Using light: http://gizmodo.com/a-new-light-based-transistor-could-comple...
Building on memristors: http://www.memristor.org/reference/research/13/what-are-memr...
http://spectrum.ieee.org/semiconductors/design/the-mysteriou...
Neural network inspiried chips: http://www.research.ibm.com/articles/brain-chip.shtml
I think we will see some breakthrough after the CPU industry goes into an existential crisis about going below 5nm. Current pipelines are just so damn expensive to replace that we will see gradual innovations. For example TPU-s[1] might be a standard in a few years like GPU-s are now.
The current trends are clearly in reducing power usage and size. That alone will be a huge innovation when I can hold a "server farm" in my pocket.