A class of Zn4O(CO2)6-based metal-organic frameworks (MOFs) is theoretically analyzed with respect to suitability as an interlayer dielectric material for applications in semiconducting devices. The static dielectric constant is calculated using the Clausius–Mossotti approach. For 3 of about 30 of the considered MOFs excellent combinations of ultralow dielectric constant, elastic bulk modulus, and gap energy are found favoring these materials as outstanding candidates for future ultralow-k dielectric materials.

No abstract

No abstract

No abstract

In molecules with ionic contributions to the binding, the contribution of nuclear displacements ͑due to the external field͒ to the static polarizability can be decisive. Using the finite field method, we optimized the structure with and without a finite external electric field by a total energy minimization and we calculated the polarizability from the induced dipole moment. In C 60 F n , fluorination mostly increases the polarizability. Only for n = 2 and 18, where the molecule without an external field has a very large dipole moment, does fluorination decrease it. For large n ͑n = 20, 36, and 48͒, the polarizability per added F atom due to nuclear displacements is increased by a factor of about 2. The validity of the additivity model has been discussed.The static dielectric constant ͑DC͒ is an important parameter, in particular, for microelectronics. Additivity models suggest that fluorination should decrease the DC of carbon compounds ͓1͔, but quantitative results are hard to predict for unique systems such as fullerenes from empirical data based on classical molecules. Additionally, the clear distinction between the electronic ͑or optical͒ and truly static polarizabilities has not always been made in these tables. Therefore, we decided to perform first principle calculations and thereby to check the validity of the additivity model in the groups of molecules under consideration.The first principle calculation of the static DC of a macroscopic system is a nontrivial task. Despite the fact that there are microscopic theories for the electronic DC ͓2-4͔, as well as for the static DC ͓5-7͔, which include, in principle, all exchange and correlation corrections as well as the local field corrections, for complex systems we have to look for simplified schemes. As long as we can identify certain weakly interacting molecules within the condensed system, as in the Van der Waals crystals, liquids or gases, we can base our calculation on the molecular polarizability ␣ defined bywhere p ind is the induced dipole moment in the molecule and E loc is the local electric field at the molecule, which includes the induced fields of all neighboring molecules. This field is considered to be constant within the molecule. p and p 0 are the total dipole moments with and without the applied electric field, respectively. If we replace the neighboring molecules by a polarizable continuum with a spherical cavity surrounding the considered molecule, we obtain the dielectric constant ⑀ from the Clausius-Mosotti formula ͑see, e.g., ͓8͔͒This approach could be refined by introducing elliptical ͓9͔ and arbitrarily shaped cavities ͓10-15͔. In the approximation leading to ͑2͒, the DC is controlled by two ingredients: the number density of molecules N / V and the molecular polarizability ␣, where the latter is the focus of this paper. For the calculation of ␣ there are several approaches. ͑i͒ In the additivity model ͓16-18͔ each atom or bond contributes a certain amount to the total polarizability, irrespective of their location and surroundings....