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Analytic optical-constant model derived from Tauc-Lorentz and Urbach tail
Optics Express
|December 14, 2016
Summary
A new, analytic Tauc-Lorentz model improves dielectric constant calculations for amorphous semiconductors. This modified model addresses mathematical shortcomings and extends material characterization to zero energy.
Area of Science:
- Materials Science
- Condensed Matter Physics
- Optoelectronics
Background:
- The Tauc-Lorentz model is widely used for dielectric constants in amorphous semiconductors.
- This model has analytical limitations and mathematical shortcomings.
Purpose of the Study:
- To present a modified, self-consistent Tauc-Lorentz model that is fully analytic.
- To overcome the mathematical limitations of the existing Tauc-Lorentz model.
- To enable optical-constant characterization down to zero energy.
Main Methods:
- Developed a modified self-consistent model integrating [E'-(E + ia)]-1 functions.
- Utilized the Tauc-Lorentz ε2 expression as a weight function.
- Created an analytic extension to incorporate the Urbach tail.
Main Results:
- The new model is fully analytic and meets optical constant mathematical requirements.
- It differs from the Tauc-Lorentz model significantly at energies near or below the bandgap.
- Successfully tested on SiC and Si3N4 optical constants, extending characterization to zero energy.
Conclusions:
- The modified Tauc-Lorentz model offers improved analytical properties.
- This new model provides accurate optical constant characterization for amorphous semiconductors.
- Enables extended material characterization down to zero energy, including Urbach tail effects.
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