I've read about this a few times in the last couple years in semiconductor trade magazines, there may be a couple old articles to search for on slashdot as well. The idea is that no other known material has better thermal characteristics as are concerned with semiconductor usage. It withstands high temperatures very well, and conducts heat very well, so would hold up better when really hot, and would also be better at transferring heat into a heatsink than current silicon materials. The original problem with using diamond was the difficulty in getting large enough pieces to fab in enough quantities to be worth the trouble.
Then come along a couple companies working on making synthetic diamond of high quality. I saw a documentary a while back that two companies, perhaps those named in the original post but perhaps someone else, I don't remember, who apparently are getting quite good at making high quality synthetic diamonds. The documentary I saw talked of one company making yellow diamonds, and the other making the clear/colorless kind. One or the other can make them rather large if they want too, which would be great for creating wafers and processing chips in the fab very similarly to how it happens now. The other one I don't remember if they were able to make something big enough to create a wafer or if it was smaller scale stuff, but that may have changed since the documentary was filmed anyway.
So from the sounds of things, it's certainly approaching the realm of real possibility to actually happen, rather than just academic talk.
Now, the hitch. Debeers (sp??) and friends in the cartel business, ahem, in the jewelry industry really really do not like the idea of synthetic diamonds of this quality being this easy to make. They SERIOUSLY do not like this. They've sponsored test equipment to check diamonds to see if they are real or synthetic in an attempt to keep the "fakes" out of jewelry stores, even if they can be made cheaper than natural stones as priced by the cartel. The best test results so far are that the synthetics are "too perfect". There's no natural flaw that is unique in each natural stone, which actually sounds good for use un semiconductors. But expect the cartel to work very hard at shutting the synthetic producers down, as it sounds they are very afraid. And that would be bad for the semiconductor industry's technology improvements.