Concentrations of electrons in intrinsic semi-conductor

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In summary, the formula for abovie is given as n t^3/2 exp(Eg/2kBT), where n is proportional to T^{3/2} \exp(Eg/(2k_BT)). This can be seen from the dimensions of each side of the equation, with n representing density and the RHS representing temperature. The T^(3/2) factor is the temperature dependent part of the equation for the effective density of states referred to the conduction band edge.
  • #1
jendrix
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Hi, I've just started using the formula for the abovie which is given as:

n t^3/2 exp(Eg/2kBT)

however instead of n= I think the sign is n is proportional, like this ∞

I was wondering which would be correct?

Thanks
 
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  • #2
jendrix said:
Hi, I've just started using the formula for the abovie which is given as:

n t^3/2 exp(Eg/2kBT)

however instead of n= I think the sign is n is proportional, like this ∞

I was wondering which would be correct?

Thanks

Yes it's definitely proportional to, not equals. That is, [itex]n \propto T^{3/2} \exp(Eg/(2k_BT))[/itex].

You can "see" this easily enough by looking at the dimensions (units) of each side of the equation. The term "n" is a density, and therefore [itex]m^{-3}[/itex] (or [itex]cm^{-3}[/itex] etc), whereas the unit on the RHS is T^1.5.

The "T^(3/2)" factor is merely the temperature dependent part of the equation for the "effective density of states referred to the conduction band edge", if you want to google that.
 
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I see now, thanks :)
 

1. What is an intrinsic semiconductor?

An intrinsic semiconductor is a pure semiconductor material that is not intentionally doped with any impurities. This means that it has an equal number of electrons and holes, resulting in a balanced concentration of both charge carriers.

2. How are concentrations of electrons in intrinsic semiconductors determined?

The concentration of electrons in an intrinsic semiconductor is determined by the properties of the material, such as its bandgap energy and temperature. It can also be affected by external factors such as light or electric fields.

3. What factors affect the concentration of electrons in an intrinsic semiconductor?

The concentration of electrons in an intrinsic semiconductor can be affected by temperature, impurities, and the presence of other charge carriers (such as holes). It can also be influenced by external factors such as light or electric fields.

4. How do concentrations of electrons in intrinsic semiconductors impact their electrical conductivity?

The concentration of electrons in an intrinsic semiconductor is directly related to its electrical conductivity. An increase in electron concentration leads to a higher conductivity, while a decrease in concentration results in lower conductivity. This is because electrons are the primary charge carriers in semiconductors.

5. How can the concentration of electrons in an intrinsic semiconductor be controlled?

The concentration of electrons in an intrinsic semiconductor can be controlled by varying the material's temperature, adding impurities through a process called doping, or applying external stimuli such as light or electric fields. These methods can increase or decrease the number of electrons in the material, thus altering its conductivity and other properties.

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