A semiconductor device has an interposer with a die attach area interior to the interposer and cover attach area outside the die attach area. A channel is formed into a surface of the interposer within the cover attach area. A dam material is formed over the surface of the interposer within the cover attach area between the channel and edge of the interposer. A semiconductor die is mounted to the die attach area of the interposer. An adhesive material is deposited in the cover attach area away from the channel and dam material. A cover, such as a heat spreader or shielding layer, is mounted to the die and interposer within the cover attach area. The cover presses the adhesive material into the channel and against the dam material to control outward flow of the adhesive material. Alternatively, ACF can be formed over the interposer to mount the cover.