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www.nanohub.org
NCN
Lecture22:Nonidealeffects
[email protected]
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Outline
1) Nonideal
effects:
Junction
recombination
3) Conclusion
Ref.SemiconductorDevicesFundamentals,Chapter6
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TopicMap
E uilibrium DC Small Lar e Circuits
signal Signal
Diode
Schottky
BJT/HBT
MOSFET
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VariousRegionsofIVCharacteristics
ln I. us on m e
2. Ambipolar transport2
3. High injection
-6,7
5. Breakdown
A
6. Trap-assisted R-G
7. Esaki Tunneling
4
5
4Alam ECE606S09
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Slide 4
MAA1 Asad: We should redraw the figure ...Muhammad Ashrafal
Alam, 1/30/2009
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ApplyingBias
qVbi
n,p
EFEVEC
EF
x
E F
q(VbiV)
,
FpEV
V
x
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(4,6)JunctionRecombination
W
0R I qA dxt=
2
1 1
( )
(
[ ]
[ ]
)
])[
(
( )
=
+ + +
i
p n
p x
p x
n x
nn x
nn
t p
pn = Ti EE = inpn == 11Assume
)1(/2 kTqV
i ennA
=
Note:DoyourememberthisHW?
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i
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(np)ProductwithintheJunction
Massactioninnonequilibrium
( ) /2( ) ( ) N P
F F kT
in x p x n e=
/2 AqV kT in e=
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Electron/HoleConcentrationsatJunction
)()( xVExE =
( )( ) /N i kTF E xn exn =
/2
[ ]/( )( ) N
A
iL
qV kT
i
kTF E qV x
n e
x ep n +=
[ ]( ) / N iLF E qV x kT
in e
+=[ ( )]/ / N iL AF E qV x kT qV kT
in e + +=
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JunctionRecombination
EFU iLN
=
VA=kT qkT /
)1( AU
i enn
][ AFNFNUUUUU
eet++ +
W
2/2/2/ AAA UUU
02 [ / 2]= +
R
FN A
I qA sinhcosh U U U
][2/2/2/ AFNAFNA UUUUUUU
i
eeet++ +=
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[ / 2]
i A
FN At cosh U U U
= +
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JunctionRecombinationinForwardBias
/ 2 n sinh Un
[ / 2]
=
+ FN At cosh U U U
( / 2)0( ) ( )
2 FN AU
Wi A
R U U
n U dx I qA sinh
e+
Emax
max( ) /( / 2 )0( ) ( )
2
Wi A
R kT qx
n U dx I qA sinh
e
E2
3ln(I)
/ 2
max2
AqV kT iDep
nkT I qA e
q
= E
VA6,7
10
4
5Effectivewidth
Excess
Carrier
at
midjunction
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JunctionLeakageinPractice
InsulatingLayer
d
n
prj rj
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JunctionRecombinationinReverseBias
inn =
W=xn+xp
(Recombinationin
2t
ep et onreg on
0 2R
Win I qA dx
2
3ln(I)
VA6,7
2
ibi A
Wnq VA V
=
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5
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Outline
1) Nonidealeffects:Junctionrecombination
2) Nonidealeffects:Impactionization
3 Conclusion
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AvalancheBreakdown
ln I. us on m e
2. Ambipolar transport2
3. High injection
-6,7
5. Breakdown
A
6. Trap-assisted R-G
7. Esaki Tunneling
4
5
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Slide 14
MAA2 Asad: We should redraw the figure ...Muhammad Ashrafal
Alam, 1/30/2009
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NonlinearityduetoImpactIonization
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Impactionization andFluxConservation
( ) ( ) ( ) ( )pn n pn n
I I I x dx x x dx x dxI+ = + +
( ) ( )n n I x dx I x I x I x+
= +
( )
( ) ( )
n n p p
n
n n p p
dx
dI x
I x I xdx = +
( )n
dI x x I xII= +
( )( )
( )
p n n
nn p n p
n
T
dxdI
Ix
I x =
x W 0
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Impactionization
( )0
'
0
(0)
( )
x
n pW dx
p
Tn
ne dxII W
I
+
=
In(0)~0
( )( )
0
'
0
1
x
n pW dxT
p n
I
e dx
+
( ) (( ) )n T Tp n I W I I W I I W + = (0) 1
T
n
pI M
I
( )0
'1
1 1
x
p nW dx
pe dx
=
x W 0
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0p
Ip(W)~0
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Impactionization'
x
W dx 0
0
1pe dx
1 p n pW = =
0
B
pA e = E
( ) ( )1 / 2
0 0
20 D n D A bi A
s s D A
qN x q N N V V
k k N N
= = +
E
ec r c e
VA0
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Position
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Impactionization:InPractice
Good.
InsulatingLayer
Bad.prj rj
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n
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JunctionEngineering Insulating
d
n
p
rj rj i-region
E E
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- - , bi(area under the curve) must be the same.
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ModernConsiderations:DeadSpace
DeadSpace
WhathappensifWisless
W
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ZenerBreakdownvs.ImpactIonization
HowdoyoudifferentiatebetweenZener
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tunnelingandimpactionization?
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Conclusion
1) Junctionrecombinationisoftenusedasadiagnostic
toolfor
process
maturity.
Defects
in
junction
arises
frommis laceddonorim urities notnecessar from
deeptrapimpurities.
varietyofdevices(e.g.avalanchephotodiodes).
3) Inthe
next
class,
we
will
discuss
AC
response
of
pn
junctiondiodes.
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