How missing linkers affect the dielectric constant of HKUST-1

The rapid development of ultra-largescale integration (ULSI) and the continuous miniaturization of feature sizes of integrated circuits approaching the nanometer (nm) scale, suggest that ultra-low dielectric constant materials will be needed, instead of the traditional SiO2 (k = 3.9). Metal-organic materials (MOFs) have features like elastic void accessibility, chemical/thermal/mechanical stability and low polarizability from the light composition. Therefore, appropriately designed MOFs promise to be the next generation of interlayer low-dielectric materials with the potential to be extremely porous, inert, and insulating. The polarization can generally be separated into different contributions: (i) electronic polarization, (ii) ionic polarization, and (iii) orientation polarization. In classical molecular dynamics (MD) simulations with non-polarizable force fields, the first contribution is absent. The HKUST-1 ({Cu3(BTC)2}n (BTC = 1,3,5-benzenetricarboxylate)) shows the lowest dielectric constant of 1.717 proved by our group previous work, so it was used to be further defect-engineered. As described above, the molecular mechanics force fields ignore the electron polarization; therefore, Drude oscillator model was selected here to be configured with UFF4MOF force field. It was proved that this combination can accurately predict the dielectric constant of pristine HKUST-1, comparing with the one calculated by quantum mechanical approach. In this work, we focused on one modulator as source of defects for HKUST-1, namely formic acid (FA). FA is a mono-dentate linker, whereas BTC is tri-dentate, therefore a partial replacement of BTC implies two missing coordination modes to Cu. In the simulations, BTC linker was partially replaced by FA, producing defect concentrations up to 50%. These defects were introduced in various random spatial arrangements, and the resulting dielectric constant was averaged across those configurations. These simulations show that the defect strategy has a substantial impact on the dielectric constant in HKUST-1. For example, a defect density of 50% induces a 16.4% reduction of the dielectric constant. This is due only to the reduced polarizability, whereas the volume is only slightly affected. The volume was shapely contracted (by 10.3%) for 50% defect case, while it still can give the lowest dielectric constant. It is attributed to the even more significant reduction of polarizability due to the less dense components. Moreover, different cell size was simulated to give a little difference. By offering molecular-level insights, this framework not only advances fundamental understanding of dielectric behavior in MOFs but also establishes a foundation for rational design strategies—ranging from linker modulation for sensor development to the methodical tailoring of dielectric response for energy-related applications.