What is the derivation of built in voltage for a P-n junction?

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SUMMARY

The built-in voltage of a P-N junction can be derived using the band diagram and the concept of Fermi energy being constant throughout the device. Additionally, it can be mathematically demonstrated by equating the drift current to the diffusion current across the junction. This derivation involves understanding the energy band structure and applying the principles of semiconductor physics. For a comprehensive mathematical proof, refer to the relevant sections of educational videos or textbooks that cover semiconductor theory in detail.

PREREQUISITES
  • Understanding of semiconductor physics
  • Familiarity with P-N junction characteristics
  • Knowledge of drift and diffusion currents
  • Basic mathematical skills for derivation
NEXT STEPS
  • Study the derivation of built-in voltage in P-N junctions using semiconductor textbooks
  • Learn about the energy band diagrams of semiconductors
  • Explore the mathematical models for drift and diffusion currents
  • Watch educational videos on semiconductor physics for visual explanations
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Students of electrical engineering, semiconductor physicists, and anyone seeking to understand the principles of P-N junctions and their voltage characteristics.

mertcan
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hi, I am looking a derivation of built in voltage, but the only thing I could find is a statement: built in voltage can be derived from band diagram with the Fermi energy constant throughout the device, or from equating the drift current through the junction equal to the diffusion current. I need some mathematical demonstrations, I tried what the statement had said, but I really lack the mathematical demonstrations for derivation. Could you provide me with proof of it ? Thanks in advance...
 
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Perhaps see second half of this vid..
 
Most likely this can only be answered by an "old timer". I am making measurements on an uA709 op amp (metal can). I would like to calculate the frequency rolloff curves (I can measure them). I assume the compensation is via the miller effect. To do the calculations I would need to know the gain of the transistors and the effective resistance seen at the compensation terminals, not including the values I put there. Anyone know those values?

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