How is a PhD student staying in their institution as a postdoc perceived by future employers?
As someone hiring post-docs and staff members, I am leery of someone doing a long (defined as ~ &gt;6 month) postdoc where they were a PhD student, particularly with their same advisor. Why? To me, the purpose of a post-doc is to have a clear demonstration that the new PhD can move into an at least slightly different area and rapidly come up to speed and be productive on something new. Staying where you are just means finishing up loose ends, whether correct or not. If in the 6+ month range, you've got some explaining to do to me in the interview.
I'm not upset by a few-month &quot;postdoc&quot; with their PhD advisor, finishing up things, as they are looking for the next position to come open. But a post-doc has to be something new - it is the time to show off your new-found abilities to learn and make progress. Why? Because that is what you are going to have to do for the rest of you career. You aren't going to keep doing your PhD project for the next 30+ years.
For my postdocs, what does showing off look like? We hand them a project, and expect that within ~3 months there should be progress sufficient for starting to submit abstracts to conferences. And then they get another new project to get going, with abstracts going out on it 3 months or so later. The point is that in the first year there should be conference presentations and papers heading out the door on the new work at my institution. They should have an interview talk based on that work. That is what a postdoc should look like, and what I look for out of their postdoc when hiring new staff members. And that does not seem to happen for a postdoc staying at their PhD institution under their PhD advisor - it is just too easy to wrap things up, not start new, well defined projects that are different.
I would like to add that for the next 2-5 years (or more based on what happens) I will be much more flexible with this. Clearly the pandemic is not going to help anybody's career trajectory, and the constraints on jobs, moving, and everything else will make life for grad students and postdocs far more complicated than usual (and everyone else, too). Still, choose wisely - what will make you better at what you want to do?