What does k mean in E-k diagram?

In summary, in the E-k diagrams for a semiconductor material, k represents the wave vector of an electron and determines the direction of motion in the crystal. It is related to the momentum of the electron and is a fundamental concept in solid state physics, as it affects the energy levels accessible to an electron in a crystal. A more precise definition can be found in textbooks on solid state physics, such as Ashcroft and Mermin.
  • #1
msaleh87
8
0
In the E-k diagrams for a semiconductor material,what exactly is k?

-is it just the quantized quantity in the bloch theorem :ψ(x+a)=exp(i.k.a)ψ(x)

-is it the wavevector of the electron wave

-does it determines the direction of the motion, i.e a given k corresponds to motion in a certain direction in the crystal and only certain energy levels E are accessible to an electron moving in this direction. Correspondingly, electrons with a certain energy E can only move in certain directions.

-is it related to the momentum of the electron. And if so, shouldn't it be related to the energy with simple relations, not those complex diagrams

please give me the exact meaning of k or tell me where to find such an precise meaning
 
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  • #2
It is a wave vector, i.e. it contains both a direction and a spatial frequency or wavelength lambda = 2pi/|k|. The momentum is [itex] p = \hbar k [/itex].

Electrons in a crystal are not free particles, due to the presence of nuclei and plenty of other electrons. Therefore the free particle dispersion relation E=p^2/2m is not valid in crystals. Instead you get the "spaghetti diagrams" of band structure. In crystals, the energy can depend on the direction of p or k.

This is the fundamental foundation of solid state physics. Read any textbook on solid state physics, for example Ashcroft and Mermin.
 

What does k mean in E-k diagram?

In an E-k diagram, k typically refers to the wavevector or the momentum of a particle. It is represented by the symbol k and is measured in units of inverse length, such as 1/Å or 1/nm.

Why is k important in E-k diagram?

K is a crucial parameter in E-k diagrams because it determines the energy and behavior of particles in a material. It helps to understand the electronic structure and properties of materials, such as their conductivity and band structure.

How is k related to the energy in E-k diagram?

K and energy are directly related in an E-k diagram. As k increases, the energy of the particle also increases. This relationship is described by the dispersion relation, which shows how the energy of a particle changes with respect to its wavevector.

Can k have negative values in E-k diagram?

Yes, k can have negative values in an E-k diagram. This usually occurs when the particle is moving in the opposite direction of the wavevector. Negative values of k can also represent the direction of the particle's spin or the direction of an external magnetic field.

How is k related to the electronic band structure in E-k diagram?

K plays a crucial role in determining the electronic band structure in an E-k diagram. The band structure is determined by the allowed values of k and the corresponding energy levels, which create energy bands. This helps to understand the behavior of electrons in a material and its electronic properties.

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