EE130/230A
Discussion 15
Peng Zheng
1
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
VA 
IC

g 0 dI C
dW
0
IC

 dx   I
   nC    C
 dVBC   W
VEC
IC
qN BW

C JC
  C JC 




 

  qN B 
Punch-Through
E-B and E-B depletion regions
in the base touch  W = 0
As |VCB| increases,
the potential barrier
to hole injection
decreases and hence
IC increases
EE130/230A Fall 2013
Lecture 27, Slide 3
R. F. Pierret, Semiconductor Device Fundamentals, Figs. 11.7-11.8
bdc
Gummel Plot and bdc vs. IC
bdc
EE130/230A Fall 2013
From top to bottom:
VBC = 2V, 1V, 0V
Lecture 27, Slide 4
C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figures 8-8 & 8-9
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
EE130/230A Fall 2013
Lecture 27, Slide 5
Notice that
b 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 practice, 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
EE130/230A Fall 2013
2
ni N B ( x)
dx
2
ni B DB ( x)
2
ni N E ( x)
dx
2
ni E DE ( x)
Lecture 27, Slide 6
Charge Control Model
A PNP BJT biased in the forward-active mode has excess
minority-carrier charge QB stored in the quasi-neutral base:
pB ( x, t )  pB (0, t )1  Wx 
qAWpB (0, t )
QB  qA  pB ( x, t )dx 
2
0
W
In steady state,
EE130/230A Fall 2013
dQB
0
dt

Lecture 27, Slide 7
iB 
dQB
QB
 iB 
dt
B
QB
B
Base Transit Time, t
p B ( x, t )
iC   qADB
x
x W
qADB p B (0, t )

W
qAWpB (0, t )
QB 
2
2 DB QB QB
iC 

2
W
t
W2
t 
2 DB
• time required for minority carriers to diffuse across the base
• sets the switching speed limit of the transistor
EE130/230A Fall 2013
Lecture 27, Slide 8
Small-Signal Model
Common-emitter
configuration,
forward-active mode:
I C   F I F 0 e qVBE / kT
R. F. Pierret, Semiconductor Device Fundamentals, Fig.12.1(a)
B
C
+
“hybrid pi”
BJT small signal model:
C
vbe

E

dI C
IC
d
qVBE / kT
gm 

 F I F 0e

dVBE dVBE
kT / q
EE130/230A Fall 2013
gm vbe

E
Transconductance:
r
Lecture 28, Slide 9
Small-Signal Model (cont.)
gm
1
dI B
1 dI C



r dVBE b dc dVBE b dc

r 
b dc
gm
C  C J , BE  C D , BE  C D , BE
CJ, BE
A s

Wdep, BE
CD,BE
dQF

dVBE
QF
forward transit time  F 
IC
 C D , BE
EE130/230A Fall 2013
where QF is the magnitude of
minority-carrier charge stored in
the base and emitter regions
d  F I C 

  F gm
dVBE
Lecture 28, Slide 10
Summary: BJT Small Signal Model
Hybrid pi model for the common-emitter configuration,
forward-active mode:
B
C
+
C
vbe
r
gm vbe

E
E
r 
b dc
gm
gm 
C  C J , BE   F g m
EE130/230A Fall 2013
Lecture 28, Slide 11
IC
kT / q 
Thanks very much for your continuous
support throughout the semester.
Good luck to the final exam!
12