Semiconductor die are assembled on a substrate by providing the semiconductor die, substrate, and an elastically deformable foil fixture preformed with one or more sunken regions having sidewalls and a bottom, and placing the semiconductor die in the one or more sunken regions so that the foil fixture is populated with a first side of the semiconductor die facing the bottom of the one or more sunken regions and a second opposing side of the semiconductor die facing away from the bottom of the one or more sunken regions. The substrate is placed adjacent the second side of the semiconductor die with a joining material interposed between the substrate and the semiconductor die. The substrate and the populated foil fixture are pressed together at an elevated temperature and pressure via first and second pressing tool members so that the substrate is attached to the second side of the semiconductor die via the joining material.