Why are there direct bandgaps? This Question has been bugging me for sometime. Some semiconductors have direct bandgaps and indirect bandgaps. So what causes a direct bandgap to occur? The physics behind ,why there are direct bandgaps? 
I collected some data on a dozen compound semiconductors from handbooks (III-Vs, II-VIs and IVs) (35+ compound semiconductors if you count multiple crystalline phases of the same material) and performed anova with crystal structure, atomic number & location of constituting elements on the periodic table as variables. I found that the biggest influence on whether a semiconductor has a direct bandgap or indirect bandgap was atomic number of constituting elements and not crystal structure or location of the constituting elements on the periodic table. Could it be because a high atomic number entails a strong nuclear field from the constituting atoms in the unit cell that somehow aligns the conduction and valence bands in momentum space? Any ideas, opinions, relevant papers?
Thanks 
 A: Firstly there is a table on wikipedia with some of this data: http://en.wikipedia.org/wiki/List_of_semiconductor_materials. It sounds like you have a little more information so if you want to post in your answer that would be nice. If you want to be a really good Samaritan you could add it to Wikipedia
There are maybe two things being asked here: 
1) Why are direct band gaps common, since if one just picked random bands out of a hat direct band gaps would be an unlikely coincidence? 
This makes sense to me. Direct band gaps are in some sense natural, since I can imagine that if I neglect some couplings (like the crystal field) I get band crossings at some symmetry point. Then  when I turn on the coupling I will end up with a direct gap at that point.  Indirect band gaps only happen when your perturbing coupling are strong enough that avoided level crossings at different points get mixed up. For example, in alot of the $IV$ indirect fcc materials like Ge, Si, AlP, you have the conduction band at the $X$ point getting pushed through the gap at the $\Gamma$ point. 
2) What explains the pattern of indirect vs. direct gaps? 
I am not convinced that there is an overarching pattern.  Compounds with similar atomic structures have very similar band structures, so it could be you're just picking up a patterns within a couple of groups, and that these patterns have no particularly deep explanation. And while your data is very nice, the statistical power of your analysis is not overwhelming, and subject to lots of uncontrolled biases. I imagine it would be more illuminating to fix some properties and look at a sequence of compounds with increasing atomic number, and see whats happening with the band structure.
If there really is a strong tendency for indirect gaps in higher atomic numbers, than the natural explanation is spin-orbit coupling. I don't really see a general argument for this to lead to indirect gaps.
A: Various crystals have their conduction and valence bands at different momentum, k-vectors.  These are called indirect band gaps.  Conversely, if the momentum vectors of the two bands are aligned to the same momentum k-vector, then it is called a direct band gap.  
In an indirect band gap, the 'kick' of momentum transfer required for a band transition is given by lattice phonons, the quanta of lattice vibrations. 
