Joule heating and heat dissipation in 3D IC technology
Introduction to the event
When Moore’s law of 2D IC Si chip technology is near ending, the most promising extension of more-than-Moore is to go to 3D IC by stacking chips vertically. However, in 3D IC the most challenging technical problem is Joule heating because of the densely stacked structure. If heat cannot be conducted away, it will lead to very serious yield and reliability problem. For example, if we want to add more functions to hand-held devices, the operations of memory, logic, and special functions must be increased, in turn power as well as battery capacity must be increased too. A larger size battery will squeeze the volume of the rest of the device, which makes the heating problem worse. To remove heat, we should have a temperature gradient. If we consider a temperature difference of 1 °C across a microstructure of 10 μm in diameter, the temperature gradient is 1000 °C/cm, which will induce thermomigration. Furthermore, Joule heating will enhance electromigration, and thermo-stress will induce stress-migration. They are of major reliability concern.
An electronic device in operation is an open system because electrical charges flow in and out of the device. While the number of charges in transport is conserved, entropy production is not. The waste heat in entropy production is Joule heating on the basis of irreversible processes. We want to design low power devices, which is a low heat production device.
In microelectronic industry, statistical analysis of failure requires the knowing of mean-time-to-failure (MTTF). Example is Black’s equation of MTTF for elctromigration. In this program, we have developed a unified model of MTTF for electromigration, thermomigration, and stress-migration on the basis of entropy production. We have verified that in Black’s equation, MTTF depends on j2 rather than j, where j is current density, which has been a controversial point for a long time. Also we have provided MTTF for thermomigration and stress-migration, which have not been given before.