How can the band-gap structure be determined using the E-k graph?

You can find the height by using the relation: V0 = (h-bar)^2 * (pie)^2 / (2*m*lambda^2)In summary, the conversation discusses determining the band-gap structure using real space lattice vectors, reciprocal lattice, and the first Brillouin zone. The individual can graph these components and sketch the E-k graph using certain equations. To determine the band-gap energy, they can use the Kronig Penney Model and calculate the height of the periodic potential barrier.
  • #1
james walshe
7
0
Hi all,
If you are given the real space lattice vectors (14 Angstroms in the x-direction and 8 Angstroms wit an angle of 91 degrees between them) and have to draw the reciprocal lattice and the the first Brillouin zone, and then using this data sketch the E-k graph and comment on the band-gap structure.

I can graph the reciprocal lattice and the first Brillouin zone, and I sketched the E-k graph using:
k=(pie/a) and k=(pie/b) where a and b are the real space lattice vectors. From this I can determine the energy of the middle of the band using:

E=((h-bar)^2 *(k)^2/(2*m))
where the two values of k were used, which gave two different energy values. Using this information how do I determine the width of the band gap or its band-gap energy.
 
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  • #2
Hi，according to the Kronig Penney Model, you should know the height of the periodic potential barrier.
 

What are Brillouin zones?

Brillouin zones are regions in the reciprocal lattice space that represent all possible allowed k-states for an electron in a periodic crystal lattice.

What is the significance of Brillouin zones?

Brillouin zones are important in understanding the electronic band structure of crystalline materials. They help determine the allowed energy states and the behavior of electrons in a crystal lattice.

How are Brillouin zones related to the E-k graph?

The E-k graph is a plot of the allowed energy states of electrons as a function of their wavevector k in the first Brillouin zone. The shape and size of the Brillouin zone directly affects the shape and behavior of the E-k graph.

How are Brillouin zones and the E-k graph used in materials research?

Brillouin zones and the E-k graph are used to study and understand the electronic properties of materials. They provide valuable information about the allowed energy states, band gaps, and electronic behavior in different materials, which is useful in designing and developing new materials for various applications.

How can Brillouin zones and the E-k graph be experimentally determined?

Brillouin zones and the E-k graph can be experimentally determined using techniques such as X-ray diffraction, electron diffraction, and angle-resolved photoemission spectroscopy. These techniques allow researchers to map out the reciprocal lattice and measure the energy states of electrons in a material, which can then be used to create the E-k graph and determine the Brillouin zones.

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