Nanoporous low-k Dielectrics

Interlayer dielectric materials isolate electrically conducting and semi-conducting features in integrated circuits.

Their properties become more and more important with shrinking interconnect dimensions due to increasing interconnect-related circuit delay. New dielectric materials with low dielectric constant k (low-k dielectrics) are needed to reduce this delay. One way to achieve progress in this direction is to introduce pores on a nanometre scale. Increasing volume fraction of pores reduces the dielectric constant, however, it also reduces the mechanical strength of the dielectric material. Therefore, a compromise between low k values and sufficient mechanical properties is needed.

Fig. 1: closed pore structure (a) open pore structure (b)

With respect to the geometrical arrangement we choose the model of randomly packed hard spheres [2,3]. The spheres and the space between them represent the pores and the solid material, respectively. The transition from a closed-pore structure to a system of interconnected pores [Fig. 1] can be carried out in the model by increasing the radii of the spheres at fixed coordinates. Our procedure for the computer simulation of packings of hard spheres is based on the force-biased algorithm [2,4,5] generalised for arbitrary size distributions.

References:

[1] H. Hermann, A. Elsner, M. Hecker, D. Stoyan, Microelectronic Engineering 81 (2005) Nr. 2-4, S. 535-543 URL

[2] A. Bezrukov, M. Bargiel, D. Stoyan, Part. Part. Syst. Charact. 19 (2002) 111–118.

[3] H. Hermann, Stochastic Models of Heterogeneous Materials, Trans Tech Publ., Zürich, 1991.

[4] W.S. Jodrey, E.M. Tory, J. Simulat. 32 (1979) 1–12

[5] J.Moscinski, M.Bargiel, ComputerPhys.Comm. 64, 183 (1991)