By plotting the ln(alpha) versus energy, you will get a term C+E/Eurbach, so it is the inverse of the slope of that curve. What it tells you is essentially the energy range for which the absorption coefficient decays to 1/e of its value for an ideal semiconductor above band gap. For an ideal semiconductor the Urbach energy is zero so the slope is infinite. The higher the Urbach energy, the wider is the region below band gap with a significant amount of tail absorbing states.
the reciprocal of the slope of the linear part of the mentioned curve.
the linear part is found at the lower photon energy region.
Dear Ayan
I agree with Ashraf. Please refer the diagram attached with this for your ready reference.
By plotting the ln(alpha) versus energy, you will get a term C+E/Eurbach, so it is the inverse of the slope of that curve. What it tells you is essentially the energy range for which the absorption coefficient decays to 1/e of its value for an ideal semiconductor above band gap. For an ideal semiconductor the Urbach energy is zero so the slope is infinite. The higher the Urbach energy, the wider is the region below band gap with a significant amount of tail absorbing states.
I recoomend you the following work which is attached as well as my old paper published in 1971 (in Russian) : https://www.researchgate.net/publication/234035038_Experimental_relationships_associated_with_Urbach%27s_rule_for_excitons_in_AIIBYi_semiconductors?ev=prf_pub
Article Experimental relationships associated with Urbach's rule for...
In the case you are dealing with absorption coefficient (alpha) data of amorphous semiconductors. Take the logarithm of alpha vs the photon energy. Identify the linear region, it is usually below the fundamental absorption region, and then fit a line. The slope is known as the Urbach slope. The inverse of the slope is the Urbach energy. It is a measure of the width of tail states into the forbidden gap.
Crystalline materials also exhibit tail states which are translated in an exponential tail absorption in alpha. Although, in this case the nature of tail states comes from thermal fluctuations and are much smaller than the observed in amorphous semiconductors the empirical Urbach rule is still applicable.
The Urbach rule can be written in the following manner:
a = aF Exp[B*(E-EF)]
(EF,aF) is the Urbach focus.
B is the Urbach slope
E is the photon energy
a is the absorption coefficient.
You can find more details in:
https://books.google.com.pe/books?id=ElyQ_wV0v0AC&printsec=frontcover&dq=Kazuo+morigaki&hl=es-419&sa=X&ved=0ahUKEwjus4LFycPLAhVG5CYKHRHxDr8Q6AEIGzAA#v=onepage&q=Kazuo%20morigaki&f=false
https://books.google.com.pe/books/about/Hydrogenated_Amorphous_Silicon.html?id=zQMwsMt4VmoC&redir_esc=y
http://link.aip.org/link/APPLAB/v72/i11/p1332/s1&Agg=doi
http://link.aip.org/link/APPLAB/v84/i4/p523/s1&Agg=doi
http://www.journals.cambridge.org/abstract_S1946427413007537
or in the forthcoming article in J. Phys. D: Appl. Phys.
The Urbach focus and optical properties of amorphous hydrogenated SiC thin films
J A Guerra, J R Angulo, S Gomez, J Llamoza, L M Montanez, A Tejada, J A Toefflinger, A Winnacker, R Weingaertner
Accepted: 16 February 2016
Dear Dr. Ayan Mukherjee
Have a nice time and good day
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...
Good morning! How is calculated slope of the straight line of plotting ln (α) against the incident photon energy (hν)?
in origin software, which is used to plot the graphs, click on graphs lines, then , there is an Analysis tab->Fitting->linear fit->open dialog-> press ok ok . you will get directly the slope values corresponding the ploted line.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science