PN Junctions - nanoHUB.org

ECE-305: Fall 2013
PN Junctions V:
IV characteristics
Professor Mark Lundstrom
Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA
[email protected]
10/17/14
outline
1)  Electrostatics under bias
2)  Ideal diode equation
2
equilibrium e-band diagram
E
qVbi
EC
EF
EF
I=0
VA = 0
EV
W
x
!xn
xp
3
effect of an applied bias
V =0
VA > 0
Where does the voltage drop?
N-side?
P-side?
junction?
4
3 resistors in series.
e-band diagram under forward bias
E
EC
Vbi ! VA
V = 0 EF
VA > 0
EV
W
x
!xn
xp
The applied voltage drops across the junction, but…
5
QFL’s split
E
EC
VA > 0
Vbi ! VA
V = 0 Fn
Fn > Fp
qVA
Fp
EV
W
x
!xn
6
xp
e-band diagram under reverse bias
E
Vbi
EC
V = 0 EF
VA < 0
EV
W
x
!xn
xp
7
e-band diagram under reverse bias
Vbi ! VA = Vbi + VR
E
Fp
EC
VA < 0
V =0
Fn
Fn < Fp
EV
W
x
8
!xn
xp
electrostatics under bias
N
P
N D = 1016
N A = 1016
W
!xn
xp
0
depletion region
1/2
Vbi =
k BT ! N D N A $
ln #
q
" ni2 &%
) 2K ! " N + N D %
,
W =+ S 0$ A
(Vbi ( VA ).
'
q
N
N
#
D A &
*
-
E (0) =
2 (Vbi ! VA )
W
xn =
NA
W
NA + ND
xp =
ND
W
NA + ND
9
key points
Vbi !
k BT " N D N A %
ln $
(difference in Fermi levels / q)
q
# ni2 '&
1/2
# 2K !
&
W = % S 0 (Vbi " VA ) (
$ qN A
'
E (0) =
10
W ) Vbi " VA
W)
1
NA
2 (Vbi ! VA )
E ( 0 ) " Vbi ! VA E ( 0 ) " N A
W
outline
1)  Electrostatics under bias
2)  Ideal diode equation
11
ECE 255
I ( mA )
! VA
0.6 ! 0.7 V
12
VA
+
NP junction in equilibrium
n0 P ! ni2 N A
n0 N ! N D
Vbi =
k BT N A N D
ln
q
ni2
qVbi
EF
EF
n0 P ni2 N A
!
= e" qVbi
n0 N
ND
P 0 = e! qVbi
k BT
= P0
p0 P ! N A
p0 N ! ni2 N D
k BT
13
NP junction under bias
P 0 = e! qVbi
k BT
nP >> n0 P
"?
P = e! q(Vbi !VA ) kBT
q (Vbi ! VA )
P >> P 0
P = P0 e
Fn
qVA kBT
nP = n0 P eqVA
14
kBT
=
ni2 qVA
e
NA
Law of the Junction
kBT
Fp
p0 P ! N A
(This assumes nearequilibrium, J ≈ 0, conditions.)
excess electrons on the p-side of junction
n0 N ! N D
nP >> n0 P
q (Vbi ! VA )
Fn
Fp
p0 P ! N A
p0 N ! ni2 N D
x
0
15
What is Δn(x) on the p-side? Ans. Solve the MCDE.
Δn(x) on p-side of junction
!n ( x )
!n ( 0 ) = nP " n p0
!n ( 0 ) =
ni2 qVA
(e
NA
kBT
" 1)
!n ( x ) = !n ( 0 ) e" x/Ln
!n ( x ) " 0
W p >> Ln
0
16
Wp
x
What is Δn(x) on the p-side? Ans. Solve the MDE.
total recombination on p-side of junction
!n ( 0 ) =
!n ( x )
ni2 qVA
(e
NA
kBT
" 1)
How many electrons recombine
per second?
One answer:
Wp
!n ( x ) = !n ( 0 ) e
" x/Ln
RTOT = A
" !n ( x ) dx
xp
#n
=
A!n ( 0 ) Ln
#n
x
0
17
total recombination on p-side of junction
!Dn
!n ( x )
d"n
dx 0
How many electrons recombine
per second?
Another answer:
!n ( x ) = !n ( 0 ) e" x/Ln
#
d"n &
D
RTOT = A % !Dn
= A n "n ( 0 )
(
dx 0 '
Ln
$
x
0
18
recombination and current
minority carriers injected across junction
FP
qVA
Fn
ID
! VA +
19
Every time a minority electron recombines on the
p-side, one electron flows in the external current.
current
!n ( 0 ) =
!n ( x )
ni2 qVA
(e
NA
kBT
" 1)
!n ( x ) = !n ( 0 ) e
W p >> Ln
I D = qRTOT = qA
I D = qA
" x/Ln
Dn ni2 qVA
(e
Ln N A
!n ( x ) " 0
x
0
20
Dn
!n ( 0 )
Ln
kBT
! 1)
diode current
Jn =
VA > 0
V =0
Jp =
" D n2 %
q!n ( 0 ) Dn
= q $ n i ' ( eqVA /kBT ( 1)
Ln
# Ln N A &
" D n2 %
q!p ( 0 ) D p
= q $ p i ' ( eqVA /kBT ( 1)
Lp
# Lp N D &
J D (VA ) = J p (VA ) + J n (VA )
21
diode current
ideal diode equation
ID
Shockley diode equation
VA
J = J 0 ( eqVA /kBT ! 1)
! D n2 D n2 $
J0 = q # n i + p i &
" Ln N A L p N D %
22
diode current
I D ( pA )
I D ( mA )
VA
VA
0.6 ! 0.7 V
23
(
)
I D = I 0 eqVA /kBT ! 1
diode current: qualitative picture
I D ( pA )
J = J 0 ( eqVA /kBT ! 1)
VA
24
NP junction in equilibrium
P0 = e
! qVbi kBT
J1
J0
qVbi
EF
EF
p0 P ! N A
J1 = J 0
25
NP junction in forward bias
P = e! q(Vbi !VA ) kBT = eqVA
J1 = J 0 eqVA /kBT
J0
J = J1 ! J 0 = J 0 ( eqVA /kBT ! 1)
26
P0
kBT
J1
J0
q (Vbi ! VA )
Fp
p0 P ! N A
NP junction in reverse bias (VR=-VA)
P = e! q(Vbi +VR ) kBT = e! qVR
P0
kBT
P << P 0
J1
J0
q (Vbi + VR )
Fp
J1 << J 0
Fn
J = J1 ! J 0 " !J 0
27
diode current: qualitative picture
I D ( pA )
J = J 0 ( eqVA /kBT ! 1)
VA
28
narrow p-side
We have assumed that WP >> Ln (long diode).
What happens if WP << Ln (short diode)?
29
narrow p-side
!n ( 0 ) =
!n ( x )
ni2 qVA
(e
NA
kBT
" 1)
#
x &
!n ( x ) = !n ( 0 ) % 1"
$ WP ('
J n = qDn
Jn = q
Dn
!n ( 0 )
Wp
W p << Ln
x
0
30
Wp
d!n ( x )
dx x=0
diode current
! D n2 $
J n = q # n i & ( eqVA /kBT ' 1)
" Wp N A %
VA > 0
V =0
! D n2 $
J p = q # p i & ( eqVA /kBT ' 1)
" Wn N D %
31
Ideal diode equation
ID
(
)
I D = I 0 eqVA /kBT ! 1
VA
long
! D n 2 D p ni2 $
I 0 = qA # n i +
&
" Ln N A L p N D %
32
short
! D n 2 D p ni2 $
I 0 = qA # n i +
" WP N A Wn N D &%

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