0-7803-XXXX-X/04/$17.00 ©2004 IEEE 20th IEEE SEMI-THERM Symposium A procedure to correct the error in the structure function based thermal measuring methods M. Rencz 1,2 , A. Poppe 1,2 , E. Kollár 2 , S. Ress 2 , V. Székely 2 , B.Courtois 3 1 MicReD Ltd., Budapest, Hungary 2 BUTE, Department of Electron Devices, Budapest, Hungary 3 TIMA Laboratory, Grenoble, France Abstract In this paper a methodology is presented to correct the sys- tematic error of structure function based thermal material pa- rameter measuring methods. This error stems from the fact that it is practically impossible to avoid parallel heat-flow paths in case of forced one-dimensional heat conduction. With the presented method we show how to subtract the effect of the parallel heat-flow paths from the measured struc- ture function. With this correction methodology the systematic error of structure function based thermal material parameter measuring methods can be practically eliminated. Application examples demonstrate the accuracy increase obtained with the use of the method. Keywords Thermal transient measurements, RC thermal models, structure functions, thermal conductivity measurement, inter- face thermal resistance measurement Nomenclature C Σ [Ws/K] cumulative thermal capacitance along a heat- flow path d denominator coefficients G [W/K] thermal conductance n numerator coefficients R [K/W] thermal resistance R Σ [K/W] cumulative thermal resistance along a heat- flow path s [1/s] jϖ: complex frequency τ [s] time-constant z [-] logarithmic time, t = exp(z) Z [K/W] thermal impedance 1. Introduction The structure function based evaluation of the thermal transient response functions 1 opened new avenues in the thermal transient testing of microelectronics structures. With the help of the structure functions die attach failures of pack- ages can be determined [2], and they can be used to determine partial thermal resistances in a heat-flow path [3]. The struc- ture functions can be obtained by direct mathematical trans- formations from the measured or simulated thermal transient response functions of the system. For a more detailed intro- duction to structure functions see [8] in this volume. Several methods have been developed to measure thermal material parameters, based on the structure function evaluation [4]. In these measurements it is exploited that the values of the structure functions and their slopes depend, among others, on material parameters. If we know the geometric parameters we can determine from the structure functions the material pa- rameters from fast and simple thermal transient measurements. The structure functions are one-dimensional representa- tions of the heat-flow path. One dimensional heat-flow can be forced in most of the practical cases in order to facilitate the structure function evaluation, but there is always a certain er- ror in these measurements. This stems from the fact that there is always a certain amount of parasitic heat-flow, that is mov- ing in other directions than the considered one dimension. In this paper we present a procedure that can be used to consider the parasitic heat-flow that is always present in the case of structure function evaluation based measurement methods, and enables correcting the measured results. 2. A procedure to correct the regular error of structure function based thermal measurement evaluation 2.1. The source of the regular error The common feature of the structure function based mate- rial parameter measuring methods is that one dimensional heat-flow is forced in the examined structure, by the applica- tion of appropriate boundary conditions. Heat is switched on at the t=0 time instant at a spot in the structure, and from that on the temperature of the same spot is recorded as the function of time, until steady state is reached. From the measured tran- sient curves the structure functions are determined by direct mathematical transformations.[5] As it was mentioned in the introduction, besides the main heat-flow path, where we force the one dimensional heat-flow, there are always more or less important parallel heat-flow paths where a part of the heat is lost. This lost heat is respon- sible for the error of the measurements. This lost heat is shown in Figure 1.