Thermal Analysis and Design of Integrated Circuit Devices.
The integrated circuit device is modeled as a multilayer structure with multiple planar heat sources embedded within the volume of the top layer. By using the eigenfunction expansion technique, the exact solution to the three dimensional steady state heat conduction equation in anisotropic composite media is derived. The solution is expressed in terms of an infinite double Fourier series when the integrated circuit device is modeled to have finite lateral dimensions. On the other hand, when the lateral dimensions are allowed to extend to infinity, the solution is conveniently expressed in the form of a double Fourier integral transform. It is shown that the CPU time required by the solution of the finite chip model is prohibitively long and expensive especially for small sources on large substrates. It is also shown that in conjunction with the method of images, the infinite multilayer plate model can exactly represent the finite chip configuration. This is very fortunate because the use of the latter model reduces the CPU requirement by a factor of from 10-1000. The results obtained using the analytical solutions are compared with results calculated by the boundary element method. The advantages of this numerical technique over the more popular finite element method in the solution of the particular thermal problems in this dissertation becomes apparent when the existence of solder voids are taken into consideration in the thermal characterization. For the single-layer structure, the temperature dependence of the thermal conductivity has been taken into account by using the Kirchoff transformation. Whether the analytical or numerical approach is utilized in the thermal design of integrated circuits, the large CPU requirement exists. This makes real-time thermal analysis and design of ICs impossible especially when several thousand up to tens of thousands of small heat sources are involved. In this dissertation, a method is presented that makes real-time thermal design at the chip level possible for the first time. The technique is called the "unit source" approach where the thermal profile due to a unit heat source is matched to a simple parametric equation in several parameters. The thermal profile over the device is obtained by superposing the profiles generated by the equation fit, shifted in position and weighted by the source power. By using the new approach, the CPU time requirement is reduced by a factor of up to several hundred thousand.
- Pub Date:
- Engineering: Electronics and Electrical; Engineering: Packaging; Physics: Condensed Matter