When I interviewed at Intel, ahem, 20 years ago, the phone screen was mostly to get a general sense of your interest and knowledge. There were some technical question, but I was just out of undergrad, so they were not design knowledge stuff so much as intelligence stuff.
The real interview interview was on-site: a gauntlet of 5 one-hour interviews. It was brutal. I don't even remember the categories. An hour on semiconductor physics, an hour on digital logic design, an hour on process technology, and hour on CPUs and computers (I was interviewing for a CPU design job.) Maybe there was one hour of general Q and A that was not technical. I do remember the whole affair was draining -- but I got the job. It was at their facility in Chandler, AZ, designing 16b microcontrollers.
It was actually a great place to start my career, since they really train you, and how else is going to teach you how to design chips? (I don't mean as a professor would, but how it's done in real life.) After a few years I wanted to work on the "big boy" x86 stuff. It turns out that was not nearly as much fun. Bigger teams and more specialization. That microcontroller group was all about soup-to-nuts generalists.
Of course, none of this is probably useful to you, it being so damn old. But I look forward to hearing back about what the process is like today!