Transcript Lecture #19 OUTLINE • pn junctions (cont’d) – Charge control model Reading: Finish Chapter 6.3 Spring 2007 EE130 Lecture 19, Slide 1

Lecture #19
OUTLINE
• pn junctions (cont’d)
– Charge control model
Reading: Finish Chapter 6.3
Spring 2007
EE130 Lecture 19, Slide 1
Minority-Carrier Charge Storage
• When VA>0, excess minority carriers are stored
in the quasi-neutral regions of a pn junction:
QN   qA

xp
n p ( x )dx
QP  qA pn ( x)dx
  qAn p ( x p ) LN
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
EE130 Lecture 19, Slide 2
xn
 qApn ( xn ) LP
Derivation of Charge Control Model
• Consider a forward-biased pn junction. The total
excess hole charge in the n quasi-neutral region is:
QP  qA  pn ( x, t ) dx
xn
• The minority carrier diffusion equation is (without GL):
pn
 2pn pn
 DP

t
x 2
p
• Since the electric field is very small,
J P  qDP
• Therefore:
Spring 2007
pn
x
(qpn )
J
qpn
 P 
t
x
p
EE130 Lecture 19, Slide 3
(Long Base Diode)
• Integrating over the n quasi-neutral region:
J P ()





1 
qA  pn dx   A  dJP  qA  pn dx
t  xn
 p  xn


J p ( xn )
• Furthermore, in a p+n junction:
A
J P ()
 dJ
P
  AJ P ()  AJ P ( xn )  AJ P ( xn )  iDIFF
J p ( xn )
• So:
Spring 2007
dQP
Q
 iDIFF  P
dt
p
EE130 Lecture 19, Slide 4
Charge Control Model
We can calculate pn-junction current in 2 ways:
1. From slopes of np(-xp) and pn(xn)
2. From steady-state charges QN, QP stored in each
excess-minority-charge distribution:
dQP
QP
 AJ P ( xn ) 
0
dt
τp
QP
 AJ P ( xn )  I P ( xn ) 
τp
 QN
Similarly, I N ( x p ) 
τn
Spring 2007
EE130 Lecture 19, Slide 5
Charge Control Model for Narrow Base
•
For a narrow-base diode, replace p and/or
n by the minority-carrier transit time tr
–
time required for minority carrier to travel across the
quasi-neutral region
– For holes on narrow n-side:
WN
1
QP  qA pn ( x)dx  qA pn ( xn )WN
xn
2
dpn
pn ( xn )
I P  AJ P  qADP
 qADP
dx
WN
QP WN 
 τ tr , p 

IP
2 DP
2

WP 
– Similarly, for electrons on narrow p-side: τ tr ,n 
2 DN
2
Spring 2007
EE130 Lecture 19, Slide 6
Summary
• Under forward bias, minority-carrier charge is stored
in the quasi-neutral regions of a pn diode.


ni2 qVA / kT
– Long base: QN  qA
e
 1 LN
NA
ni2 qVA / kT
QP  qA
e
 1 LP
ND






1 ni2 qVA / kT
e
 1 WP
– Short base: QN  qA
2 NA
1 ni2 qVA / kT
QP  qA
e
 1 WN
2 ND
Spring 2007
EE130 Lecture 19, Slide 7
• The steady-state diode current can be viewed as the
charge supply required to compensate for charge
loss via recombination (long base) or collection at the
contacts (short base)
QN QP
– Long base: I 

τn τ p
LN DN
LP DP

and

Note that
τn
LN
τ p LP
QN QP
– Short base: I 

τtr,n τtr, p
where τ tr ,n
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2

WP 

2 DN
τtr, p
EE130 Lecture 19, Slide 8
2

WN 

2DP