Understanding Electron Effective Mass in Crystals

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SUMMARY

The discussion clarifies the concept of electron effective mass in crystals, specifically addressing two definitions. Both definitions presented—regarding the behavior of electrons in a periodic potential and under external force—are essentially the same and lack precision. The correct understanding involves recognizing that the effective mass, denoted as m^*, is derived from quantum mechanical principles rather than classical mechanics. For a comprehensive definition, refer to the Wikipedia article on effective mass in solid-state physics.

PREREQUISITES
  • Understanding of solid-state physics concepts
  • Familiarity with quantum mechanics principles
  • Knowledge of periodic potentials in crystals
  • Basic grasp of classical mechanics (F=ma)
NEXT STEPS
  • Study the quantum mechanical derivation of effective mass
  • Explore the role of periodic potentials in solid-state physics
  • Learn about the implications of effective mass in semiconductor physics
  • Investigate the relationship between effective mass and electronic band structure
USEFUL FOR

Students and researchers in solid-state physics, materials scientists, and anyone interested in the behavior of electrons in crystalline structures.

hokhani
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I have got confused about electron effective mass in crystals. Which of the definitions below are correct?

1) When an electron is in a crystal with periodic potential, it behaves such as a free electron with effective mass m^*

2) when an external force is applied on the electron in a crystal, the electron behaves such as a free electron with effective mass m^*
 
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hokhani said:
I have got confused about electron effective mass in crystals. Which of the definitions below are correct?
1) When an electron is in a crystal with periodic potential, it behaves such as a free electron with effective mass m^*
2) when an external force is applied on the electron in a crystal, the electron behaves such as a free electron with effective mass m^*
But these are pretty much identical statements - they are both sloppy statements of the same definition.
The first one fails to state what it means by "behavior" while the second implies F=ma ... the actual definition uses the quantum mechanical analogy to F=ma.
http://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)#Definition
 
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