Transient thermal analysis of global interconnects based on transmission lines

Abstract

In this paper, an efficient numerical method is proposed for transient thermal analysis of global interconnects. The thermal behaviour of global interconnects is modelled as two dimensional heat transfer. The horizontal heat conduction along the line is described by the differential form of one dimensional heat diffusion equation, and the vertical heat conduction from the line to the substrate is modelled by the corresponding thermal transmission lines with the input admittance reduced by one moment matching technique. Then finite difference method is adopted to solve the proposed heat diffusion equation and the transient thermal response of global interconnects can be obtained. Numerical results show that the proposed method is more efficient than thermal field solver based on finite element method, and more accurate than equivalent thermal circuit solutions, with accuracy above 98%. I. [NTRODUCTION Rapid technology scaling enables hundreds of millions of transistors to be densely packed into a single chip. Therefore, high temperature problems caused by huge heat dissipation seriously affect performance and reliability of integrated circuits [1]. Since the peak temperature often appear at the top of the chip, which deteriorates the interconnect performance by increasing the interconnect resistance. The signification of accurately estimating the thermal behaviours of interconnects increases rapidly.Until this date, numerous efforts have been made to estimate interconnects temperature distribution. Three dimensional (3�) thermal fields of interconnects can be accurately simulated with numerical methods, such as finite difference method (FOM) [2], finite element method (FEM) [3] and boundary element method (BEM) [4], etc. These methods require a large number of computational nodes, which lead to long computational time. To improve efficiency, various approaches were proposed, including analytical solutions [5][6] and equivalent thermal circuit solutions [7] [10], which trade lengthy computational time for reduced resolution and accuracy. The equivalent thermal resistance circuits in [7][8] neglect thermal capacitance and hence are suitable for fast analysis of the steady-state louie heating in interconnects. To allow for transient thermal analysis of interconnects, the equivalent thermal resistance-capacitance (RC) circuits were proposed in [9][[0]. However, the transmission line effect on transient thermal profile of global interconnects should be considered due to high thickness of insulator and long length of interconnects. In this paper, a FDM-based method is proposed for transient thermal analysis of global interconnects. One dimensional heat conduction equation along the line is derived with the vertical heat dissipation modelled as a thermal transmission line and simplified with one moment matching technique. Numerical results from the method are compared with those from FEM and the equivalent thermal RC circuit solution. It is shown that the proposed method is more accurate than the thermal RC circuit solut...