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Question
When an electron goes from the valence band to the conduction band in silicon, its energy is increased by 1.1 eV. The average energy exchanged in a thermal collision is of the order of kT which is only 0.026 eV at room temperature. How is a thermal collision able to take some to the electrons from the valence band to the conduction band?
Solution
Fermi level: it is the energy level occupied by the highest energy electron.
In an extrinsic semiconductor for example in n-type semiconductor, fermi level lies close to the conduction band so it needs a very small amount of energy to excite the electron from fermi level to conduction band. This energy is comparable to the thermal excitation energy. So even at room temperature,these semiconductors can conduct.For a p-type semiconductor, fermi level lies close to valence bane because here conduction takes place majorly via holes.So by the thermal excitation,a bond is broken and an electron hole pair is created.Out of this,hole comes to the valence band for conduction or equivalently an electron goes to the conduction band. In an intrinsic semiconductor, no impurity is doped so fermi level lies at the centre of band gap. Here only few electrons get sufficient energy via repeated thermal collisions to jump from the fermi level to the conduction band.Hence the conductivity of intrinsic semiconductor is less as compared to extrinsic semiconductor.
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