A preassembly semiconductor device comprises substrate soldering structures extending toward chip soldering structures for forming solder connections with the chip soldering structures, i.e., the chip and the substrate are in preassembly positions relative to one another. The height of the substrate soldering structures is greater than the height of the chip soldering structures. A pre-applied underfill is contiguous with the substrate and is sufficiently thick so as to extend substantially no further than the full height of the substrate soldering structures. In another embodiment the height of the chip soldering structures is greater than the height of the substrate soldering structures and the pre-applied underfill is contiguous with the semiconductor chip and sufficiently thick so as to extend substantially no further than the full height of the chip soldering structures. A process comprises manufacturing semiconductor assemblies from these devices by soldering the semiconductor chip and the substrate to one another.