The moons phases, including the half-moon, are not caused by something covering or shadowing the moon. Instead, they are a result of the angle between the sun, the moon, and the earth. The sun always lights up the half of the moon that faces toward it, and since the moon revolves around the earth about once every 29 and a half days, we get to see it at a little bit different angle each day. When the moon is lined up so that it is between us and the sun, the dark side of the moon will face toward us and we see it as new or crescent, and when it is lined up to one side or the other so that it is about the same distance from the sun as we are, we see it from the side so that it appears "half full" (these are the "first quarter" and "last quarter" moons) . Therefore, the half-moon is simply the result of the angle between the sun, the moon, and the earth.