Difference between Intrinsic & Extrinsic Behaviour of a Semiconductor

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Intrinsic and extrinsic behavior in semiconductors is closely related to the position of the Fermi level, which varies with donor and acceptor concentrations at a given temperature. Intrinsic behavior occurs when the Fermi level is near the midpoint between the valence and conduction bands, while extrinsic behavior is characterized by the Fermi level being closer to either band. Determining the temperature at which a semiconductor like silicon reverts to intrinsic behavior requires understanding the intrinsic carrier concentration and its temperature dependence, which is not provided in the discussion. The challenge lies in finding a suitable equation that relates these factors, as only approximate expressions for the chemical potential are available. Further research into the temperature variation of intrinsic carrier concentration is necessary to resolve this issue.
Claude Bile
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1. What is the difference between extrinsic and intrinsic behaviour in a semiconductor? How can you determine what temperature a semiconductor material such as Silicon will revert to intrinsic behaviour, given the donor, intrinsic carrier concentration and the energy gap?

- I am thinking that intrinsic/extrinsic behaviour is related to the Fermi level and the donor and acceptor concentrations at a temperature, T. Intrinsic behaviour has the Fermi level close to midway between the valence and conduction bands, with nearly equal concentrations of donor and acceptor ions. Extrinsic behaviour has the Fermi level close to the conduction band (or valence band). I am looking for confirmation as to whether this is correct, and if not, where I am going wrong.

- I do not have an equation that gives a direct answer to this question. The best I have managed is gaining approximate expressions for the chemical potential for both intrinsic and extrinsic behaviour and showing at which temperature they are both valid. My main difficulty is that we are only given the intrinsic carrier concentration at room temperature and are not told how it varies with temperature. Is there an equation that gives this also, with only the information given above as stated in the 1st paragraph?
 
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