Computation of the temperature field of multilayer load-bearing structures by numerical methods

Abstract

Modern approaches to the electronic means design include modeling of thermophysical processes occurring in the apparatus being developed. At the same time, a common task in thermophysical modeling is the problem of determining the temperature field of the supporting structure of an electronic device (board, substrate). Knowledge of the quantitative indicators of the supporting structure temperature field directly affects the prediction of the entire electronic device reliability. The load-bearing structures of electronic devices are increasingly made in the form of multilayer structures where conductive, insulating and semiconductor layers can be present. These features impose new requirements on the development of mathematical models, algorithms, application software packages for calculating the temperature fields of the supporting structures of electronic means. The article considers the process of modeling the temperature field for the supporting structures of electronic means using common software systems MathCAD and SolidWorks. The whole variety of supporting structures of electronic means is divided into three categories: conditionally one-dimensional, conditionally two-dimensional and three-dimensional. It is shown that the temperature fields of conditionally one-dimensional (rods) and conditionally two-dimensional (single-layer boards and substrates) structures should be calculated by the finite difference method in the MathCAD software package. Temperature fields of three-dimensional load-bearing structures, including complex geometric configurations, should be calculated using the finite element method in the SolidWorks software package. The developed algorithms for calculating temperature fields are verified by solving a test problem. Comparative analysis has shown that the discrepancy between the calculation results relative to the test problem does not exceed 0.8%. The developed algorithms for calculating the temperature field can be practically useful in the engineering activities of the developer of electronic equipment.