Understanding Electron Effective Mass in Crystals

In summary, there are two definitions for electron effective mass in crystals. The first states that when an electron is in a crystal with periodic potential, it behaves as a free electron with effective mass m^*. The second states that when an external force is applied on the electron in a crystal, it behaves as a free electron with effective mass m^*, but both definitions are essentially saying the same thing and are not entirely accurate in their wording. The actual definition uses the quantum mechanical analogy to F=ma.
  • #1
hokhani
483
8
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 [itex]m^*[/itex]

2) when an external force is applied on the electron in a crystal, the electron behaves such as a free electron with effective mass [itex]m^*[/itex]
 
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  • #2
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 [itex]m^*[/itex]
2) when an external force is applied on the electron in a crystal, the electron behaves such as a free electron with effective mass [itex]m^*[/itex]
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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1. What is electron effective mass in crystals?

Electron effective mass in crystals is a measure of how easily an electron can move within a crystal lattice. It is a property that describes the behavior of electrons in a crystalline solid and is affected by the crystal structure, lattice vibrations, and other factors.

2. How is electron effective mass determined?

Electron effective mass is determined through various experimental techniques, such as electrical conductivity measurements, angle-resolved photoemission spectroscopy, and cyclotron resonance. Theoretical calculations, such as density functional theory, can also be used to calculate effective mass.

3. Why is understanding electron effective mass important?

Understanding electron effective mass is important for studying the electronic properties of materials, such as their electrical conductivity and optical properties. It is also crucial for designing and optimizing electronic devices, such as transistors and solar cells.

4. How does electron effective mass vary in different crystals?

Electron effective mass can vary significantly in different crystals due to variations in crystal structure, composition, and temperature. For example, in metals, the effective mass is typically low, while in semiconductors, it can vary greatly depending on the type and concentration of dopants.

5. Can electron effective mass be manipulated?

Yes, electron effective mass can be manipulated through various methods, such as applying external electric or magnetic fields, doping the crystal with impurities, or changing the crystal structure through strain or pressure. These manipulations can alter the electronic properties of materials, making them useful for various applications.

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