EE130/230A Discussion 15 Peng Zheng 1. Early Voltage, V A Output resistance: A large V A (i.e. a...
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Transcript of EE130/230A Discussion 15 Peng Zheng 1. Early Voltage, V A Output resistance: A large V A (i.e. a...
1
EE130/230A Discussion 15
Peng Zheng
Early Voltage, VAOutput resistance:
C
A
EC
C
I
V
V
Ir
1
0
A large VA (i.e. a large ro ) is desirable
IB3
IC
VEC0
IB2
IB1
VA
JC
B
B
JCC
C
BC
nCC
CCA C
WqN
qN
C
W
I
I
dV
dx
dW
dI
I
g
IV
0
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
Gummel Plot and bdc vs. IC
bdc
From top to bottom:VBC = 2V, 1V, 0V
bdc
EE130/230A Fall 2013 Lecture 27, Slide 4 C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figures 8-8 & 8-9
Gummel NumbersFor a uniformly doped base with negligible band-gap narrowing, the base Gummel number is
B
BB D
WNG
(total integrated “dose” (#/cm2) of majority carriers in the base, divided by DB)
E
BWW
NN
DD
nGG
EE
B
B
E
Bi
Ein
1
1
1
1
2
2Emitter efficiency
11 /2
/2
kTqV
B
ikTqV
B
BiC
EBEB eG
qAne
WN
DqAnI
GE is the emitter Gummel numberEE130/230A Fall 2013 Lecture 27, Slide 5
dxxD
xN
n
nG
B
BW
Bi
iB )(
)(0 2
2
B
E
LW
LW
NN
DD
n
dc G
G
BEE
B
B
E
Bi
Ein
2
21
2
2
1Notice that
In practice, NB and NE are not uniform, i.e. they are functions of x
The more general formulas for the Gummel numbers are
dxxD
xN
n
nG
E
EW
Ei
iE )(
)(0 2
2
EE130/230A Fall 2013 Lecture 27, Slide 6
Charge Control Model
B
BB
B Qi
dt
dQ
Wx
BB tptxp 1),0(),(
WB
BB
tpqAWdxtxpqAQ
0 2
),0(),(
A PNP BJT biased in the forward-active mode has excessminority-carrier charge QB stored in the quasi-neutral base:
In steady state,B
BB
B Qi
dt
dQ
0
EE130/230A Fall 2013 Lecture 27, Slide 7
Base Transit Time, tt
2
),0( tpqAWQ B
B
Bt D
W
2
2
• time required for minority carriers to diffuse across the base • sets the switching speed limit of the transistor
t
BBBC
BB
Wx
BBC
Q
W
QDi
W
tpqAD
x
txpqADi
2
2
),0(),(
EE130/230A Fall 2013 Lecture 27, Slide 8
Small-Signal Model
Transconductance:
vber gmvbe
C
E
B
E
C
+
Common-emitter configuration,forward-active mode:
kTqVFFC
BEeII /0
qkT
IeI
dV
d
dV
dIg CkTqV
FFBEBE
Cm
BE
//
0
“hybrid pi” BJT small signal model:
EE130/230A Fall 2013 Lecture 28, Slide 9
R. F. Pierret, Semiconductor Device Fundamentals, Fig.12.1(a)
Small-Signal Model (cont.)
, mFBE
CFBED
C
FF
gdV
IdC
I
Q
BE
F
dV
dQC BED,
BEdep
s
W
AC
,BEJ,
m
dc
dc
m
BE
C
dcBE
B
gr
g
dV
dI
dV
dI
r
11
BEDBEDBEJ CCCC ,,,
where QF is the magnitude of minority-carrier charge stored in the base and emitter regions
forward transit time
EE130/230A Fall 2013 Lecture 28, Slide 10
Summary: BJT Small Signal Model
vber gmvbe
C
E
B
E
C
+
Hybrid pi model for the common-emitter configuration, forward-active mode:
m
dc
gr
mFBEJ gCC ,
qkT
Ig C
m /
EE130/230A Fall 2013 Lecture 28, Slide 11
12
Thanks very much for your continuous support throughout the semester.
Good luck to the final exam!