S. Kugler: Lectures on Amorphous Semiconductorsa 1 Optical properties

S. Kugler: Lectures on Amorphous Semiconductorsa 2 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. 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 3 Absorption coefficient α is defined by I(z) = I o exp {- α z} Absorption coefficient α is defined by I(z) = I o exp {- α z} where I(z) is the flux density if incident light is I o, z is the distance measured from the incident surface. Hence where I(z) is the flux density if incident light is I o, z is the distance measured from the incident surface. Hence α = - (1/I(z)) dI(z)/dz

S. Kugler: Lectures on Amorphous Semiconductorsa 4 Absorption

5 Tauc law (Tauc plot, A region) The absorption coefficient, α, due to interband transition near the band-gap is well described: The absorption coefficient, α, due to interband transition near the band-gap is well described: αħω = B (ħ ω – E g ) 2 ħω is photon energy, E g is optical gap. ħω is photon energy, E g is optical gap. This Tauc plot defines the optical gap in amorphous semiconductors. This Tauc plot defines the optical gap in amorphous semiconductors.

S. Kugler: Lectures on Amorphous Semiconductorsa 6

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8 Urbach tail (B region) The absorption coefficient at the photon energy below the optical gap (tail absorption) depends exponentially on the photon energy: 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/E u ) α(ħ ω) ~ exp (ħ ω/E u ) where E u is called Urbach energy. where E u is called Urbach energy.

S. Kugler: Lectures on Amorphous Semiconductorsa 9 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: 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/E d ), E d belongs to the width of the defect states. C region is rather sensitive to the structural properties of materials. E d 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 10 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: k photon = k i – k f. (k photon, k i and, k f are the wave numbers of photons, electron of initial and final states. 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: k photon = k i – k f. (k photon, k i and, k f are the wave numbers of photons, electron of initial and final states.

S. Kugler: Lectures on Amorphous Semiconductorsa 11 Since k photon is much smaller than k i and k f, we can rewrite the selection rule: Since k photon is much smaller than k i and k f, we can rewrite the selection rule: k i = k f. k i = k f. 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. 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!