T f Jn ntff tune NINE T -...
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Recap of semiconductor undoped n p Nc 1.5 10 N type CAS P n No p n p small p type B f NA n _nina small Driftcurrent Jp P Gop Pfllp E 1 T f Jn ntff tune NINE T
Transcript of T f Jn ntff tune NINE T -...
Recap of semiconductorundoped n p Nc 1.5 10
N type CAS P n No p npsmall
p type B f NA n_nina smallDriftcurrentJp PGop Pfllp E1
T
f Jn ntff tune NINET
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Current in Semiconductor (2):Diffusion Current - Holes
• If hole distribution is non-uniform, holes will move from high to low concentration areas
• Flux ∝ - [conc. gradient]
• Current flows since holes carry charge:
"#$%&'' = )*# −,- .,.*#: hole diffusion coef. [cm2/s]
• Note: since hole carries positive charge, hole diffusion and hole current are in the same direction
Hole Diffusion
O 0
adPd
Handp
0 high
i tx
lowslopfo n tO
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Current in Semiconductor (2):Diffusion Current - Electrons
• Similarly, electron diffusion also causes current to flow, but in opposite direction since electron carries negative charge
!"#$%&& = (−*)," −-. /-/
= *,"-. /-/
,": electron diffusion coef. [cm2/s]
!"#$%&& : [A/cm2]
• In Si, – Dn = 35 cm2/s – Dp = 12 cm2/s
Electron Diffusion
O Oa
oE
f Jndiff Un 3Up12 3Dp
D
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Einstein Relationship
Dn
µn
=Dn
µn
=VT =kTq
VT : Thermal voltageAt room temperature, VT = 26 mV
Proof: Total electron current:
Jn = Jn−drift + Jn−diff = qn(x)µnE + qDndn(x)dx
E = − dφdx
, φ : potential
n(x) = n0e−
(−qφ )kT = n0e
φVT : Boltzmann distribution
In equilibrium, no net current flow
⇒ qn(x)µnE + qDndn(x)dx
= 0
n(x)µnE +Dndn(x)dφ
dφdx
= 0
n(x)µnE +Dn1VTn(x)
#
$%
&
'( −E( ) = 0
Dn
µn
=VT
OO 6mVat F 300K
Assume MX
Jn nlnHln Et Dnddn
p0Eddx 0 potentialequilibrium
n noeta.rs LnoTBoltzmann's dist
naDUntd tDn qo
Eine
n
fhkisl
nyxjlln Dn.nl fTp 0
I
Dn TMn on_Un E
DµIn kBqI V CmsEtan
off a
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