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