Hi FY, excellent description of the thermal effects on such layered structures. 

But - just to mention for the laymen here: The root of the problem of the mismatch is simply caused by the dimensions of the atoms. We should not forget that we are here dealing with monocrystalline structures of extremely high purity. 

So reducing to one dimension - we have a top layer of Silicon SiSiSiSiSiSi - and on this, we want to put a layer of InP. Obviously the length of SiSi is not the same as InP

SiSiSiSiSiSi
InPInPInP
or
GaAsGaAsGaAs

Et voilà, this is the mismatch.

Well, in reality, the differences are much smaller, but enough to create steps in the layers - defects creating a lot of problems. Bright scientists found a lot of tricks to solve or heal these issues. And to this then comes the problem of thermal changes in these distances. I doubt that anyone can solve these problems properly. Optical engines have to be very robust! So let us go OI - or hopefully later - with Poet's GaAs!