"Nanotechnology" is not well defined word. A few years ago it basically meant "very small things made in cleanrooms" (and before that "molecular robots" etc) but nowadays the meaning seems to have shifted to reasearch on e.g. nanoparticles used in sunscreen or even biochemistry (there was a letter in New Scientist a few week ago from a researcher who had just concluded that he was working in the field of nanoscience; he found this somewhat confusins since for the past 30 years he had been under the impression that he was a biochemist). Unfortunately, it has become a buzzword.
So, it is very difficult to recommend anything unless you are more specific. Generally speakning an eduction in a "basic" science such as physics or chemistry is probably best; much of the work (regardless of the definition used) i still very much basic research meaning a background e.g. EE is probably not as useful.