A Self-similarity Model For Dielectric Constant Of Porous Ultra Low-k Dielectrics

Porous materials have been studied extensively for many applications such as catalysts, adsorbents, membranes, sensors, and waveguides etc.The semiconductor industry is continuing its quest to create ever more powerful microprocessor and memory chips by ultra-large-scale integration (ULSI) through the continual reduction of the minimum size of device features. Along with this goes a corresponding increase in device density on the chip, which in turn results in an increase in the number of wiring levels and a reduction in the wiring pitch. As device dimension shrinks to less than 0.25μm, the dense interconnect will cause a significant increase in propagation RC delay, crosstalk noise, and power dissipation. These will seriously degrade the performance of deep submicron integrated circuits. In order to improve circuit performance, new materials with lower dielectric constant than conventional Si02 (k=4.0) are needed. So it can be added pores in skeleton medium to decrease the dielectric constant, because the dielectric constant of the air in pores is 1. However, the analyze of relative permittivity of porous dielectrics is based on the model that the pores is spherical. And there is some limitation for real materials. To simulate the real porous materials better, we use self-similarity model to analyze the dielectric constant.In this paper, fundamental concepts and theories of dielectrics are briefly reviewed firstly, then fractal geometry and fractal characters of porous media are introduced. Finally, a fractal model for the ultra low-k dielectrics is derived regarding the dielectric constant by using self-similarly fractal geometry (Sierpinski carpet). The results predicted by the present fractal model show that the model predictions are in good agreement with the available experimental data. This verifies the validity of the proposed model.