3-D Substrate Modelling

Ember™ can generate a 3-D finite difference (3DFD) mesh and compute temperature from

• the temperature map at the base of the substrate (e.g. from a package model) and
• heat sources and coordinates  on the top of the substrate (e.g. power estimates from  standard cells).

The mesh becomes finer as it approaches the substrate's top surface to provide a high resolution temperature map.

Ember™ couples each interconnect resistor to its local substrate temperature.

The example below (from ibmpg1) shows the substrate temperature solution, with Ember™-constructed "resistors" connecting the centroids of 3DFD elements and showing the temperature evolution from the cool base of the substrate.

The view below shows the underside of the substrate temperature solution.

The 3-D substrate temperature solution (below, left) forms the local substrate temperature for every interconnect resistor.  

The  temperature pattern is visible in the interconnect temperature distribution (below, right).  Here the colour range has been compressed to 0.25 < T < 1.0 to emphasise the lower temperature interconnects.  The big red spots are the high temperature regions around the VDD bumps and the smaller spots indicate the VSS bumps. 

The 3-D substrate temperature for ibmpg5 was obtained by taking the current sources as heat sources and assuming T=0 at the base of the substrate.  

The view below shows the substrate temperature solution (colour scale 0.25<T<0.40 C).