This paper presents a new technique for the monolithic heterogeneous integration of compound semiconductor devices with silicon integrated circuits, and establishes the theoretical foundation for a key element of the process, tailored magnetic attraction and retention. It is shown how a patterned thin film of hard magnetic material can be used to engineer the attraction between the film and nanopills covered with a soft magnetic material. With a suitable choice of pattern, it is anticipated that it will be possible to achieve complete filling of recesses in the surface of fully-processed integrated circuit wafers, preparatory to subsequent processing to fabricate the nanopills into heterostructure devices integrated monolithically with the pre-existing electronics.Singapore-MIT Alliance (SMA)