Each semiconductor has a direct and an indirect band gap; whichever is lower determines the nature of the band gap. The band gap is a property of the lattice constant; the band gap can be changed by varying the lattice constant. The lattice constant can be changed by various ways, e.g by applying pressure by heating or cooling or by mixing with another semiconductor. Both the direct and the indirect band gap will change with the lattice constant but at different rates. Hence there is a possibility that at a certain lattice constant, the direct band gap becomes lower than the indirect band gap; in that case the semiconductor will behave as a direct bad gap semiconductor. 

The band structure can be modified by strain or my reducing crystal size to the quantum dot level. Quantum dots generally have a modified band structure, whether Ge or Si QDs have a direct gap is still a matter of debate but there is evidence that their gap is "more" direct, also because due to the small size and Heisenbergs uncertainty principle there is an uncertainty in momentum (remember direct and indirect just means whether there is a momentum difference between Ec minimum and Ev maximum).

As regards strain, Ge can be strained sufficiently to make the gap direct by strong doping, which allows Ge lasers to be built. There's a few publications by Rodolfo Camacho on the topic. Not sure if the same is possible for Si.

Each semiconductor has a direct and an indirect band gap; whichever is lower determines the nature of the band gap. The band gap is a property of the lattice constant; the band gap can be changed by varying the lattice constant. The lattice constant can be changed by various ways, e.g by applying pressure by heating or cooling or by mixing with another semiconductor. Both the direct and the indirect band gap will change with the lattice constant but at different rates. Hence there is a possibility that at a certain lattice constant, the direct band gap becomes lower than the indirect band gap; in that case the semiconductor will behave as a direct bad gap semiconductor. 

I also think, it could be possible for some situations. To existing in literature, some examples of which http://www.ncbi.nlm.nih.gov/pubmed/23098085. Dr. Snow Samares already explained perfectly it.

It is possible  if additional confinement is added. For example, in nanowires one can have direct bandgap even if the bulk semiconductor has indirect bandgap. Check the literature, for example here http://pubs.acs.org/doi/abs/10.1021/nl061888d

http://pubs.acs.org/doi/abs/10.1021/nl061888d

Dear Layth Mokhles ,

I Send to you a paper and I hope that the paper is good for you to describe the conversion method

Best Regards

Try making your substrate with different processes to  achieve  different lattice strains. Or try to induce lattice strain on your indirect bandgap structures ( you can do that by annealing or mechanical deformation etc) . Hopefully one of your processes will reveal direct bandgap properties. 

For my knowledge, the indirect band gap of Ge is successfully  converted to direct band gap by tensile strain and n-type doping. Mechanical strain and epi on GaAs are optional ways to apply tensile strain.  For Si, because of the big gap between direct and indirect band gap, there is still no method to achieve it, though the band structure can be adjusted by strain. If you can obtain quantum dot of Si and Ge in certain size, I believe you can get the direct band gap. 

I agree with above answers, Bandgap can be modified under strain. Also change from indirect to direct bandgap has been observed when bulk semiconductor has been reduced to nano scale, as in MoS2 while the bulk material is an indirect bandgap material, its atomic layer MoS2 is direct bandgap material.

Germanium can be converted to a direct-bandgap semiconductor by a combination of tensile strain and n-type doping.  In (bulk) silicon this approach can hardly work because of the big difference between the indirect and direct band gaps. However, in tensile-strained silicon nanocrystals a concerted action of quantum confinement (i.e. indirect bandgap opening) and strain (direct band gap shrinking) can lead to the hoped-for effect. See K.Kůsová et al.: Advance Material Interfaces  Vol. 1 (2014), 1300042. DOI: 10.1002/admi.201300042.  

I agree with the above discussions. How about from direct into indirect bandgap?

One can convert direct band gap into an indirect one  by using an action opposite to that  converting  Si nanocrystals into a direct band gap material, namely, by applying compressive strain. See S. H. Tolbert et al., Phys. Rev. Lett. 73, 3266 (1994): In this work the authors induce indirect band gap in (direct semiconductor) CdSe nanocrystals using external compressive strain.