We report designs for a silicon-on-insulator (SOI) one-dimensional (1D) photonic crystal (PhC) nanocavity with modulated mode-gap barriers based on the lowest dielectric band. These cavities have an ultrahigh theoretical quality factor (Q) of 10(7)-10(8) while maintaining a very small modal volume of 0.6-2.0 (lambda/n)(3), which are the highest Q for any nanocavities with SiO(2) under-cladding. We have fabricated these SOI 1D-PhC cavities and confirmed that they exhibited a Q of 3.6 x 10(5), which is also the highest measured Q for SOI-type PhC nanocavities. We have also applied the same design to 1D PhC cavities with air claddings, and found that they exhibit a theoretical quality factor higher than 10(9). The fabricated air-cladding 1D Si PhC cavities have showed a quality factor of 7.2 x 10(5), which is close to the highest Q value for 1D PhC cavities.