Converting an indirect gap material to direct one

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For which reason some of materials have direct gap and the other have indirect gap?
In other words, what we have to do to convert a direct gap material to indirect one?
 
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This is a question of the electronic structure. In direct band gap materials, the valence and the conduction band have a maximum and minimum at k=0, respectively. In the semiconductors Si or Ge, both the valence and the conduction bands are made up of p orbitals (this is exact at k=0, at other values of k, other orbitals like s, will contribute, too), which leads to a direct band gap. In other materials, the valence band may be s but the conduction band p type, which leads to a different picture. Also polar bonding as in III-V semiconductors may lead to a shift of band maxima and minima.
 
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They can change indirect band gap silicon (single crystal and polycrystalline) into direct bandgap by making it amorphous
 
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