Methods of estimating warpage of interposers and methods of manufacturing semiconductor package by using the same

A method of manufacturing a semiconductor package comprising an interposer comprising a through electrode passing through a substrate, and a plurality of metal wiring layers and a plurality of insulating layers on the substrate, the method comprising:

• deriving a warpage reference value by using sample interposers;
• and
• deriving an expected cumulative warpage of the interposer so that the interposer has an expected warpage that is greater than or equal to the warpage reference value,
• wherein the deriving of the warpage reference value comprises:
• performing a temperature sweep test at a plurality of temperatures by using the sample interposers with different pattern densities of the metal wiring layers, and measuring warpages according to the plurality of temperatures;
• deriving a warpage slope, as a function of temperature, of each of the sample interposers;
• deriving a warpage model by linearly fitting the warpage slope with respect to an average pattern density of the metal wiring layers in each of the sample interposers;
• and
• calculating a room temperature warpage reference value of the interposer based on the warpage model.

A method of manufacturing a semiconductor package comprising an interposer comprising a through electrode passing through a substrate, and a plurality of metal wiring layers and a plurality of insulating layers on the substrate, the method of forming the interposer comprising:

• deriving a warpage reference value by using sample interposers;
• deriving an expected cumulative warpage of the interposer so that the interposer has the expected cumulative warpage that is greater than or equal to the warpage reference value;
• and
• manufacturing the interposer,
• wherein the deriving of the warpage reference value comprises:
• performing a temperature sweep test at a plurality of temperatures by using the sample interposers with different pattern densities of the metal wiring layers, and measuring warpages according to the plurality of temperatures;
• deriving a warpage slope, as a function of temperature, of each of the sample interposers;
• deriving a warpage model by linearly fitting the warpage slope with respect to an average pattern density of the metal wiring layers in each of the sample interposers;
• and
• calculating a room temperature warpage reference value of the interposer based on the warpage model,
• wherein the deriving of the warpage model comprises linearly fitting the warpage slope with respect to the average pattern density of the metal wiring layers according to an equation:
• WS=a*PD+b,
• wherein WS is the warpage slope, PD is the average pattern density, a is a first constant, and b is a second constant.