Theoretical study on the dielectric constant of interlayer dielectrics

Propagation delay of signals by interlayer dielectrics in LSI interconnects is
becoming a dominant issue. Materials of low dielectric constant have been
widely studied in order to reduce the delay of signals. In this study we try
to design theoretically novel low-k materials based on ab initio quantum
chemical methods and the density functional perturbation theory (DFPT).
The Clausius-Mossotti equation shows that dielectric constants are related to
polarizabilities of materials and a low dielectric constant corresponds to a
small polarizability and a small number density of a material. We calculated
molecular volumes and polarizabilities of oligomers: hydrocarbon C_{n}H_{2n+2} and
fluorocarbon C_{n}F_{2n+2}, based on the HF, MP2 and B3LYP methods using the 6-31G**
basis set. Dielectric constants of their polymers were then obtained by
extrapolation. Quantum chemical calculations have been carried out using the
program GAUSSIAN98. Next, we applied the DFPT to the calculation of dielectric
constants of periodic organic polymers using pseudopotential. Calculations
have been carried out using the program ABINIT. The results nicely agree with
that of quantum chemical calculations.
We are currently studying amorphous carbon nitrides, a-CN_{x},
which are noticed
as potential low-k materials. The x-dependence in dielectric constants of
CN_{x} will also be discussed.