The Uncertainty Analysis Method Of Thermal Problem In3d Ic

With the appearance of three dimensional integrated circuit (3D IC), the integration of chip is increasing quickly. Due to the advantages of lower power consumption and s-maller package size, thermal effect is more prominent, which deteriorates performance of electronic devices, or even destructed. Since some new technologies have not been pro-duced, it is extremely difficult to make experiment simulation under the current equipment and processes. Finite element simulation can provide predictions of detailed thermal and stress distributions, so it becomes indispensable for IC design. The deterministic parame-ters and certain models are often used in actual analysis. In the design and manufacturing process, there exist some uncertainty factors that affect the thermal effect of3D IC. For the research of uncertain parameters, safety factor method is an old method and still wide-ly used. But the result of this method is too conservative, and has significant limitations. Interval analysis provides a path to study such uncertainties. Based on interval operations including interval arithmetic, the technique calculates the interval between the upper and lower bounds. It is particularly useful when statistical information is not sufficient to describe the probability distribution of the uncertain parameters, or only the range of the uncertain parameters is known, and the response of the interval range is desirous. In addition, interval analysis has important engineering application value and theoretical significance.In this paper a series of research has been carried out around uncertainty and its inverse analysis for3D IC. The main contents are as follows:(1)3D finite element numerical simulation models have been established using ANSYS for TSV-based (Through Silicon Via)3D IC. The parameters were regarded as determin-istic parameter, so the models were certain finite element models. Based on the heat dissipation of working process, the thermal and stress fields of3D IC structures were ob-tained by coupled thermal-stress analysis. The effects of various geometric parameters and thermal properties have been analyzed.(2) Considering the uncertainties of thermal parameters in the actual heat transfer problems, interval analysis algorithms were given. The interval procedures were written for steady state, transient and hyperbolic interval heat conduction problems. The uncertain parameters and initial boundary conditions were seemed as interval variables. The precise algorithm in time domain was empolyed. Based on the theory of interval analysis and perturbation method, formulas of interval parameters were derived. The temperature interval range was obtained through the numerical model.(3) General numerical models were presented to analyze the interval inverse steady, transient and hyperbolic heat conduction problem for TSV-based3D IC, with Bregman distances and weighted Bregman distances as regularization terms. The interval inversion procedures were written, combined with the inverse procedures and interval analysis. By using interval perturbation method, homotopy method and regularization method, the direct and inverse models were established for uncertainties. The inverse problems were implicitly formulated as optimization problems, using squared residues between the calcu-lated and measured quantities as the objective function of the inverse identification. The proposed numerical models can identify single and combined interval thermal parameters and boundary conditions accurately and efficiently.