Derivation of Carrier Concentration (ni)

In summary, the derivation of carrier concentration, also known as ni, is a process used to calculate the number of free charge carriers present in a semiconductor material at thermal equilibrium. It takes into account the material's bandgap energy, temperature, and intrinsic properties. This calculation is important in understanding the electrical properties of a material and in designing electronic devices. The formula for calculating carrier concentration takes into consideration the effective densities of states, bandgap energy, temperature, and intrinsic properties. Temperature has a direct impact on carrier concentration, increasing it as temperature increases. Assumptions made in this derivation include thermal equilibrium, no impurities, and a perfect crystal structure.
  • #1
m_keown2000
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< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

I am following a lecture on carrier concentration and I got to the point where the instructor said that for homework, derive the carrier concentration equation ni, which equals:https://www.physicsforums.com/attachments/81076

To derive ni you need to compute the following integral which I am having trouble solving:

Snapshot1.jpg


where:
Snapshot2.jpg


I tried Integration by parts and no luck. Any help would be greatly appreciated.
 

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  • #2
90make the variable change assume X = (E-[E][/C]/kT)
 

What is the derivation of carrier concentration?

The derivation of carrier concentration, also known as ni, is a process used to calculate the number of free charge carriers (electrons or holes) present in a semiconductor material at thermal equilibrium. It takes into account the material's bandgap energy, temperature, and intrinsic properties.

Why is the derivation of carrier concentration important?

The derivation of carrier concentration is important because it helps us understand the electrical properties of a semiconductor material. It is also crucial in designing and optimizing electronic devices, such as transistors and diodes.

What is the formula for calculating carrier concentration?

The formula for calculating carrier concentration is ni = (Nc * Nv)1/2 * e-Eg /2kBT, where ni is the intrinsic carrier concentration, Nc and Nv are the effective densities of states in the conduction and valence bands respectively, Eg is the bandgap energy, kB is the Boltzmann constant, and T is the temperature in Kelvin.

How does temperature affect carrier concentration?

Temperature has a direct impact on carrier concentration, as shown in the formula mentioned above. As temperature increases, the intrinsic carrier concentration also increases. This is due to the fact that at higher temperatures, more electrons in the valence band gain enough thermal energy to jump to the conduction band, creating more free charge carriers.

Are there any assumptions made in the derivation of carrier concentration?

Yes, there are some assumptions made in the derivation of carrier concentration. These include assuming that the material is in thermal equilibrium, that the material is undoped (no impurities), and that the material is a perfect crystal (no defects or imperfections).

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