Nanotechnology is an area of applied physics, chemistry and biology. its concepts and the problems it addreses are part of these three natural sciences.
It is not a fundamental science, since its foundations are sustained on fundamental sciences.
It is not a field of engineering since it doesn't look for solving technological problems exclusively and/or innovate for goods that increase people's life quality.
Is not an innovation, since Nanotechnology at the base is just a concept, an approach. The innovation could be the final product which may be created from the deep understanding of a given phenomenon observed in a particular branch of science. And even less and invention, since the first people who started to use the term "Nanotechnology" didn't invent anything, they just gave a name to an approach, based on things we had previously invented: Quantum mechanics, electornics, molecular physics, solid state physics, etc. .. my opinion.