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Drift current – due to E-field → Ohm’s law: J = E where = conductivity ≡ mobility Drift velocity: v = E
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Conduction processes in semiconductors
Two form of charge carrier transport(1) Drift (due to E-field)(2) Diffusion (due to density gradient)
for two types of charge carriers(a) n-type (electrons)(b) p-type (holes)
Drift current – due to E-field
→ Ohm’s law: J = sE
where s = conductivity m ≡ mobility
Drift velocity: v = mE
Conductivity of semiconductorss = sn + sp
sn = qmnn electrons
sp = qmpp holes
Mobility: scattering by(a) lattice(b) ionized impurities
Mobilities for silicon [7.3-2]
Where Tn = T/300
NI = total density of ionized impurities
Diffusion current
holes:
electrons:
where Dn , Dp are defined as the diffusion coefficients for electrons and holes, respectively
dxdpqDJ pp
dxdnqDJ nn
Relationship between mobility and diffusion coeffcients
Dn = mnVT
Dp = mpVT
VT = kT/q ≡ thermal voltage
Electrical current in semiconductors
J = J(drift) + J(diffusion)
pn JJJ
Two transport mechanisms
Two types of charge-carriers
dxdnqDExnqJ nnn )(m
dxdpqDExpqJ ppp )(m
For n = n(x) and equilibrium conditions
Equilibrium → EF = same everywhere. So for n=n(x) then EC = EC(x) (and likewise for Ei and EV)
Induced E-field
dxdn
xnV
dxdn
xnqkTE T )(
1)(
1
Equilibrium: Current = 0 = Jn(drift) + Jn(diffusion)
dxdnqD
dxdn
xnV
qn nT
n
)(0 m