Low-k porous dielectrics for microelectronics Interconnect technologies need lower $\epsilon_r$, interlayer
dielectrics (ILDs) to minimize the interconnect capacitances. These materials are called low-k dielec-
trics. Consider fluorinated silicon dioxide, also known as fluorosilicate glass (FSG), which has an $\epsilon_r$
of 3.2. Using Equations 7.96, 7.97, 7.102, calculate the expected effective dielectric constant if the
ILD is 30 percent porous?
$\epsilon_{r1} = 1$
$\epsilon_{r2} = 3.2$ (host dielectrics) $v_1 = 0.3$
Eq. 7.96 logarithmic mixture rule (Lichtenecker formula)
$\ln \epsilon_{r,eff} = v_1 \ln \epsilon_{r1} + (1 - v_1) \ln \epsilon_{r2}$
Eq. 7.97 Maxwell-Garnett formula
$\frac{\epsilon_{r,eff} - \epsilon_{r2}}{\epsilon_{r,eff} + 2\epsilon_{r2}} = v_1 \frac{\epsilon_{r1} - \epsilon_{r2}}{\epsilon_{r1} + 2\epsilon_{r2}}$
Eq. 7.102 Bruggeman mixture rule
$v_1 \frac{\epsilon_{r1} - \epsilon_{r,eff}}{\epsilon_{r1} + 2\epsilon_{r,eff}} + (1 - v_1) \frac{\epsilon_{r2} - \epsilon_{r,eff}}{\epsilon_{r2} + 2\epsilon_{r,eff}} = 0$
