*5.2.1. Graft Polymers*

Graft copolymers are a special type of branched copolymer in which the side chains are structurally distinct from the main chain. The Figure (3) depicts a special case where the main chain and side chains are composed of distinct homopolymers.

**Figure 3.** Special cases of grafted polymer

Kung-Hwa wei et al. reported a polyimide grafted polyhedral oligomeric silsesquioxane (POSS). They presented the dielectric constants and densities of the POSS/polyimide nanocomposites (figure 4). The dielectric constants of the POSS/polyimide nanocomposites decreased as the amount of POSS increased. The maximum reduction in the dielectric constant of POSS/polyimide nanocomposites was found to be about 29%, compared to 16 mol% POSS/polyimide to pure polyimide (*k*) 2.32 vs 3.26. However, these graft polymers exhibited a slightly lower glass transition temperature about 40oC and increased thermal expansion efficient (CTE) from 31.9 ppm/K to 57.1 ppm/K after the grafting of POSS. [32]

Low Dielectric Materials for Microelectronics 69

*5.2.2. Hyperbranched Polymer* 

measured at 2 MV.

end-group functionalities and molecular weights.

Hyperbranched polymers are densely branched structures with large number of reactive groups. They are polymerized from monomers with mixed reactivities, commonly denoted A2B or A3B monomers, thus giving branched structures with exponential growth, in both

One property often mentioned of hyperbranched polymers is the non-Newtonian relationship between viscosities and molecular weight, where hyperbranched polymers showed *low viscosities* at *high molecular weights.* For coating applications, this should be highly interesting in terms of microelectronics, where they may be used as an aid in critical patterning applications for **back**-**end**-of-line (BEOL) inter-level dielectric (**ILD**) materials.

Jitendra et al. showed that dense hyperbranched carbosiloxane (HBCSO) thin films have better mechanical properties than traditional organosilicates.[34] These materials are obtained by sol-gel processing of methane-bridged hyperbranched polycarbosilanes (HBPCSs), with the incorporated methane bridges being reminiscent of the systems described above (Figure 6). For example, Young's moduli of 17-22 GPa are obtained for films with dielectric constants ranging from 2.6 to 3.1. These materials have excellent electrical properties, breakdown voltages higher than 5 MV/ cm, and leakage currents 10-8 A/cm2

It was also shown that the HBPCS structure is of considerable importance in determining

the properties of the thin films generated after sol-gel processing.

**Figure 6.** Chemical repeat units found in HBPCS precursors.

**Figure 4.** POSS/polyimide nanocomposites by grafted method

Another researcher studied about polyimide with grafted POSS structure. By introducing a polymerizable methyl methacryl functional groups to POSS and subsequent free-radical graft polymerization to an ozone treated polyimide, POSS grafted polyimide structures were obtained. Copolymers with dielectric constants approaching 2.2 could be achieved in the PI-*g*-PMA-POSS film containing 23.5 mol % MA-POSS. In this approach, POSS content could be easily tuned by the grafting ratio of MA-POSS.[33]

**Figure 5.** Synthesis of PI-*g*-PMA-POSS for low dielectrics
