We performed a band calculation, based on the LCAO (linear combination of atomic orbitals) method, for the InAs-GaSb superlattice. Of possible semiconductor combinations the InAs-GaSb is of special interest because of indications that at a heterojunction interface the bottom of the conduction band of InAs lies below the top of the valence band of GaSb. Our results show that the InAs-GaSb superlattice is a semiconductor when the layers of the constituent materials are thin, and becomes a semimetal when the layer thicknesses are increased. The critical InAs thickness for this transition is approximately 115 , over which the electrons from the valence band of GaSb "flood" the conduction band of InAs. For the thick-layer limit, we treat the problem in a Fermi-Thomas approximation. © 1978 The American Physical Society.