Simple Intrinsic Semiconductor Question

In summary, the equation for intrinsic carrier concentration (ni) is proportional to the exponential of negative band gap energy (Eg) divided by 2 times Boltzmann's constant (k) and temperature (T) in Kelvins. This factor of 2 represents the two charge carriers (hole and electron) present in the material. The reason for using Eg/2 instead of 2Eg in the equation is based on the derivation of the formula.
  • #1
bartersnarter
13
0

Homework Statement


Can anyone explained to me the factor of 2 in the equation for the intrinsic carrier concentration?

Homework Equations


ni is proportional to exp(-Eg/2kT)
where ni is the intrinsic carrier concentration, Eg is the band gap energy, k is Boltzmann's constant, and T is temperature in Kelvins.

The Attempt at a Solution


I understand that there are two charge carriers (a hole in the valence band and a free electron in the conduction band), but I don't understand why it is Eg/2 and not 2Eg.
 
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  • #2
Why would you think that it should be 2Eg?
Have you ever looked-up how the formula for intrinsic concentration is obtained?
 

Related to Simple Intrinsic Semiconductor Question

What is an intrinsic semiconductor?

An intrinsic semiconductor is a type of material that has electrical properties similar to that of an insulator at low temperatures, but can conduct electricity at higher temperatures due to the presence of impurities or defects in its crystal structure.

What is the difference between intrinsic and extrinsic semiconductors?

Intrinsic semiconductors are pure materials with no intentional impurities, while extrinsic semiconductors have been intentionally doped with impurities to alter their electrical properties.

How does temperature affect the conductivity of intrinsic semiconductors?

The conductivity of intrinsic semiconductors increases with temperature due to the increased thermal energy causing more electrons to break free from their bonds and become mobile charge carriers.

What are the two types of carriers in intrinsic semiconductors?

The two types of carriers in intrinsic semiconductors are electrons and holes. Electrons are negatively charged and flow from the negative to positive terminal, while holes are positively charged and flow in the opposite direction.

What is the band gap in intrinsic semiconductors?

The band gap in intrinsic semiconductors is the energy difference between the valence band (where electrons are bound to atoms) and the conduction band (where electrons are free to move and conduct electricity). This energy gap determines the material's conductivity and can be altered by doping with impurities.

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