At absolute zero temperature conduction band is empty but at 300K there are large number of free electrons are available at the conduction band.My question is how the electrons in valence band move to conduction band gaining just the thermal energy? As far as i know thermal energy at room temperature nearly 26 mev which very less than the band gap energy suppose for Si it is 1.1ev.
If we're talking about Si, there aren't many electrons in the conduction band, only about 1010 cm-3 (for ideally-clean Si). 26 meV is indeed the average phonon energy, but as you know, not all phonons are at the average energy. The intrinsic carrier density for semiconductor can be calculated using:
n=p=(NV⋅NC)1/2 exp(-Eg/2kBT)
The term -Eg/2kBT is quite a large negarive exponent, meaning only a small fraction of the available CB,VB edge states would be populated at room temperature.
If you take a look at smaller band gaps (Ge, InAs) you can see that a few 100s of meV can translate to orders of magnitude higher intrinsic carriers, whereas slightly larger gaps (GaAs) have an opposite effect.
This is answered in any upper level textbook on materials science. The chapter on electrical properties of semiconductors always provides an explanation of the process of promotion of free electrons via thermal excitation. The end result is an equation of the form
\rho = \rho_o \exp (-\Delta E_g / 2 k_B T )
where \rho is the number density of charge carries and \Delta E_g is the gap energy.
If we're talking about Si, there aren't many electrons in the conduction band, only about 1010 cm-3 (for ideally-clean Si). 26 meV is indeed the average phonon energy, but as you know, not all phonons are at the average energy. The intrinsic carrier density for semiconductor can be calculated using:
n=p=(NV⋅NC)1/2 exp(-Eg/2kBT)
The term -Eg/2kBT is quite a large negarive exponent, meaning only a small fraction of the available CB,VB edge states would be populated at room temperature.
If you take a look at smaller band gaps (Ge, InAs) you can see that a few 100s of meV can translate to orders of magnitude higher intrinsic carriers, whereas slightly larger gaps (GaAs) have an opposite effect.
Dear colleague Subhasis Das, Have a nice time and good day
According to Maxwell–Boltzmann distribution, A particle speed probability distribution indicates which speeds are more likely: a particle will have a speed selected randomly from the distribution, and is more likely to be within one range of speeds than another.
According to Maxwell–Boltzmann distribution many electrons may have high velocity consequently high energy enables them to cross the valence band conduction band.
i wish that may be useful and can help you
@A. Eldenglawey
Thanks for your response..
But as far as i know that electrons follow Fermi-Dirac distribution.How can you associate Maxwell-Boltzmann distribution in this present scenario ?
Electron as a particle follow the statistical distribution. and you can compare the two distributions for velocity of electrons.
> as far as i know that electrons follow Fermi-Dirac distribution ...
Yes. However, when convolved with the population distribution to give the number density of states (NDOS), you end with a Maxwell-Boltzmann distribution. This illustration shows the developments for metals and intrinsic semiconductors.
Dear Subhasis,
I saw your message today. Also saw all the answers given by respective professors.
I can say you one thing related to this, i.e., if you want to get a general idea, to have a visualization in your mind regarding this, just think that it is a statistical case. Where some of the electrons transfer their energy to some of the other electrons, and hence some of them reach in the conduction band. The number of electrons leave the VB is not equal to the number of electrons reached at CB. some of them transfer the energy to others and come back.
An good analogy will be, if one person is shouting, and it is audible up to 200 meters, then if 20 people will shout like him at once from that particular place, then definitely it will audible to 400-500 meters. :)
Best regards
Madhusudan Mishra
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