What is the relationship between Urbach energy and the Optical band gap?
The optical absorption spectra of semiconductors give information about optical properties and composition of materials. Three main regions can be distinguished: (1) region of weak absorption, which is arise from defects and impurities, (2) absorption edge region associated with disorder of the system and affecting a real value of the energy gap and (3) the region that determine the optical band-gap energy which value is associated with crystallite size.
The Urbach energy is associated with 2nd region.
please check this link for good explanations
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Abdelkader Hafdallah The Urbach energy is given by the following equation
α=α0exp(hν-Eg/Eu)
where
α is the absorption coefficient
α0 is a constant absorption
Eg is the bad gap energy
Eu is the Urbach energy
There are different mechanisms of light absorption by semiconductors; which are interband absorption, absorption by free charge carriers, absorption by the crystalline lattice, dopant absorption, excitonic absorption and weak tail absorption.
The fundamental absorption (interband absorption), which leads to the generation of electron-hole pairs as a result of optical excitation of electrons from the valence band to the conduction band, which is equal to the band gap of the semiconductor. In this description, semiconductors are described as being able to absorb photons above but are transparent to photons below the band gap energy.
Urbach energy or Urbach edge (EU) is below the band gap energy governed by the structural disorder, imperfection and passivation at the surface. Any modification or deviation from the ideal structure results curvature in the band shape. Thus, the analysis of the optical absorption in the spectral range corresponding to the tails of the density of states allows to determine the Urbach energy and thereby characterize the degree of material imperfection. It is to be noted that the density of states in three-dimensional semiconductors increases further from the band gap. For this reason, the absorption coefficient, increases with energy.
The Urbach energy quantifies the steepness of the onset of absorption near the band edge, and hence the broadness of the density of states. A sharper onset of absorption represents a lower Urbach energy.
Franz Urbach evaluated this property systematically in crystals. He used silver bromide for his study while working at the Kodak Company in 1953. Regarding the Urbach energy, the following points are to be noted that;
· It is temperature-dependent
· It is from few meV to hundreds of meV
· It also indicates the disorder of phonon states.
· It varies inversely to the band gap energy Eg
The last point states that there is an inverse relation between Urbach energy and optical band gap, which means that a sample having a narrower band gap is expected to have a wider band tail. The Urbach energy is not to be confused with the activation energy since activation energy describes the disorder associated with one band, not both bands.
By re-arranging the Urbach equation and comparing with the straight-line equation, the Urbach energy is the inverse slope, if lnα is plotted along the y-axis and hv along the x-axis.
In the following video tutorial, I have explained the Urbach energy with diagrams and calculated its value from the UV-Vis absorbance data using OriginLab. Link of the video is
https://youtu.be/Klh3LwUgZoU
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