# Band Gap Theory

I attached a picture.

In the first figure, we see that the difference between bands is rather large. We see that electrons do not occupy all the energy levels from energy 0 to Fermi energy level. There are forbidden band gaps.

But in the second figure, I see that the electrons occupy everything from energy 0 to the Fermi energy level (so there are no forbidden band gaps like the first figure shows) So, what is happening?

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nasu
Gold Member
The diagram on the left is a plot of the Fermi-Dirac distribution at zero K. It is not the band structure. In the band gap the density of levels is zero. The F-D does not have to be zero.

On both figures I see the energy axis.

In the first figure, I see electrons not occupying certain energy levels on this energy axis. In the second figure, I see electrons occupying all energy levels from energy level 0 to Fermi energy level on this energy axis.

ehild
Homework Helper
Insulators and semiconductors have a fully occupied valence band and an empty conduction band at low temperatures. There is a band-gap, forbidden energies, between them.
In case of metals, the conduction band is not empty even at 0 K. Half of the states in the conduction band are occupied. The electrons occupy the lowest levels at 0 K. It is shown in the figure on the right.

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In metals, at 0K, the conduction band is empty. The band, where the Fermi level resides, is separated into a valence band and a conduction band. The valence band is fully occupied while the conduction band is empty. If the temperature increases, for example room temperature, then the electrons need little energy to go in the conduction band.
You are confusing the conduction band with the allowed band where the Fermi level resides.

But I am asking about something else. In the second figure, I don't see band gaps like in the first figure.

I think I figured it out.

I think the 0 on the axis is the 0 for the probability, and not the energy.

Maybe in the figure, we see only the valence and conduction band. We don't see everything. And at 0K, the valence band is fully occupied like the figure shows, while the conduction band is empty.

I mistaken the 0 to belong to the energy axis.

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ehild
Homework Helper
In metals, at 0K, the conduction band is empty. The band, where the Fermi level resides, is separated into a valence band and a conduction band. The valence band is fully occupied while the conduction band is empty. If the temperature increases, for example room temperature, then the electrons need little energy to go in the conduction band.
You are confusing the conduction band with the allowed band where the Fermi level resides.
https://en.wikipedia.org/wiki/Valence_and_conduction_bands
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. The valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it. This distinction is meaningless in metals as the highest band is partially filled, taking on the properties of both the valence and conduction bands.

But I am asking about something else. In the second figure, I don't see band gaps like in the first figure.

I think I figured it out.

I think the 0 on the axis is the 0 for the probability, and not the energy.

Maybe in the figure, we see only the valence and conduction band. We don't see everything. And at 0K, the valence band is fully occupied like the figure shows, while the conduction band is empty.

I mistaken the 0 to belong to the energy axis.
The right figure shows the highest band with any electrons in it at 0 K. All states with energy below the Fermi level are filled, all above it are empty. The vertical axis is the energy above the bottom of the band. That is, why no band gap is shown. The figure is not clear, but the red circles might represent the occupied states.

nasu
Gold Member
In metals, at 0K, the conduction band is empty. The band, where the Fermi level resides, is separated into a valence band and a conduction band. The valence band is fully occupied while the conduction band is empty. If the temperature increases, for example room temperature, then the electrons need little energy to go in the conduction band.
You are confusing the conduction band with the allowed band where the Fermi level resides.

But I am asking about something else. In the second figure, I don't see band gaps like in the first figure.

I think I figured it out.

I think the 0 on the axis is the 0 for the probability, and not the energy.

Maybe in the figure, we see only the valence and conduction band. We don't see everything. And at 0K, the valence band is fully occupied like the figure shows, while the conduction band is empty.

I mistaken the 0 to belong to the energy axis.
The second figure does not represent a band structure at all. It is a plot of the F-D function. You can see F(E) on the x axis.
these red circle are meaningless. The density of electrons depends both on density of states and the probability to occupy that state. So there is no point to show these electrons there.