Transcript Optical properties - BUTE Institute of Physics

Optical
properties
S. Kugler: Lectures on Amorphous
Semiconductorsa
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General aspects
Optical absorption and luminescence
occur by transition of electrons and holes
between electronic states (bands, tail
states, gap states). If electron-phonon
coupling is strong enough self-trapping
occurs.
S. Kugler: Lectures on Amorphous
Semiconductorsa
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
Absorption coefficient α is defined by
I(z) = Io exp {- α z}
where I(z) is the flux density if incident
light is Io, z is the distance measured from
the incident surface. Hence
α = - (1/I(z)) dI(z)/dz
S. Kugler: Lectures on Amorphous
Semiconductorsa
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Absorption
S. Kugler: Lectures on Amorphous
Semiconductorsa
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Tauc law (Tauc plot, A region)
The absorption coefficient, α, due to
interband transition near the band-gap is
well described:
αħω = B (ħ ω – Eg)2
ħω is photon energy, Eg is optical gap.
This Tauc plot defines the optical gap in
amorphous semiconductors.
S. Kugler: Lectures on Amorphous
Semiconductorsa
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S. Kugler: Lectures on Amorphous
Semiconductorsa
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S. Kugler: Lectures on Amorphous
Semiconductorsa
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Urbach tail (B region)
The absorption coefficient at the photon
energy below the optical gap (tail
absorption) depends exponentially on the
photon energy:
α(ħ ω) ~ exp (ħ ω/Eu)
where Eu is called Urbach energy.
S. Kugler: Lectures on Amorphous
Semiconductorsa
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C region
In addition, optical absorption by defects
also appears at energy lower than optical
gap. Likewise α is written as another
exponential function of photon energy:
α(ħω) ~ exp (ħω/Ed),
Ed belongs to the width of the defect
states. C region is rather sensitive to the
structural properties of materials.
S. Kugler: Lectures on Amorphous
Semiconductorsa
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Direct/indirect transition

In the case of crystalline semiconductors
(without defects, there is no localized
state) photoluminescence occurs by
transition between the bottom of the
conduction band and the top of the
valence band. k selection rule must be
satisfied: kphoton = ki – kf . (kphoton, ki and,
kf are the wave numbers of photons,
electron of initial and final states.
S. Kugler: Lectures on Amorphous
Semiconductorsa
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Since kphoton is much smaller than ki and kf, we
can rewrite the selection rule:
ki = kf.
The semiconductors satisfying this condition is
called direct-gap semiconductors. c-Si is not
satisfying k-selection rule (indirect-gap
semiconductor). Transition is allowed by either
absorption of phonons or their emission.
There is no k vector in amorphous
systems!
S. Kugler: Lectures on Amorphous
Semiconductorsa
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