Research is not really where you work on spec-compliant
products. That's "development". Research in analog ICs
might be technologies, topologies, etc.
As a "lifer" analog IC designer, research is seldom done
(as a fraction of time spent). On a new-to-world or new-
to-company part there will be some experimentation and
you could call this "research", but often more practical
than theoretical. Because you're on a schedule and you
have to get it done, clever idea or not.
The innovations remaining to be discovered, are probably
about problems that are just becoming identified (as
other elements of the environment evolve, they present
new needs for some other IC to satisfy - for example,
ten years ago nobody cared about sub-bandgap voltage
references; now with core voltages below 1V, that's a
thing. What's next? I dunno. Somebody tells me they
need it, and I'll get to "research", cut-and-try style.
The company will expect you to attempt to meet at
least the key specs of interest. No sane company will
let an intern loose on valued product unsupervised.
You will (I expect) have a mentor who will parcel out
goals and actions, and want you to take initiative
from there.