Potential Barrier for different types of junctions

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Discussion Overview

The discussion revolves around calculating the potential barrier in different types of junctions, specifically metal-semiconductor, metal-metal, and p-n junctions. Participants explore various methods and formulas for determining the potential barrier, including the use of work functions and band energy considerations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about calculating the potential barrier using work functions for different junction types.
  • Another participant suggests that the barrier shape is typically modeled with self-consistent calculations, which depend on the specific structures involved.
  • A participant mentions that the height of the barrier can sometimes be derived from band mismatches.
  • There is a question about whether the potential barrier in a p-n junction can be determined by the difference in Fermi energy between p-type and n-type materials.
  • One participant advises sketching band profiles to better understand the formulas related to potential barriers and notes that band bending occurs at the junction.
  • A later reply emphasizes that calculating the potential barrier generally involves using Poisson's equation for band bending and Schrödinger's equation for charge distribution.

Areas of Agreement / Disagreement

Participants express various methods for calculating potential barriers, but there is no consensus on a single approach or formula. The discussion remains unresolved regarding the best method to apply in different junction scenarios.

Contextual Notes

Participants reference multiple formulas and methods without clarifying specific assumptions or conditions under which these methods apply. There is also a lack of consensus on the educational context or specific junction types being discussed.

Joseph8022
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Hi all,
How I can calculate the Potential Barrier when we have a metal- semiconductor, metal- metal, or p-n junction ? Can I calculate the Potential Barrier by using a workfuncion?
 
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Welcome to PF;
The exact shape of the barrier is usually modeled using self-consistent calculations - depending on the exact structures being modeled.

The height of the barrier can sometimes be worked out from the band-mismatch.
 
Simon Bridge said:
Welcome to PF;
The exact shape of the barrier is usually modeled using self-consistent calculations - depending on the exact structures being modeled.

The height of the barrier can sometimes be worked out from the band-mismatch.

Thank you! I have a lot of formulas for calculating the Potential Barrier, and I get confused with them. I'm not sure about it ! In p-n junction, can I find the Potential Barrier by finding the difference in Fermi energy of the p and n-type junction? What about if I have a metal-semiconductor junction ?
 
You should be able to make out what your formulas are about by sketching the band profiles next to each other.
At the junction you'd get some band bending irl.
 
Simon Bridge said:
You should be able to make out what your formulas are about by sketching the band profiles next to each other.
At the junction you'd get some band bending irl.


Thank you, again ! I need to know the formula for calculating the Potential Barrier in p-n junction, please, write it down if you know it.
 
In general?

It's a self-consistent calculation using Poisson's equation to work out the band bending and the Schrödinger equation to work out the charge distribution. Rinse and repeat. What level education are you doing this at? Did you have a specific p-n junction in mind?
 

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