Ebers-Moll model
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN Bipolar Junction Transistor
VBE
-
- +
+
VCB
Emitter
Base
Collector
N-doped
P-doped
N-doped
NdE
NaB
NdC
VCB
+
-
C
B
VBE
+
-
E
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
1
PNP Bipolar Junction Transistor
VBE
-
- +
+
VCB
Emitter
Base
Collector
P-doped
N-doped
P-doped
NaE
NdB
VCB
+
-
NaC
C
B
VBE
E
+
-
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Basic Operation
VBE < 0
-
- +
+
VCB=0
Emitter
Base
Collector
P-doped
N-doped
P-doped
N aE
NdB
N aC
WE
 xn 0 x p
WB
WC
Suppose:
The base-emitter junction is forward biased
VBE  0
The base-collector junction is zero biased
VCB  0
This biasing scheme will put
the device in the “forward
active” operation (to be
discussed fully later)
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
2
PNP BJT: Basic Operation
VBE < 0
-
VCB=0
- +
+
electrons
N aE
WE
swept holes
holes
NdB
 x p 0 xn
WB
N aC
WC
E-field
Consider the action in the base first (VBE < 0 and VCB = 0)
• The holes diffuse from the emitter, cross the depletion region, and enter the base
• In the base, the holes are the minority carriers
• In the base, the holes diffuse towards the collector
• As soon as the holes reach the base-collector depletion region they are immediately
swept away into the collector by the strong electric fields in the depletion region
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Electron-Hole Populations
VBE < 0
-
VCB=0
- +
+
electrons
N aE
WE
Consider the base first:
swept holes
holes
NdB
N aC
 x p 0 xn
WB
WC
E-field
In the base, the hole population can be written as:
p  x   pno  p'  x 
Equilibrium hole density
pno 
Excess hole density
ni2
NdB
In the base, the excess electron population satisfies the differential equation:
 p'  x 
2
x 2

p'  x 
L2p
0
Boundary
conditions
 q VBE

 e KT  1





2  qVBC
n
p'  x n  WB   i  e KT  1  0

NdB 


p'  x n  
ni2
NdB
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
3
PNP BJT: Electron-Hole Populations
VBE < 0
-
VCB=0
- +
+
p'  x 
electrons
N aE
WE
holes
NdB
 x p 0 xn
WB
swept holes
N aC
WC
E-field
• Ignore carrier recombination (i.e. assume Lp = ∞)
 2 p'  x 
x 2
 q VBE

 e KT  1





2  qVBC
ni  KT
 1  0
e
p'  x n  WB  

NdB 


Boundary
conditions
p'  x n  
0
Solution is:

x  x n  ni2
p'  x   p' x p   1 

WB  NdB

ni2
NdB
 qVBE

 e KT  1  1  x  x n 

 
WB 


ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Electron-Hole Populations
VBE < 0
-
VCB=0
- +
+
p'  x 
electrons
N aE
swept holes
holes
NdB
N aC
 x p 0 xn
WE
Consider the emitter now:
WB
WC
E-field
In the emitter, the electron population can be written as:
n  x   n po  n'  x 
Equilibrium electron density
n po 
Excess electron density
ni2
N aE
In the emitter, the excess electron population satisfies the differential equation:
 n'  x 
2
x
2

n'  x 
L2n
0
Boundary
conditions
 q VBE

 e KT  1




n'  x p  WE   0
n'  x p  
ni2
N aE
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
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PNP BJT: Electron-Hole Populations
VBE < 0
-
VCB=0
- +
+
p'  x 
electrons
n'  x 
N aE
WE
holes
NdB
 x p 0 xn
WB
swept holes
N aC
WC
E-field
• Ignore carrier recombination (i.e. assume Ln = ∞)
 2 n'  x 
x 2
 q VBE

 e KT  1




n'  x p  WE   0
Boundary
conditions
n'  x p  
0
ni2
N aE
Solution is:
x  x p  ni2


n'  x   n'  x p   1 
WE  N aE

 qVBE

 e KT  1  1  x  x p 

 
WE 


ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Area = A
PNP BJT: Electron and Hole Current Densities
VBE < 0
-
- +
+
N aE
VCB=0
N aC
NdB
J p x 
Jn x 
WE
In the base:
• The hole current is:
 x p 0 xn
J p  x   q D p
Dp
 px 
 qni2
x
NdBWB
WC
 qVBE

 e KT  1




In the emitter:
• The electron current is:
J n  x   q Dn
 n x 
Dn
 qni2
x
N aEWE
 qVBE

 e KT  1




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Area = A
PNP BJT: Terminal Currents
VBE < 0
-
- +
+
N aE
N aC
NdB
Jn x 
VCB=0
J p x 
IE
 x p 0 xn
WE
WC
Emitter current:
• The current flowing out of the emitter is the sum of the total electron and total hole
currents in the emitter:
qVBE

D p 
 Dn
 e KT  1

I E  qni2 A

 N aE WE NdBWB 

ECE 315 – Spring 2007 – Farhan Rana – Cornell University
VBE < 0
PNP BJT: Terminal Currents
-
- +
+
Area = A
VCB=0
IB
N aE
N aC
NdB
Jn x 
J p x 
IE
WE
IC
 x p 0 xn
E-field
WC
Collector Current:
• The current going into the collector is due to the holes that got swept from the Base
through the Base-Collector depletion region by the electric-fields:
qV

 D p  KTBE
 e
 1
IC  qni2 A


 NdBWB 

Base Current:
• The current going into the Base is due to the electrons that got injected from the base
into the emitter:
 Dn
I B  qni2 A
 N aE WE

 e

qVBE
KT

 1


ECE 315 – Spring 2007 – Farhan Rana – Cornell University
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VBE < 0
PNP BJT: Terminal Currents
-
- +
+
Area = A
VCB=0
IB
N aE
N aC
NdB
Jn x 
J p x 
IE
IC
 x p 0 xn
WE
WC
qVBE

D p 
 Dn
 e KT  1

I E  qni2 A


 N aE WE NdBWB 

qVBE


D

 KT
p
 e
 1
IC  qni2 A

 NdBWB 

qVBE


 Dn  KT
 1
I B  qni2 A
 e


N
W
 aE E 

VCB=0
IC
+
-
C
B
IB
E
VBE<0 +
-
IE
IE  IB  IC
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Circuit Level Parameters
Current gain F :
Current gain of the BJT in the forward active
operation is defined as the ratio of the collector
and base currents:
F
D p N aE WE
I
 C 
I B NdBWB Dn

IC   F I B
Typical values of F are between 20-200 and:
F :
VCB=0
+
-
C
IC = FIE = FIB
B
VBE<0
N aE  NdB  N aC
In the forward active operation F is defined as
the ratio of the collector and emitter currents:
IB
+
-
E
IE
I E  I B  IC
Dp
F 
IC

IE
NdBWB
Dp
Dn

N aE WE NdBWB
Transistor relation:
F and F are related:

F 
IC   F I E
F
1  F
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
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PNP BJT: Ebers-Moll Model for Forward Active Operation
VBE  0
Suppose:
VCB  0
IC
VC
 F IF
VB
C
VB
IC
VC
IB
B
IES
IB
E
IF
VE
VE
IE
IE
qVBE

D p 
 Dn
 e KT  1
I F  qni2 A



 N aE WE NdBWB 

 qVBE

 I ES  e KT  1




The circuit level simplified model with an ideal diode and a current-controlled
current source models the PNP transistor in the forward active operation
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Forward and Reverse Active Operations
VBE  0
VCB
IC
+
-
C
VCB  0
B
VCB  0
VBE
E
+
-
IE
Forward active operation
IB
+
-
VBE
IC
IB
R  
F 
IC
IE
R 
F
1  F
E
IE
Reverse active operation
F 
F 
C
B
VBE  0
IB
IC
+
-
VCB
R 
IE
D p N aCWC

I B NdBWB Dn
IE
IC
R
1  R
In a well designed transistor:  F   R
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
8
PNP BJT: Ebers-Moll Model for Reverse Active Operation
VCB  0
Suppose:
IC
VBE  0
VC
VC
IC
ICS
C
VB
IR
VB
IB
B
 R IR
IB
E
VE
VE
IE
IE
qVCB

D p 
 Dn
 e KT  1
I R  qni2 A


 N aCWC NdBWB 

 qVCB

 ICS  e KT  1




The circuit level simplified model with an ideal diode and a current-controlled
current source models the PNP transistor in the reverse active operation
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Ebers-Moll Model and Terminal Currents
Terminal currents:
VC
IC
VC
IC
 F IF
C
VB
B
ICS
IR
VB
IB
IB
E
IES
VE
 R IR
IF
VE
IE
IE
I R  ICS
 qVCB
 e KT


 qVBC
 e KT

 1  ICS




 qVBE

 qVEB
I F  I ES  e KT  1  I ES  e KT







 1

 And

 1


IB  1   F IF  1   R IR
IC   F IF  IR
I E  IF   R I R
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9
PNP BJT: Different Regimes of Operation
IC
VC
Reversed
biased
 F IF
ICS
VC
Forward
biased
 F IF
IR
VB
ICS
IES
IES
VBE  0
VCB  0
IB
IES
Reversed
biased
VE
IE
Forward Active
R IR
IF
Forward
biased
VE
ICS
IR
VB
IB
 R IR
IF
Forward
biased
 F IF
IR
VB
IB
Forward
biased
IC
IC
VC
 R IR
IF
VE
IE
IE
VCB  0
VCB  0
VBE  0
VBE  0
Reverse Active
Saturation
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Regimes of Operation - I
In forward active operation:
IC
IB  0
C
B
VCE
IB
I IN
E
IE
Since:
+
-
VCB  0
VCE  VCB  VBE
 In forward active operation: VCE  VBE
qV

 D p  KTBE
 e
IC  qni2 A
 1   F I B

 NdBWB 
  Independent
IC
VBE
VCE
VBE  0
of VCE
Forward active:
Base-emitter junction forward biased
Base-collector junction reversed biased
I B  0 VBE  0 VCB  0
Forward active
IB <0 & IC = F IB
VCE < VBE
Saturation:
Base-emitter junction forward biased
Saturation Base-collector junction forward biased
IB <0
I B  0 VBE  0 VCB  0
VCE > VBE
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
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Carrier Densities in Different Regimes of Operation
Forward active:
VBE < 0
-
VCB ≤ 0
- +
+
n'  x 
N aE
WE
Saturation:
p'  x  electrons
electrons
holes
NdB
 x p 0 xn
WB
N aC
holes
WC
N aE  NdB  N aC
VBE < 0
-
VCB > 0
- +
+
electrons
n'  x 
p'  x 
holes
N aE
NdB
 xn 0 x p
WE
n'  x 
electrons
N aC
holes
WB
WC
The forward biased base-collector junction reduces the magnitude of the
collector current!
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
PNP BJT: Regimes of Operation - II
IC
Forward active:
Base-emitter junction forward biased
Base-collector junction reversed biased
C
B
VCE
IB
+
-
I B  0 VBE  0 VCB  0
E
I IN
Saturation:
Base-emitter junction forward biased
Base-collector junction forward biased
IE
IC
IB = 0 (cutoff)
Curves for
increasing |IB|
Forward active
IB <0 & IC = F IB
VCE ≤VBE
VCE
I B  0 VBE  0 VCB  0
Cutoff:
Base current zero
VCE  VBE
Saturation
IB <0
VCE >VBE
IB  0
Reverse active:
Base-emitter junction reverse biased
Base-collector junction forward biased
I B  0 VBE  0 VCB  0
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11
PNP BJT: A Simple Amplifier Circuit
Current gain (in forward active regime):
VDD
E
IIN
IC
 F
IB
IE
B
IB
Load line equation:
C
IC
VCE   IC R  VDD
VC

IC  
VDD  VCE
R
IC
 VDD
R
IB = 0 (cutoff)
Curves for
increasing |IB|
VCE

Lesson: Don’t let the basecollector junction become
forward biased
VCE  VBE
Forward active
IB <0 & IC = F IB
VCE ≤VBE
VDD
R
Saturation
IB <0
VCE >VBE
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
A Silicon PNP BJT
Metal base contact
Insulator
(SiO2)
N+ (contact)
N (base)
Metal emitter contact
P+ (emitter)
Metal collector contact
Insulator
(SiO2)
Insulator
(SiO2)
P (collector)
P+ (contact layer)
P (substrate)
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