EECS 105 Fall 2003, Lecture 14
Lecture 14:
Bipolar Junction Transistors
Prof. Niknejad
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Lecture Outline
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Department of EECS
Diode Small Signal Model
Diode Charge Storage (6.4.4)
Diode Circuits
The BJT (7.1)
BJT Physics (7.2)
BJT Ebers-Moll Equations (7.3)
BJT Small-Signal Model
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Diode Small Signal Model

The I-V relation of a diode can be linearized
qVd qvd
d  vd )
 q (VkT

I D  iD  I S  e
 1  I S e kT e kT


2
3
x
x
ex  1  x   
2! 3!
 qv
I D  iD  I D 1  d 
kT

iD 
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


qI D
vd  g d vd
kT
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Diode Capacitance

We have already seen that a reverse biased diode
acts like a capacitor since the depletion region
grows and shrinks in response to the applied field.
the capacitance in forward bias is given by
Cj  A



S
X dep
 1.4C j 0
But another charge storage mechanism comes into
play in forward bias
Minority carriers injected into p and n regions
“stay” in each region for a while
On average additional charge is stored in diode
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Charge Storage
pn 0 e
p side
n p 0e
q (Vd  vd )
kT
n side
q (Vd  vd )
kT
Extra charge
Stored in diode
pn 0
np0
-Wp



-xp
xn
Wn
Increasing forward bias increases minority charge density
By charge neutrality, the source voltage must supply equal
and opposite charge
1 qI d
T
A detailed analysis yields: Cd 
2 kT
1
Time to cross junction
C d  g d T
(or minority carrier lifetime)
2
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Ideal BJT Structure

IC
Collector (N)
Base (P)
Emitter (N)



IB


VCE
VBE

IE

Emitter (P)
VEB

IE

VEC
Base (N)
IB
Collector (P)

 IC
NPN or PNP sandwich (Two back-to-back diodes)
How does current flow? Base is very thin.
A good BJT satisfies the following
IC   I E
I C  I B
Department of EECS
IC  I S e
qVBE
kT
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Actual BJT Cross Section
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Vertical npn sandwich (pnp is usually a lateral structure)
n+ buried layout is a low resistance contact to collector
Base width determined by vertical distance between emitter
diffusion and base diffusion
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Layout
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Emitter area most important layout parameter
Multi-finger device also possible for reduced base resistance
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Schematic Symbol
IC   I B
IB

VCE
VBE

IE




IC  I S e
qVBE
kT
VC
VB
VE
Collector current is control by base current linearly
Collector is controlled by base-emitter voltage
exponentially
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Collector Characteristic
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Ground emitter
Fix VCE
Drive base with
fixed current IB
Measure the
collector current
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Collector Characteristics (IB)
Saturation Region
(Low Output Resistance)
Breakdown
Linear Increase
Reverse Active
(Crappy Transistor)
Forward Active
Region
(Very High Output Resistance)
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Base-Emitter Voltage Control
Saturation Region
(Low Output Resistance)
~0.3V
Breakdown
Exponential Increase
Reverse Active
(Crappy Transistor)
Forward Active
Region
(High Output Resistance)
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Transistor Action
recombination

Collector (n)
VCB  0


e
Base (p)
h
h
h
VBE  0
e

Emitter (n+)
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Base-emitter junction is forward biased and collector-base junction is
reverse biased
Electrons “emitted” into base much more than holes since the doping of
emitter is much higher
Magic: Most electrons cross the base junction and are swept into
collector
Why? Base width much smaller than diffusion length. Base-collector
junction pulls electrons into collector
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Diffusion Currents

Minority carriers in base form a uniform diffusion current. Since emitter
doping is higher, this current swamps out the current portion due to the
minority carriers injected from base
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Currents
Collector current is nearly identical to the (magnitude)
of the emitter current … define
IC   F I E
Kirchhoff:
 F  .999
 I E  IC  I B
DC Current Gain:
IC   F I E   F ( I B  IC )
F
IC 
IB  F IB
1F
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F
.999
F 

 999
1   F .001
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Origin of αF
Base-emitter junction: some reverse injection of holes
into the emitter  base current isn’t zero
Some electrons lost due to
recombination
E
Typical:
Department of EECS
 F  .99
B
C
 F  100
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Collector Current
Diffusion of electrons across base results in
J ndiff
qVBE
qD
n
 n pB 0  kT
 qDn

e
dx  WB 
dn p
 qDn n pB 0 AE 
IS  

WB


IC  I S e
Department of EECS
qVBE
kT
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Base Current
Diffusion of holes across emitter results in
J pdiff
qVBE
qD
p




dpnE
p nE 0
kT
 qDp

 1
e
dx  WE  

 qDp pnE 0 AE
IB  
WE

Department of EECS

  qVkTBE
 1
e


University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Current Gain
 qDn n pBo AE 
 

W
Dn   n pB 0  WE 
IC 
B


F  
 



I B  qDp pnEo AE   Dp   pnE 0   WB 


W
E


Minimize base width
ni2
N A, B
N D,E
 n pB 0 

 2 
ni
N A, B
 pnE 0 
N D,E
Maximize doping in emitter
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Ebers-Moll Equations
Exp. 6: measure E-M parameters
Derivation: Write emitter and collector currents in terms
of internal currents at two junctions




I E   I ES eVBE / Vth  1   R I CS eVBC / Vth  1




I C   F I ES eVBE /Vth  1  I CS eVBC /Vth  1
 F I ES   R ICS
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Ebers-Moll Equivalent Circuit
Building blocks: diodes and I-controlled I sources
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Forward Active Region
B-C junction is not forward-biased  IR is very small
Typical Values:
VBE  0.7
VCE  0.2
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Simplified Ebers-Moll
Forward-Active Case:
IB
B
IC
C
IC   F I B
VBE  0.7
E
Saturation: both diodes are forward-biases  batteries
IB
B
VBE  0.7
IC
C
VCE  0.1
E
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Analogy from MOSFET s.s. model:
iD  f vGS , vDS , vBS 
Department of EECS
iC  f vBE , vCE 
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Transconductance gm

The transconductance is analogous to diode
conductance
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Transconductance (cont)

Forward-active large-signal current:
iC  I S e
vBE / Vth
(1  vCE VA )
• Differentiating and evaluating at Q = (VBE, VCE )
diC
dvBE
Q
q

I S e qVBE / kT (1  VCE VA )
kT
diC
gm 
dvBE
Department of EECS
Q
qI C

kT
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Comparison with MOSFET


Typical bias point: drain/coll. current = 100 A;
Select (W/L) = 8/1, nCox = 100 A/V2
BJT:
qI
I
gm 
I C 100μ
gm 

 4mS
Vth 25m

MOSFET:
C
kT

C
Vth
2I D
gm 
VGS  VT
2I D
W
gm 
 2 Cox I D  2  100μ  8  100μ  400μS
VGS  VT
L
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Base Currents
Unlike MOSFET, there is a DC current into the
base terminal of a bipolar transistor:
I B  IC F   I S F  eqVBE / kT (1  VCE Vth )
To find the change in base current due to change
in base-emitter voltage:
iB
vBE
Department of EECS

Q
iB
iC
iC
Q
vBE

Q
1

gm
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Small Signal Current Gain

Department of EECS
iC
 F
iB
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Input Resistance rπ
 r 
1
iB

vBE
Q
1 iC

 vBE

Q
gm

In practice, the DC current gain F and the small-signal
current gain o are both highly variable (+/- 25%)
Typical bias point: DC collector current = 100 A
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Output Resistance ro
Why does current increase slightly with increasing vCE?
Collector (n)
WB
Base (p)
Emitter (n+)
Model: math is a mess, so introduce the Early voltage
iC  I S e vBE / Vth (1  vCE V A )
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Graphical Interpretation of ro
slope~1/ro
slope
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Small-Signal Model
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
BJT Capacitances
Base-charging capacitance Cb: due to minority carrier
charge storage (mostly electrons in the base)
Cb  g m F
Base-emitter depletion capacitance: CjE= 1.4 CjEo
Total B-E capacitance: C = CjE + Cb
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 14
Prof. A. Niknejad
Complete Small-Signal Model
Department of EECS
University of California, Berkeley