Numerical Modelling of Thermal Conditions of Integrated Circuits with the Summary Approximation Method

Melnik (R.)V.N.

Electronic Engineering. Microelectronics, 5, 46-49, 1990

Abstract:

When formulating mathematical models for many problems in electronics, such as for the analysis of thermal conditions of integrated circuits (IC), we often have to deal with situations where relaxed regularity assumptions on the a priori unknown solutions are required. Indeed, in the analysis of IC thermal conditions, thermal characteristics of elements located on the curcuit are usually different. Another challenge in mathematical electronics lies with the fact that we often have to deal with multi-dimensional mathematical models and therefore the development of efficient numerical approximations for such models in this field is essential. The method of summary approximation provides a way to develop such approximations. It allows us to reduce the problem to additive difference schemes, or more generally to additive vector schemes, for both steady-state and time-dependent problems with general types of boundary conditions. We demonstrate the efficiency of this method in the context of problems of thermal management of ICs.