Disclosed are semiconductor die structures that enable a die having a vertical power device to be packaged in a wafer-level chip scale package where the current-conducting terminals are present at one surface of the die, and where the device has very low on-state resistance. In an exemplary embodiment, a trench and an aperture are formed in a backside of a die, with the aperture contacting a conductive region at the top surface of the die. A conductive layer and/or a conductive body may be disposed on the trench and aperture to electrically couple the backside current-conducting electrode of the device to the conductive region. Also disclosed are packages and systems using a die with a die structure according to the invention, and methods of making dice with a die structure according to the invention.