Thermal interface material having different thicknesses in packages

A package comprising:

• a stack comprising:
• an interposer;
• a first device die and a second device die over and bonded to the interposer;
• a package substrate underlying and bonded to the interposer;
• and
• an encapsulating material encircling each of the first device die and the second device die;
• a metal cap comprising:
• a top portion;
• and
• a skirt portion underlying and connected to the top portion;
• an adhesive adhering the skirt portion to the package substrate;
• and
• a thermal interface material comprising:
• a planar portion having a substantially uniform thickness;
• and
• a protruding portion protruding up or down from the planar portion, wherein the protruding portion overlaps a corner portion of the stack.

A package comprising:

• a package substrate;
• an interposer over and bonded to the package substrate;
• a device die over and bonded to the interposer;
• a metal cap comprising:
• a top portion over the device die, wherein the top portion comprises a plurality of recesses, each recessing from a bottom surface of the top portion into the top portion;
• and
• a skirt portion encircling the device die and the interposer therein, wherein the skirt portion is adhered to the package substrate, and the skirt portion comprises four side portions;
• and
• a thermal interface material between and contacting the device die and the metal cap, wherein the thermal interface material extends into the plurality of recesses of the top portion of the metal cap.