What are the laws for shooting dead an intruder in your home?

I had recently had someone threaten me on Xbox live. Saying they know my address. And they told me my address, and told me that they were quote "Coming to get me." So I warned them that I own a 9 millimeter handgun. And if they came to get me, I wouldn't hesitate to use it. So now I'm just curious. Is it possible that I could face charges for shooting and killing a man if he is intruding my home? I wouldn't shoot him if he was in my yard. I would simply call the police. But what if he physically entered my home. Do I have the right to shoot them on the spot? I am honestly freaked out by this man, seeing as I have no idea who he is. And he wasn't even playing the game we were on, it's like he entered my lobby specifically to threaten me. And proceeded to tell me personal things about my life. He was talking about my pets, my car. And even made a reference to my favorite resteraunt that I liked to eat at on weekends. I have seen the stalker trolling videos on YouTube. And I don't think this is a prank. The man was not using a voice changer. And he had a really distinct voice. Creepy, the way he spoke, so calm, we eerily realistic to me. This obviously wasn't one of my friends. And in this day and age, it's not hard to stock someone without them noticing. So I am legit freaked out, and do believe someone may be stalking me. And now my phone has been receiving unknown phone calls, and wheni answer they hang up. I think they are waiting for me to fall asleep. I have my gun close.