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## Optical properties

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**Optical properties**S. Kugler: Lectures on Amorphous Semiconductorsa**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**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**Absorption**S. Kugler: Lectures on Amorphous Semiconductorsa**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 ħωis photon energy, Eg is optical gap. This Tauc plot defines the optical gap in amorphous semiconductors. S. Kugler: Lectures on Amorphous Semiconductorsa**Urbach tail (B region)**The absorption coefficient at the photon energy below the optical gap (tail absorption) depends exponentially on the photon energy: α(ħω) ~ exp (ħ ω/Eu) where Eu is called Urbach energy. S. Kugler: Lectures on Amorphous Semiconductorsa**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**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, kiand, kfare the wave numbers of photons, electron of initial and final states. S. Kugler: Lectures on Amorphous Semiconductorsa**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