Can a woman use test-tube fertilization after the death of her husband?

A few years ago I heard that some non-Muslim "Pop-Star" wanted the sperms from her husband to be kept for later in-vitro fertilization as she and her husband failed to conceive and he also had cancer. So what if a woman wanted to have a child from her husband and unfortunately he died, but she could do an in-vitro (or test-tube) fertilization would that be halal in Islam? And on what basis would it be considered halal or haram (For example: because her husband died he (and therefore "intercourse" with him or his sperms) would be considered haram for her)? What if she did so when she knew he would die for example? I think this could also be a major issue for inheritance matters ('idah)!