Apparatus and methods for carrying out biochemical processes directly on a substrate are provided. A substrate assembly includes a cartridge that removably supports a substrate in a fixed position, and a reaction containment member that is removably located on top of the substrate. The reaction containment member includes one or more cavities that form chambers directly above one or more target locations on the surface of the substrate. The chambers can be used to conduct biochemical processes directly over the substrate, as well as to perform thermal cycling of material contained inside the chamber using a heating element disposed directly on the substrate. The substrate assembly is preferably used in combination with a processing machine that dispenses materials into the chambers and that conducts biochemical reactions of materials contained within the chambers, without requiring the substrate assembly to be moved from one location to another location during the processes.