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How can I know which one is direct bandgap material and which one is indirect?

Why does Germanium have an indirect bandgap? How can be it become a direct bandgap material?

Here, I have attached a picture where I have calculated the direct and indirect bandgap of Germamium.

I increased its pressure by reducing the cellsize.

Is there any way of understanding, which one has a direct bandgap and which one has an indirect band gap?

enter image description here

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    $\begingroup$ Do you mean how to determine whether a material has direct band gap without actually doing a calculation, or how to determine whether a material has direct band gap from calculation results? $\endgroup$
    – wzkchem5
    Commented Sep 10, 2022 at 15:57

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In order to know if your material has direct/indirect band gap, you need to calculate the electronic band structure: Energy vs k.

Then, you look for the smaller $\Delta E$ between the bottom of the conduction band (BCB) and the top of the valence band (TVB). If this $\Delta E$ occurs for the same value of k, then you have a direct band gap material, otherwise, you will have an indirect band gap material.

The image bellow correspond to the Germanium1. As you can see, the smaller $\Delta E$ occurs between the BCB at k = $\langle 111 \rangle$ ($L$ point) and TVB at k $= \langle 000 \rangle$ ($\Gamma$ point).

enter image description here

About Why?, I recommend to watch the Richard Feynman interview about magnets here.

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