Transient thermal behaviour of a substrate subjected to the activation of an electronic chip and surface cooling

Abstract

<p>Controlling the temperature of electronic components is a major interest for the electronics industry. Indeed, the lifetime of the components is directly dependent on the temperature levels reached in the electronic boards. Then, it is essential to predict the chip temperature evolution in order to maximize their lifespan. The electronic boards are more and more complex. They are multi-layers composed of different materials. The numerical resolution of the heat transfer equations in these systems requires very fine meshes and therefore very high computation times. It is possible to standardize the characteristics of these multilayer boards in order to treat them as a homogeneous material. The study presented in this work uses this approach and deals with the transient thermal behaviour of a substrate and its chip. The entire surface of the electronic board is cooled by convection. The developed model assumes that the surface convection coefficient is known, constant and uniform. The heat transfer by conduction in the substrate is based on an axisymmetric assumption on the longitudinal dimensions of the exchange surface (r, theta) and an assumption of semi-infinite medium in the transversal direction of the plate (thickness z). These assumptions are verified if, on the one hand, the activation times of the electronic chips are low enough and the dimensions of the chip is small compared to the electronic board. In these conditions, a fully analytical model is developed considering two successive integral transforms: a Laplace transform for the temporal variable, and a Hankel transform for the radial variable. An explicit expression of the temperature of the surface heated by the component is established, requiring very short computation times compared to numerical simulations. This model can be easily incorporated into a dimensioning code for electronic devices to predict their temperature.  It can also be used as a direct model in an inverse procedure for identifying parameters on electronic boards.</p>