Derivation of Carrier Concentration (ni)

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SUMMARY

The discussion centers on deriving the carrier concentration equation (ni) in semiconductor physics. The user seeks assistance in solving a specific integral related to ni, which involves a variable change where X = (E - [E]/C)/kT. The user attempted integration by parts but was unsuccessful. The integral is crucial for understanding carrier concentration in semiconductors, particularly in the context of thermal energy and energy levels.

PREREQUISITES
  • Understanding of semiconductor physics
  • Familiarity with integration techniques, specifically integration by parts
  • Knowledge of thermal energy concepts (kT)
  • Basic grasp of energy band theory in solids
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  • Study the derivation of the carrier concentration equation ni in semiconductor physics
  • Learn advanced integration techniques, focusing on variable substitution methods
  • Explore the relationship between energy levels and carrier concentration in semiconductors
  • Review the principles of thermal equilibrium in semiconductor materials
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m_keown2000
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< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color]

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

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