You can use artificial turf but I wouldn't suggest it unless you have the perfect circumstances where there are no neighbors on each side of you and no windows close by. It will look like a eyesore not being formed that way with the rest of the houses and the weeds that grow up in the places your tires don't go over is a pain in the ass to maintain with edging and controlling the weeds. When you edge around the tire treads eventually you will be deep enough for flying debris that will cause flying debris like rocks for breaking windows or you neighbors. There's many other options but it's hard to give advice without seeing the driveway and surroundings. The grass is called Sod. Artificial grass/Turf is what they use to play in a lot of minor down to little league fields.