There's an interesting interview with Dr. Welser, the Director of the Nanoelectronics Research Initiative (NRI). The NRI was established in 2004 in order to develop post-silicon CMOS computing technologies, which will be needed by 2020 if not earlier.
Here are the Graphene related questions:
Question 5 : Is graphene currently the front-runner in the race to supplant silicon? Is it considered a more suitable candidate than carbon nanotubes?
Answer: Graphene is currently one of the materials we are focusing on, and it does have a number of advantages. It has very high switching speed, and it should be feasible to fabricate graphene FETs. Even more interesting for NRI post-FET switch research is the unique physics in graphene that could lead to completely new devices based on pseudospintronics or other state variables. Graphene is pure carbon, so it is strong enough to withstand the acids and caustic elements used in semiconductor fabs. So a hybrid chip containing both silicon and graphene is a real possibility.
Question 6 : When will the first logic gate based on one of these nanoelectronics technologies emerge?
Answer: We have already seen individual switches made from flakes of graphene. At some point there should be a breakthrough - some researcher will figure out how to make a uniform layer of graphene across a wafer. That should hopefully happen within the next couple of years, and we will need it to happen within that time frame if we are to have working products by 2020.