Hi stehe -- this is a very good question. First of all, I would find out in your organization (including contacting your legal counsel or whoever handles oversight of nonpublic personal information/personal identifying information) to see if you are able to collect emails. In our organization, we are not able to collect emails through surveys.
In my experience, it's functionally easier to ask participants to provide their email in a text box in the last question--I'm not quite sure of the mechanics of a popup but that seems like it could work, though it would have to be coded in Javascript or something similar.
To your point, you could also provide your email in the end of survey message and invite participants to contact you for an interview. You could also do this through your other messaging.
I hope that helps!