The present work illustrates a novel method of bonding compound semiconductor wafers to AlN or AlN/diamond heat spreaders using a graded intermediate layer. The procedure is illustrated using In–Ga solder to bond GaSb (111) wafer to commercial AlN substrate. Thermal conductivity of three bonded structures was evaluated using the 3-ω method. The experimental measurements of thermal conductivity of the multilayer were simulated using the analysis applicable to a layered structure. The results illustrate that the thin intermediate graded layer has a thermal conductivity above that of GaSb and therefore does not form an insulating layer. Bonding ZnO (002) wafer to commercial AlN substrate using zinc film that is subsequently oxidized is illustrated. The advantages of the graded intermediate layer to bond the heat spreaders such AlN or AlN/diamond are highlighted.