Ph.D’s in design are extremely rare. the oldest program in the country at IIT has only issues 29 in its entire eighty plus years.
Unlike the Master’s degee, in most of academia, a candidate selcts an individual (committe chair) who’s work is of interest, and that professor largely dictates to the student what to research for their degree. For example, you choose human factors as an area, then look around at all the recent publications to find a university or professor who you’d like to work for.
This approach might work best for you in ID as well.