Integrated circuit dies are mounted to the interconnection leads on frames of tape automatic bonding (TAB) film. Thereafter, each frame of the TAB film with the attached integrated circuit die is affixed to an electrically insulating, thermally conductive plate to form a sandwich structure. A number of sandwich structures are bonded together to form a stack of sandwiches. The interconnection leads of each sandwich in the stack are selectively electrically connected to the interconnection leads of other sandwiches in the stack to form a system of electrically interconnected integrated circuits. The system is compact and has short interconnection paths between integrated circuits so that the propagation delays of signals between integrated circuits are minimized.