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Lecture 28
OUTLINE
The BJT (cont’d)
• Small-signal model
• Cutoff frequency
• Transient (switching) response
Reading: Pierret 12; Hu 8.8-8.9
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 2
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 3
ExampleA BJT is biased at IC = 1 mA and VCE = 3V. dc = 90, F = 5ps, T = 300K. Find (a) gm , (b) r , (c) C .
Solution:
(a)
(b) r = dc / gm = 90/0.039 = 2.3 k
(c)
siemens)(milliqkTIg Cm mS 39V
mA39
mV 26
mA 1)//(
ad)(femto fargC mF fF 19F109.1039.0105 1412
EE130/230A Fall 2013 Lecture 28, Slide 4
Cutoff Frequency, fT
The cutoff frequency is defined to be the frequency (f = /2) at which the short-circuit a.c. current gain equals 1:
CBEJFTac qIkTC
f/2
1at 1
,
CBEJFdc
BEJmFdcm
mm
b
c
bemc
bbbe
qIkTCj
Cgjg
g
Cjr
g
i
i
vgi
Cjr
iiv
//1
1
//1)(
/1admittanceinput
,
,
vber gmvbe
C
E
B
E
C
+
EE130/230A Fall 2013 Lecture 28, Slide 5
fT is commonly used as a metric for the speed of a BJT.
Si/SiGe HBT by IBM
For the full BJT equivalent circuit: ceBCJCBCJBEJF
T rrCqIkTCCf
,,, /2
1
To maximize fT:
• increase IC
• minimize CJ,BE, CJ,BC
• minimize re, rc
• minimize F
EE130/230A Fall 2013 Lecture 28, Slide 6
Base Widening at High IC: Kirk Effect
• At very high current densities (>0.5mA/m2), the density of mobile charge passing through the collector depletion region exceeds the ionized dopant charge density:
sat
CCCCdepsatC v
JqNqnqNqnvJ ,
increasing IC
For a NPN BJT:
The base width (W) is effectively increased (referred to as “base push out”)
F increases and hence fT decreases.
•This effect can be avoided by increasing NC increased CJ,BC , decreased VCE0
EE130/230A Fall 2013 Lecture 28, Slide 7 C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 8-18
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 8
BJT Switching - Qualitative
EE130/230A Fall 2013 Lecture 28, Slide 9
R. F. Pierret, Semiconductor Device Fundamentals, Figs. 12.3-12.4
Turn-on Transient Response
•The general solution is:
•Initial condition: QB(0)=0 since transistor is in cutoff
B
BBB
B QI
dt
dQ
BtBBBB AeItQ /)(
)1()( / BtBBBB eItQ
rL
CC
rt
tBBB
t
B
C
ttR
V
tteItQ
ti
B
01)(
)(
/
where IBB=VS/RS
BBB
LCCBr
IRV
t
/
1
1ln
EE130/230A Fall 2013 Lecture 28, Slide 10 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 12.5
Turn-off Transient Response
• The general solution is:
• Initial condition: QB(0)=IBBB
B
BBB
B QI
dt
dQ
BtBBBB AeItQ /)(
BtBBBB eItQ /1)(
sdt
tBBB
t
B
sdCC
C
tteItQ
ttI
tiB
/1)(
0
)(
BBB
tCCBsd
II
t1
ln
EE130/230A Fall 2013 Lecture 28, Slide 11 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 12.5
Reducing B for Faster Turn-Off• The speed at which a BJT is turned off is dependent on the
amount of excess minority-carrier charge stored in the base, QB, and also the recombination lifetime, B.
– By reducing B, the carrier removal rate is increased
Example: Add recombination centers (Au atoms) in the base
EE130/230A Fall 2013 Lecture 28, Slide 12
Schottky-Clamped BJT• When the BJT enters the saturation mode, the Schottky
diode begins to conduct and “clamps” the C-B junction voltage at a relatively low positive value. reduced stored charge in quasi-neutral base
EE130/230A Fall 2013 Lecture 28, Slide 13 R. F. Pierret, Semiconductor Device Fundamentals, Fig. 12.7