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EE130 Lecture 20, Slide 1Spring 2007
Lecture #20
OUTLINE
• pn Junctions (cont’d)
– small-signal model
– transient response• turn-off
Reading: Chapters 7, 8
EE130 Lecture 20, Slide 2Spring 2007
Small-Signal Model of the Diode
kTqVkTqV eIdV
deI
dV
d
dV
dI
RG /
0A
/0
AA
AA )1(1
qkT
IeI
kT
qG DCkTqV
//
0A
CR=1/Gva
i
Small-signal conductance :
dt
dvCGvi a
a
Small signal equivalent circuit:
+
EE130 Lecture 20, Slide 3Spring 2007
Review: Charge Storage in pn-Diode
EE130 Lecture 20, Slide 4Spring 2007
2 types of capacitance associated with a pn junction:1. CJ depletion capacitance
(due to variation of depletion charge)
2. CD diffusion capacitance (due to variation of stored minority charge in the quasi-
neutral regions)
For a one-sided p+n junction, QP >> QN
so Q = QP + QN QP:
qkT
IG
dV
dI
dV
dQC
/
τττ DCp
pA
pA
D
EE130 Lecture 20, Slide 5Spring 2007
What are three ways to reduce Cdep?
WA
dV
dQC s
A
depJ
Depletion Capacitance
np
W
“insulator” conductorconductor
EE130 Lecture 20, Slide 6Spring 2007
Total pn-Junction Capacitance
• CD dominates at moderate to high forward biases
• Cdep dominates at low forward biases, reverse biases
1/
τ /DCD kTqVAe
qkT
IC
WAC s
J
DCCC JR=1/Gva
i
+
EE130 Lecture 20, Slide 7Spring 2007
NqA
VV
A
W
C Ss 2Abi
22
2
2J
)(21
CJ-vs.-VA (Reverse Bias)
EE130 Lecture 20, Slide 8Spring 2007
If the slope of the (1/Cdep)2 vs. VA characteristic is -2x1023
F-2 V-1, the intercept is 0.84V, and A is 1 m2, find the lighter and heavier doping concentrations Nl and Nh. Solution:
ln 2i
lhbi
n
NN
q
kTV 318026.0
84.0
15
202
cm 108.1106
10
eeN
nN kT
qV
l
ih
bi
315
28141923
2
cm 106
)cm101085.812106.1102/(2
)/(2
AqslopeN sl
Example
EE130 Lecture 20, Slide 9Spring 2007
Summary: Small Signal Model
qkT
IG DC
/
qkT
IC
/
τ DCD
W
AC s
J
)1( /0
A kTqVDC eII
DJ CCC
Depletion capacitance
Diffusion capacitance
Conductance
EE130 Lecture 20, Slide 10Spring 2007
Transient Response of pn Diode• Suppose a pn-diode is forward biased, then suddenly
turned off at time t = 0. Because of CD, the voltage across the pn junction depletion region cannot be changed instantaneously.
The delay in switching between the ON and OFF states is due to the time required to change the amount of excess minority carriers stored in the quasi-neutral regions.
EE130 Lecture 20, Slide 11Spring 2007
Turn-Off Transient• In order to turn the diode off, the excess minority
carriers must be removed by net carrier flow out of the quasi-neutral regions and/or recombination– Carrier flow is limited by the switching circuitry
EE130 Lecture 20, Slide 12Spring 2007
Decay of Stored ChargeConsider a p+n diode (Qp >> Qn):
t
i(t)
t
vA(t)
ts
ts0
pxx
n
qAD
i
dx
dp
n
For t > 0:
pn(x)
EE130 Lecture 20, Slide 13Spring 2007
Examples (qualitative)
t
i(t)
ts
Increase IF
t
i(t)
ts
Increase IR
t
i(t)
ts
Decrease p
EE130 Lecture 20, Slide 14Spring 2007
Storage Delay Time ts
• ts is the primary “figure of merit” used to characterize the transient response of pn junction diodes
• By separation of variables and integration from t = 0+ to t = ts, noting that
and making the approximation
We conclude that
sp
pR
p
pp ttQ
IQ
idt
dQ
0
ττ
ppF tQI τ/)0(
0)( sp ttQ
R
Fps I
It 1lnτ