Has my fast been invalidated by the emission of semen after waking up from sleep, and must I make up the days of fasting, or is it permissible to pay expiation?

It is incumbent upon a Muslim to ask people of knowledge about matters of their religion that are unclear to them. As for the specific issue, it appears that the questioner did not intentionally invalidate the fast, because the semen was discharged during sleep, and a sleeping person is not held accountable. His fast is valid as long as he did not cause its discharge, similar to someone who had intercourse at night and then semen was discharged during the day; in that case, his fast is valid.