We predict it is possible to achieve high-efficiency room-temperature spin injection from a mag- netic metal into InAs-based semiconductors using an engineered Schottky barrier based on an InAs/AlSb superlattice. The Schottky barrier with most metals is negative for InAs and positive for AlSb. For such metals there exist InAs/AlSb superlattices with a conduction band edge perfectly aligned with the metals Fermi energy. The initial AlSb layer can be grown to the thickness required to produce a desired interface resistance. We show that the conductivity and spin lifetimes of such superlattices are sufficiently high to permit efficient spin injection from ferromagnetic metals.