We propose a novel type of photonic crystal cavity with a flattened and elongated central hole. The confinement capability of the cavity for the TE mode is studied using the 2D-FDTD method. The holes immediately around the cavity are shifted in a space modulation scheme in order to optimize the confinement capability of the proposed cavity. The change in the spatial confinement as well as quality factor of the cavity with respect to modulation depth are studied and reported. The ferroelectric Barium Titanate (BaTiO3), which has a large electrooptic coefficient, is used as the base material of the proposed cavity. The effect of applied bias on the properties of the cavity is also studied. To make the calculations as realistic as possible, the dispersive and absorptive nature of the material has been taken into account. Despite the absorptive nature of BaTiO3 as well as the finite extent of the photonic crystal, the calculated quality factor compares favorably with previously reported values in literature.