How can you derive the effective mass?

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Discussion Overview

The discussion revolves around the derivation of the effective mass of electrons in the context of band structure in solid-state physics. Participants explore the mathematical manipulation of energy equations and the conditions under which effective mass can be derived.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions how to derive the effective mass from the energy of the band structure and whether it involves algebraic manipulation of the energy equation.
  • Another participant confirms that the derivation is valid only close to the minimum for electrons or maximum for holes in the band structure.
  • A third participant references a lecture from the Colorado School of Mines that discusses the derivation of effective mass using Newton's second law, though they express difficulty in locating the initial equation in the provided resource.
  • A participant introduces classical physics concepts of kinetic energy and momentum, suggesting a connection to quantum mechanics through the relationship between momentum and wave vector.

Areas of Agreement / Disagreement

Participants generally agree that the effective mass can be derived through algebraic manipulation near band extrema, but there is no consensus on the specific equations or methods to be used, and some aspects remain unresolved.

Contextual Notes

Limitations include the dependence on the specific conditions near band extrema and the potential missing assumptions regarding the applicability of classical mechanics to quantum scenarios.

bluejay27
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I have seen that the energy of the band structure is defined in the following form. How do you obtain this form of the equation? Additionally, how can you obtain the effect mass of the electron? Do you just manipulate algebraically the equation of the energy of the band structure and solve it for for the m_e*?
 

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In classical physics, kinetic energy is 1/2 mv^2 or p^2/2m.
In QM the momentum p=hbar k...
 

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