  We analyze the influence of the dielectric constant of the slab on the
quality factor (Q) in slab photonic crystal cavities with a minimized vertical
losses model. The higher value of Q in high-epsilon cavity is attributed to the
lower mode frequency. The Q ratio in a high-epsilon (silicon) vs. low-epsilon
(diamond) slab is examined as a function of mode volume (Vm). The mode volume
compensation technique is discussed. Finally, diamond cavity design is
addressed. The analytical results are compared to 3D FDTD calculations. In a
double heterostructure design, a Q=2.6*10^5 is obtained. The highest Q=1.3*10^6
with Vm=1.77*(lambda/n)^3 in a local width modulation design is derived.
