An apparatus is for plasma dicing a semiconductor substrate of the type forming part of a workpiece, the workpiece further including a carrier sheet on a frame member, where the carrier sheet carries the semiconductor substrate. The apparatus includes a chamber, a plasma production device configured to produce a plasma within the chamber suitable for dicing the semiconductor substrate, a workpiece support located in the chamber for supporting the workpiece through contact with the carrier sheet, and a frame cover element configured to, in use, contact the frame member thereby clamping the carrier sheet against an auxiliary element disposed in the chamber.