As per studies, it is noticed that as the Energy Band Gap decreases, the electrical conductivity increases. But is there any Mathematical Form available to know.....
How i can calculate the Electrical Conductivity from Energy Band Gap?
Dear M. Fazal-Ur-Rehman,
As you stated, the energy band gap of a solid material is directly linked to its conductivity such as insulators, semiconductors and conductors. How does the mathematical link between two properties of a material, depend on its chemical elements and structure. For each individual material, the mathmetical relationship between its energy band gap and conductivity are very different.
There is a discussion a while ago from research gate forum for your reference.
Hope it helps.
https://www.researchgate.net/post/What_is_the_relationship_between_the_energy_band_gap_and_conductivity
For a gapped material, the signature of intrinsic semiconductivity is a linear decrease in ln(G) with reciprocal temperature (1/T). The slope of the line is proportional to the energy required to generate charge carriers, (typically populate the conduction band). There are lots of sources describing this effect. For example:
https://fog.ccsf.edu/~wkaufmyn/ENGN45/Course%20Handouts/15_ElectricalProps/06_TemperatureConductivitySemiConductor.html
Measurement of the conductance for a range of temperatures can therefore be used to obtain the band gap. One plots ln(G) versus (1/T) and extracts Eg from the slope.
If the material is doped, has multiple types of charge carriers, or lacks a band gap, the thermal dependence of conductivity will deviate from this zero-order picture. Oxide powders can display strikingly non-linear ln(G) versus (1/T) behavior. An example may be found here:
Article A dual-carrier adsorbate-modulated surface conductance model...
Conductivity depends on both the carrier density (n) and mobility (mu). n can be controlled by temperature, doping, and other means. Thus, it is not very meaningful to discuss its bandgap dependence, unless one is interested in the intrinsic carrier density. It is more meaningful to ask how mu could depend on the bandgap. For the materials belong to to the same groups (e.g., GaAs vs. InAs), typically the material with a smaller bandgap tends to have a smaller effective mass, which is favorable for having a larger mu. However, mu also strongly depends on the electron-phonon coupling. Therefore, simple relation between mu and bandgap does not exist theoretically. In reality, the dependence is even less obvious, because what you normally see are the best reported values, which might not reflect the intrinsic potential.
Dear Fazal,
I derive here a relation between the energy gap and electric conductivity (see eq.24).
Preprint Absorption coefficient and optical conductivity: a quantum perspective
Dear Fazal Ur Rehman,
I believe that the following article will answer your question.
https://iopscience.iop.org/article/10.1088/1674-4926/34/11/113001/pdf
Dear Fazal Ur Rehman ,
The conductivity of as semiconductor material is given by
sigma= q un n0+ qup p0,
where mu is the mobility n0 and p0 are the electron concentration and hole concentration at thermal equilibrium. According to doping if one is majority the other will be minority and its conductivity is negligible. This is because of the mass action law p0 n0=ni^2.
So if the material is doped its conductivity will be controlled by doping and this is the strength of the semiconductors.
However if the material is intrinsic p0=n0=ni and the conductivity will be determined by the energy gap since ni^2 is proportional to exp - Eg/kT and specifically:
ni^2= Nc Nv exp - Eg/kT
where Nc, and Nv are the effective density of sates in the conduction band and valence band respectively.
So, as Eg increases the intrinsic material conductivity will be appreciably reduced.
For more information please refer to the book:Book Electronic devices with physical insight
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