Semiconductor temperature

[demLara]

Hello
I have got a question and i don't know the answer. Please help me.
I have a n doped semiconductor. How does the number of conduction electrons depends on temperature and compare the situation to an intrinsic semiconductor?
Do i look at the intrinsic density, because when it is n doped than n is much bigger than p and the multiplication will be dominated by n. Then i would know the temperature dependence for intrinsic T^3/2 *exp ?
Thanks in advance

 

[Gordianus]

The answer is rather long. I'd suggest reading John McKelvey's "Solid State and Semiconductor Physics". He fully develops how electron and hole concentration vary with temperature.

 

[Gandes]

Try to read about vacuum diode, it uses heat depend transfer. Look also at semiconductor diode to have more reliable info.

 

[Henryk]

I can offer you a short answer.
There are three temperature regions. At very low temperatures, that is, k_BT <is less than ionization energy of the donor state, the carriers are frozen out - number of electrons in the conduction band is vary small and the material is essentially an insulator. This occurs at cryogenic temperatures.
The second region is when the k_BT is larger than ionization energy of the donor states but much less than energy gap. In this region, all the donor states are ionized and the number of electrons is essentially independent of the temperature.
The third regions is when the temperature is large enough so that the intrinsic carrier concentration becomes equal or greater than the concentration of donors.
In that region, the semiconductor is pretty much intrinsic with the same number of electrons and holes.