I am teaching and doing research work in Solid State Electronic Devices and Materials, which is a subset of Materials Science & Engineering - a branch of Applied Physics. I want to know if this falls within the domain of Physics Stackexchange.
Yes of course, Condensed Matter Physics in general is one of the largest single subfields of Physics. I am guessing then you would start with an introductory course in Solid State Physics. So feel free to bring up your questions here in physics stackexchange.
Yes! Solid state physics is physics, and is therefore on topic.
Of course, there are more conditions on whether or not an individual question fits the site besides just the general field of study. In particular, note that what we call engineering questions are off topic, so something like "What's the most cost efficient material to use in this application?" is probably off topic. "How do I fabricate this device?" is a gray area - it might be on topic, it might not, and it probably warrants more discussion if it comes up. I mention this not to be intimidating, but just because solid state electronics are studied both from a pure science standpoint and an engineering one.
Also, for such a large field, solid state/condensed matter/materials science is IMO quite underrepresented on the site at the moment. Don't be discouraged if at first it seems like the community consists entirely of particle physicists and general relativists. Hopefully we can attract a larger user base with some good questions and answers.