I could offer a general perspective from my own experience from about 8 years ago in the field of Computer Science.
Unless your mind is very strongly set on one very specific topic within your subject (which I doubt it might be at this stage), the key is to show interest in a few fields related to the department (or professor) thus showing interest as well as flexibility. The reason being that, the professor you'll be working with is very likely an expert with a much more informed perspective on the matter than you so you are very likely going to benefit from their input on the matter given your interest in something they know a lot about. In many cases, I think what is expected of you is some degree of relevant experience in the field which you could leverage in coming up with original work (unless you already have, in which case it is a big plus). I would also add that bringing up names of other professors you have worked with, who your prospective supervisors might also know, could benefit you. Not sure how things work in Germany, but it doesn't hurt to contact the professor directly expressing your interest in working with her/him.
I received a PhD grant from the university (in London) based on my proposal, which started with responding to an email from a professor (who eventually became one of my supervisors) to a mailing list seeking PhD grant applications. I was interested in one particular area, and noticed that so was the professor, so I emailed back expressing my interest in working with him. He then suggested that I put together a roughly four page long PhD proposal (as required by the university) and offered to give me feedback and a letter of support for it. He also got another professor on board who was interested not in my specific topic but a related topic that could make the proposal stronger. They sent me a few papers to read, which I did and included it in my proposal. Both of them offered strong letters of support for my application and I finally received the grant.
I know there's not any one way to go about it, but I hope this one would give you some perspective on how it could work.