Electro-Migration Model Parameters Sensitivity Analysis Based on the Monte Carlo Method

With the narrowing of the size and the improvement of integration, Integrated Circuit devices' reliability is increasingly becoming the focus of attention. The Electro-Migration is the one of many reasons to cause circuit malfunction. When the Integrated Circuits is working, certain current goes through the metal interconnect inside, and the metal ion moves in the effect of the "electronic wind", making certain parts of the conductor produces empty or whisker and hill, which is Electro-Migration phenomena. The migration will cause the failure of the electrical connection, which can reduce the reliability of the structure of Integrated Circuit. The physical model established the relation between EM phenomena and current density, geometry size, material properties and the temperature distribution of the metal line, which can evaluate the electric wire lifetime under the impact of Electro-Migration. The sensitivity analysis of the electric parameters is very significant for improving the reliability of the IC. Based on the classical EM failure physical model equation of Black, this paper analyzes this model by using the Monte Carlo method. Firstly, confirms the four parameters of distribution in the Black equations. Then, analyzes the Monte Carlo method about the value of sampling N, the value of r* in the limit equations, and the finally number of digits effective sensitivity. And then, analysis the four parameters using the Matlab, mainly considers four parameters' change; Change three parameters and fix the remaining one.; Two parameters change, two parameters fixed; A parameter change, three parameters fixed. Eventually, get the sensitivity order of the parameters in Black equations. This paper is useful for the physical model parameter sensitivity analysis of reliability (Ogawa E. T, 2002) and life prediction of the product.