How to calculate the gap for a solid?

In summary, to calculate the energy gap for a solid using the Kronig-Penney model, set up a simple infinite potential field with periodic potential bumps. The solution can be found using parametric equations with sines, and the gaps are identified where there is no solution. This method can be found in various solid state books such as Kittel and Ashcroft and Mermin.
  • #1
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Hello everyone:

Do you know how to calculate the energy gap (the forbitten band) for a solid from the Kroning-Penney model?
 
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  • #2
check any solid state book, Kittel comes to mind as does Ashcroft and Mermin.
 
  • #3
It has been a while since I have done this.

But I believe the answer you are looking for is:

Set up a simple infinite potenential field consisting of a perriodic array of potential bumps. (i think the only one I have worked out for my self is the case of a Delta function comb)

Then you have a parametric equation with sines in it. Because the solution can not be greater than 1 (maximum of sin(x) = 1) you find areas where there is no solution. Those are you gaps.

I know I have seen this in Kittel, Griffiths (quantum mechanics) and a couple other places.
 

Related to How to calculate the gap for a solid?

What is the definition of a "gap" for a solid?

A gap for a solid is the distance or difference between the highest occupied energy level and the lowest unoccupied energy level in the material. It represents the energy required for an electron to transition from the valence band to the conduction band.

How do you calculate the gap for a solid?

The gap for a solid can be calculated by subtracting the energy of the highest occupied energy level (valence band) from the energy of the lowest unoccupied energy level (conduction band). This can be determined through various experimental techniques such as spectroscopy or theoretical calculations using quantum mechanics.

What factors can affect the gap for a solid?

The gap for a solid can be affected by a variety of factors, including the type of material, its crystal structure, temperature, and external influences such as pressure or electric fields. The gap can also be modified through the addition of impurities or defects in the material.

Why is the gap for a solid an important characteristic to study?

The gap for a solid is an important characteristic to study because it provides information about the electronic properties of the material. It can affect various physical properties such as conductivity, band structure, and optical properties. The gap is also crucial for understanding the behavior of semiconductors and their applications in electronic devices.

What are some common methods for measuring the gap for a solid?

Some common methods for measuring the gap for a solid include optical absorption spectroscopy, photoluminescence spectroscopy, and electrical conductivity measurements. Other techniques such as X-ray diffraction and electron energy loss spectroscopy can also provide valuable information about the gap and electronic structure of a solid material.

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