What is physical meaning of activation energy? I know that the activation energy can be estimated by Arrhenius equation. It has been observed that the activation energy is usually less than the band gap in semiconductors, then how these thermally activated carriers can contribute to conductivity?
Well, if you see any intrinsic semiconductor, then effective chemical potential energy (Fermi energy) lies exactly in the middle of the band-gap. This (Fermi energy) is average value of energy of electron in that semiconductor available at the Fermi-level. So if you want to excite that electron into conduction band ( only then you will get conducting electron and thus conductivity), then you must supply the energy exactly equal to the difference of the energy between conduction band and present Fermi energy level (which is equal to (E_c - (E_f)/2, where E_c is the conduction band energy level and E_f is the Fermi energy level , which lies in the middle of the band gap ). The probability that the thermal energy will able to excite this electron int conduction band is exp(-( E_c- E_f)/KT). You has called it as Arrhenius equation in your question . Of-course this term will be multiplied the density of states present at the Fermi energy level, and frequency factor to get the Rate of transition from Fermi energy into conduction band. In extrinsic semiconductor (where Fermi energy is very close but still below the conduction band for N-type and Fermi energy above the valance band for p-type material), analysis will be the same, but keep in mind that electron and hole energy scale vary opposite to each other.
In semiconductors, activation energy is the energy that is needed by a carrier to overcome a potential barrier in order to complete a process, such as conduction or a reaction. For conduction by electrons, the activation energy is the difference between the Fermi level and the conduction band.
However, I suggest to follow the link below, which has nice scientific discussions on activation energy of semiconductors and conductors. Read the answers of researchers.
https://www.researchgate.net/post/What_is_the_physical_meaning_of_the_negative_activation_energy_for_the_electrical_conductivity
Vk Singh , your problem is that you think at 0 Kelvin, where maximum energy of electron is equal to the Valance band maximum energy. However, at any non zero Kelvin, there are few electrons whose energy is greater than the valance band maximum energy. There are small chance that few electron also exist in conduction band minima (but for current you need to give them direction using electric field generated by battery). This is one of the precise region why Fermi energy fall in the middle of the band-gap. So, although electron exist spatially below the conduction band ( you said it valance band, but they have higher energy than the valance band maxima energy due to temperature), only small energy (E_c -E_f) less than the band-gap energy required to promote them into conduction band.
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