Transition from tile to carpet

What would be the best way to transisiton from tile to carpet when there is a height difference of about 1/2 - 3/4 of an inch

Is this in a doorway or an open room?

Doorway

Metal or wood

Probably metal but was wondering a way to go without either or does there have to be one or the other with a 1/2" to 3/4" drop from the tile to the carpet

Tim, if your able to or want to hire a carpet man to do this, the best way to rememdy your height difference is to pull back the carpet if there is tackstrip there remove it, then place window shims up to the tile, reinstall the tackstrip leaving enough room to tuck the edge of the carpet to the tile you can tweak the shim & carpet height together to get the correct transtion for your sitation, I have been using shims to finish tile to carpet for years upon years, noone can ever till what I have done underneath there carpet, hope this helps.

Cedar shakes for roofing just like Denny said is what is done round here