Please give some suggestion to calculate Urbach Energy Tail. I am wanting to know the Characterization tool.
Dear Abdul,
A similar question to yours was posted earlier in ReserachGate. Here are the links. Maybe you'll find the answer to your question.
https://www.researchgate.net/post/How_can_I_calculate_Urbach_Energy_from_lnalpha_vs_photon_energy_curve2
https://www.researchgate.net/post/How_can_we_calculate_Urbach_energy_from_optical_spectra
https://www.researchgate.net/post/What_is_Urbach_energy_urbach_tail_and_when_it_is_necessary_to_calculate_it
https://www.researchgate.net/post/How_do_you_calculate_Urbach_energy
With my best regards
Prof. Bachir ACHOUR
Dear colleague Abdul Moyez
Have a nice time and good day
Herein fined how to calculate Urbach tail or Urbach energy.
Due to the format of Equation please check the Equation No. and see in the attach file.
The Urbach tail
The exponential tail occurring at the absorption of most amorphous semiconductors, could be interpreted as arising from transition between localized states, if the density of states in the deep tails varies exponentially with energy, such an edge is expected Davis et al [*] E. A. Davis and N. F. Mott, Phil. Mag. 22 (1970) 903.] gave the following agreements as evidence against such an interpretation.
How to calculate Absorption and extinction coefficient?
T, R and d are used to calculate the absorption coefficient, α
according to [[**]J. Tauc (Ed.). Amorphous and Liquid Semiconductors, Plenum, New York, 1976]. [**]A. El-Denglawey, M. Dongol, M.M El-Nahass, J. Lumin 130 (2010) 801.]:
Equation No.………………………….…….…… (1)
α is given by:
Equation No...………………………………… (2)
The calculated α is included within high absorption region (α ≥ 104 (cm)-1).
Extinction coefficient, k is calculated by using:
Equation No.……………………………….…. (3)
How to calculate The Urbach tail?
An absorption edge of semiconductors corresponds to the threshold of charge transition between the highest nearly filled band and the lowest nearly empty band. According to inter-band absorption theory, the film’s Urbach tail can be calculated according to [[**]J. Tauc (Ed.). Amorphous and Liquid Semiconductors, Plenum, New York, 1976].
(1) The empirical relation for this tail can be represented as :
α = α0 exp {hν/Ec}
Ln(α) = Ln(α0) + hν/Ec
on Y axes put Ln(α)
on X-axes put (hν)
Y = c + m x
C is the intercept = Ln(α0)
M is the slope = 1/ Ec
; α0 is a constant, and Ec is The Urbach tail or band tail width.
(2) Urbach edges occur in many amorphous and crystalline semiconductors
within rang of α less than 10^(-4)
(3) The temperature dependence of the slopes frequently follows the above relation at least at high temperature.
The observed exponential edges suggest that the breading is dominated by the random internal electric fields due to either to the lack of long range order or the presence of defects. [*] E. A. Davis and N. F. Mott, Phil. Mag. 22 (1970) 903.
Ec can be calculated from the plot of ln(α) ) vs. (hν) for the films represent a straight line, indicating that the absorption threshold characteristic an exponential absorption edge. The Urbach tail increases as the increasing of disorder and hence the localized states, which cause increasing of band tailing. The range of calculation is 1-2 eV of hν.
Dear Dr. Abdul Moyez
Peace be upon you
Along the absorption coefficient curve and near the optical band edge there is an exponential part called Urbach tail. This exponential tail appears in the low crystalline, poor crystalline, the disordered and amorphous materials because these materials have localized states which extended in the band gap. In the low photon energy range, the spectral dependence of the absorption coefficient (α) and photon energy (hν) is known as Urbach empirical rule, which is given by the following equation:
α = αo exp (hν/EU)
where αo is a constant and EU denotes the energy of the band tail or sometimes called Urbach energy, which is weakly dependent upon temperature and is often interpreted as the width of the band tail due to localized states in the normally band gap that is associated with the disordered or low crystalline materials. Taking the logarithm of the two sides of the last equation, hence one can get a straight line equation. It is given as follows:
ln α = ln αo + (hν/EU)
Therefore, the band tail energy or Urbach energy (EU) can be obtained from the slope of the straight line of plotting ln (α) against the incident photon energy (hν).
For more details, you can go to these links:
https://www.researchgate.net/publication/281495242_Influence_of_composition_on_optical_and_dispersion_parameters_of_thermally_evaporated_non-crystalline_Cd50_S50-xSex_thin_films?ev=prf_pub
https://www.researchgate.net/publication/283338024_Effect_of_Se_addition_on_optical_and_electrical_properties_of_chalcogenide_CdSSe_thin_films
Good luck and my best wishes
Article Influence of composition on optical and dispersion parameter...
Article Effect of Se addition on optical and electrical properties o...
Which characterization is needed to calculate Urbach Energy? I have UV-Vis data, Can I convert it to calculate Urbach Energy?
Dear Abdul Moyez
You need to the absorbance or transmittance data of UV-vis spectroscopy. Just if you have the spectral variation of the absorption coefficient (alpha) versus the incident wave length, then calculating
ln α = ln αo + (hν/EU)
Then plotting [ln α] Vs (hν) you get st. line of slope equals 1/EU .
Even If you don't have alpha, you can determine it from the transmission spectra.
Alpha = 1/d * ln (1/T),
where (d) is the sample thickness and (T) is the transmittance. Moreover, the optical energy gap (Eg), the extinction coefficient (k) and many other parameters can be obtained from (Alpha) measurements. .
Good luck
Abdul Moyez 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
- Badges
- Science topic
- Similar topics
- Physics
- Condensed Matter Physics
- Solid State Physics
- PEAKS