The International Technology Roadmap for Semiconductors (ITRS), a collaboration of world's major semiconductor companies, predicts transistors will stop shrinking in 2021. The latest ITRS report claims it will no longer be economically viable to shrink transistors after 2021, but Moore's Law will probably continue for a bit longer thanks to the adoption of 3D packaging and new cooling techniques:
First, ITRS expects that chip makers and designers will begin to move away from FinFET in 2019, towards gate-all-around transistor designs. Then, a few years later, these transistors will become vertical, with the channel fashioned out of some kind of nanowire. This will allow for a massive increase in transistor density, similar to recent advances in 3D V-NAND memory.
The gains won't last for long though, according to ITRS: by 2024 (so, just eight years from now), we will once again run up against a thermal ceiling. Basically, there is a hard limit on how much heat can be dissipated from a given surface area. So, as chips get smaller and/or denser, it eventually becomes impossible to keep the chip cool. The only real solution is to completely rethink chip packaging and cooling. To begin with, we'll probably see microfluidic channels that increase the effective surface area for heat transfer. But after that, as we stack circuits on top of each other, we'll need something even fancier.