Thermal energy is approximately 0.025 eV at room temperature. Electrons must be raised to conduction band for conduction to take place. How is it possible by this less energy of room temperature to raise the electrons across the band gap of 1 eV ?
There are serious errors in the previous answers.
Free carriers are generated by both the intrinsic and the extrinsic process. Carrier generation by doping is the extrinsic process. The intrinsic carrier generation can happen in all semiconductors - both pure and impure, and all intrinsic carrier generation mechanisms create e-h pairs.
Intrinsic carrier generation can happen by the thermal process, by the photon process, or by the electric field process. The photon process is the simplest to visualise - if the photon energy is larger than the band-gap energy, then each such photon creates an electron-hole pair, both of which are free carriers. The photo-electron is in the conduction band, and the photo-hole is in the valence band.
In the case of the thermal generation, the intrinsic carrier density - ni - is very strongly dependent upon the thermal energy kT: ni = Constant X exp(-EG/2kT), where EG is the band-gap. In Si, at 300 K, the intrinsic carrier density is around 1.6 X 1010/cm3, which is many orders of magnitude smaller than the atomic density in Si.
The physical picture is the following. The world of electronics is probabilistic; no electron probability is 0, unless the temperature is 0 K and/or the energy is infinite. Therefore, at any temperature other than 0 K, there is a finite probability of an electron being excited to a higher energy eigenstate, unless that eigenstate is at infinity.
Hi Raajeshwar,
Your don't take the electrons from the valence band to the conduction band. All semiconductors, if they are really pure and crystalline (i/e without defects) are insulators. it is only when u dope other elements, one gets free carriers. For example, in Gallium Nitride (GaN) the bandgap is 3.4 eV, that means u have to give that much energy to take an electron from the full valence band to the empty conduction band.
However, when silicon(Si) is doped into GaN, Si has a oxidation state of +4, so it makes energy levels just below the conduction band. Such a band is also known as an impurity band. The energy difference from these impurity band to the conduction band is usually meV. This much energy is possible at room temperature, so that's why on doping, the extra electron from the impurity band can go to the conduction band. If the band structure of the conduction band is parabolic, then these free electrons obey the free electron equation E = h2k2/2me* .. (where me* is the effective mass)...
The same story happens when u doped Mg (oxidation state +2) into GaN. It will make an impurity level or band, just above the valence band, so the free carriers, in this case will then travel through the valence band.
Hello Raajeshwar and Paritosh,
there are more aspects to consider here:
For one, at any temperature some electrons will gain enough energy to rise into the conduction band. Remember that temperature is just a convenient number to describe the distribution of energy between particles at equilibrium, and that this distribution has a finite value for all energies.
On a more practical note, no existing crystal is truly pure and without defects, and this will also increase the carrier concentration. To give an example, intrinsic silicon has a carrier concentration of about 1010 electrons / cm3 at 300 K.
There are serious errors in the previous answers.
Free carriers are generated by both the intrinsic and the extrinsic process. Carrier generation by doping is the extrinsic process. The intrinsic carrier generation can happen in all semiconductors - both pure and impure, and all intrinsic carrier generation mechanisms create e-h pairs.
Intrinsic carrier generation can happen by the thermal process, by the photon process, or by the electric field process. The photon process is the simplest to visualise - if the photon energy is larger than the band-gap energy, then each such photon creates an electron-hole pair, both of which are free carriers. The photo-electron is in the conduction band, and the photo-hole is in the valence band.
In the case of the thermal generation, the intrinsic carrier density - ni - is very strongly dependent upon the thermal energy kT: ni = Constant X exp(-EG/2kT), where EG is the band-gap. In Si, at 300 K, the intrinsic carrier density is around 1.6 X 1010/cm3, which is many orders of magnitude smaller than the atomic density in Si.
The physical picture is the following. The world of electronics is probabilistic; no electron probability is 0, unless the temperature is 0 K and/or the energy is infinite. Therefore, at any temperature other than 0 K, there is a finite probability of an electron being excited to a higher energy eigenstate, unless that eigenstate is at infinity.
Thermal energy 0.025 eV is average energy,calculated from F-D statistics.consider,in VB many electrons hit an electron till its energy is equal to 1.1 eV band gap of silicon and send it to CB.now as mentioned in above answers CB density 1010 /cm-3 is very small as compare to atomic density 1023 /cm-3. So, there are enough no of electrons who can transfer energy to these 1010 electron which will jump to CB ultimately.Actually no is more no than 1010. because its an continuous process of excitation and relaxation otherwise CB density will increase with time.
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