Lecture #20
OUTLINE
• pn Junctions (cont’d)
– small-signal model
– transient response
• turn-off
Reading: Chapters 7, 8
Spring 2007
EE130 Lecture 20, Slide 1
Small-Signal Model of the Diode
Small signal equivalent circuit:
i
+
va
R=1/G
C

dva
i  Gva  C
dt
Small-signal conductance :
G
1
dI
d
d


I 0 (e qVA / kT  1) 
I 0 e qVA / kT
R dVA dVA
dVA
I DC
q
qVA / kT
G
I 0e

kT
kT / q
Spring 2007
EE130 Lecture 20, Slide 2
Review: Charge Storage in pn-Diode
Spring 2007
EE130 Lecture 20, Slide 3
2 types of capacitance associated with a pn junction:
1. CJ
depletion capacitance
2. CD
diffusion capacitance
(due to variation of depletion charge)
(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:
τ p I DC
dQ
dI
CD 
 τp
 τ pG 
dVA
dVA
kT / q
Spring 2007
EE130 Lecture 20, Slide 4
Depletion Capacitance
p
n
W
“insulator”
conductor
CJ 
dQdep
dVA
A
conductor
s
W
What are three ways to reduce Cdep?
Spring 2007
EE130 Lecture 20, Slide 5
Total pn-Junction Capacitance
i
+
va
R=1/G
C  CJ  CD

CJ  A
s
W
τI DC
CD 
 e qVA / kT  1
kT / q


• CD dominates at moderate to high forward biases
• Cdep dominates at low forward biases, reverse biases
Spring 2007
EE130 Lecture 20, Slide 6
CJ-vs.-VA (Reverse Bias)
2(Vbi  VA )
1
W2
 2 2  2
2
A q S N
CJ
A s
Spring 2007
EE130 Lecture 20, Slide 7
Example
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 mm2, find the
lighter and heavier doping concentrations Nl and Nh.
Solution:
N l  2 /( slope  q s A2 )
 2 /( 2 10 23 1.6 10 19 12  8.85 10 14 10 8 cm 2 )
 6 1015 cm 3
2
qV
0.84
kT N h Nl
ni kTbi
10 20 0.026
18
3
Vbi 
ln

N

e

e

1
.
8

10
cm
h
2
q
Nl
6 1015
ni
Spring 2007
EE130 Lecture 20, Slide 8
Summary: Small Signal Model
C  C J  CD
I DC  I 0 (e qVA / kT  1)
Depletion capacitance
Diffusion capacitance
Spring 2007
A s
CJ 
W
Conductance
τI DC
CD 
kT / q
EE130 Lecture 20, Slide 9
I DC
G
kT / q
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.
Spring 2007
EE130 Lecture 20, Slide 10
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
Spring 2007
EE130 Lecture 20, Slide 11
Decay of Stored Charge
Consider a p+n diode (Qp >> Qn):
Dpn(x)
i(t)
ts
t
vA(t)
dpn
For t > 0:
dx
Spring 2007
x  xn
i

0
qAD p
EE130 Lecture 20, Slide 12
ts
t
Examples (qualitative)
Increase IF
i(t)
i(t)
ts
Spring 2007
Decrease tp
Increase IR
t
i(t)
ts
EE130 Lecture 20, Slide 13
t
ts
t
Storage Delay Time ts
• ts is the primary “figure of merit” used to characterize
the transient response of pn junction diodes

Qp 

i
  I R 


dt
τp
τ
p


dQ p
Qp
0  t  ts
• By separation of variables and integration from t = 0+
to t = ts, noting that I F  Q p (t  0) / τ p
and making the approximation Q p (t  t s )  0
 IF 

We conclude that t s  τ p ln 1 
 IR 
Spring 2007
EE130 Lecture 20, Slide 14