Optic

S. Kugler: Lectures on Amorphous S. Kugler: Lectures on Amorphous SemiconductorsaSemiconductorsa

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Optical Optical propertiesproperties


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General aspectsGeneral aspects

Optical absorption and Optical absorption and luminescence occur by transition of luminescence occur by transition of electrons and holes between electrons and holes between electronic states (bands, tail states, electronic states (bands, tail states, gap states). If electron-phonon gap states). If electron-phonon coupling is strong enough self-coupling is strong enough self-trapping occurs. trapping occurs.


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Absorption coefficient Absorption coefficient αα is defined by is defined by I(z) = II(z) = Ioo exp {- exp {- αα z} z}

where where I(z) I(z) is the flux density if is the flux density if incident light is incident light is IIoo, , z z is the distance is the distance measured from the incident surface. measured from the incident surface. Hence Hence

αα = = - (1/I(z)) dI(z)/dz - (1/I(z)) dI(z)/dz


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Absorption Absorption


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Tauc law (Tauc plot, A region)Tauc law (Tauc plot, A region)

The absorption coefficient, The absorption coefficient, αα, due to , due to interband transition near the band-interband transition near the band-gap is well described:gap is well described:

ααħħωω = B (ħ = B (ħ ωω –– E Egg))2 2

ħħωω is photon energy, is photon energy, EEg g is optical gap.is optical gap.

This Tauc plot defines the optical This Tauc plot defines the optical gap in amorphous semiconductors.gap in amorphous semiconductors.


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Urbach tail (B region)Urbach tail (B region)

The absorption coefficient at the The absorption coefficient at the photon energy below the optical gap photon energy below the optical gap (tail absorption) depends (tail absorption) depends exponentially on the photon energy:exponentially on the photon energy:

αα((ħħ ωω) ) ~~ exp (ħ exp (ħ ωω/E/Euu)) where where EEuu is called Urbach energy. is called Urbach energy.


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C regionC region

In addition, optical absorption by In addition, optical absorption by defects also appears at energy lower defects also appears at energy lower than optical gap. Likewise than optical gap. Likewise αα is written is written as another exponential function of as another exponential function of photon energy:photon energy:

αα((ħħωω) ) ~~ exp (ħ exp (ħωω/E/Edd),),

EEd d belongs to the width of the defect belongs to the width of the defect states. C region is rather sensitive to states. C region is rather sensitive to the structural properties of materials.the structural properties of materials.


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Direct/indirect transitionDirect/indirect transition

In the case of crystalline semiconductors In the case of crystalline semiconductors (without defects, there is no localized (without defects, there is no localized state) photoluminescence occurs by state) photoluminescence occurs by transition between the bottom of the transition between the bottom of the conduction band and the top of the conduction band and the top of the valence band. valence band. kk selection rule must be selection rule must be satisfied: satisfied: kkphotonphoton = k = kii – k – kff . (. (kkphotonphoton, k, kii andand, , kkff are the wave numbers of photons, are the wave numbers of photons, electron of initial and final states.electron of initial and final states.


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Since Since kkphotonphoton is much smaller than k is much smaller than kii and and kkff, , we can rewrite the selection rule:we can rewrite the selection rule:

kkii = k = kff..

The semiconductors satisfying this condition The semiconductors satisfying this condition is called direct-gap semiconductors. c-Si is is called direct-gap semiconductors. c-Si is not satisfying k-selection rule (indirect-gap not satisfying k-selection rule (indirect-gap semiconductor). Transition is allowed by semiconductor). Transition is allowed by either absorption of phonons or their either absorption of phonons or their emission.emission.

There is no k vector in amorphous There is no k vector in amorphous systems!systems!

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