Increasing demand for ultrahigh-density data storage devices has fueled significant interest in the probe-based data storage devices and FeRAM using ferroelectric thin films. However, in order to achieve over terabit storage density, the writing scheme of independent nanometer domains is required. Conventional top-down process including FIB or etching process is complex and difficult to achieve nano-scale $PbTiO_3$ dot arrays without lattice damages. Bottom-up process using self-assembly technique is one of the promising approaches to fabricate $PbTiO_3$ nanostructures. Herein, ferroelectric $PbTiO_3$ nanostructures have been fabricated using two different procedures that involve gas phase reaction using sputter and furnace onto self assembled $TiO_2$ dot arrays. The first procedure enables the fabrication of structures with smaller size as observed by Atomic Force Microscopy (AFM) topography and quantitative analysis, contrary to the second procedure. The ferroelectric character of the nanostructures is demonstrated using Piezoelectric Force Microscopy (PFM). The ferroelectric properties were degraded due to the $TiO_x$ layer showing low piezoresponse values and leakage behaviors, revealed by the piezoelectric hysteresis loops. However, it was observed clear signals in amplitude and phase images at the condition of furnace / $600\degC$. As the PbO penetrates deeper into the $TiO_x$ layer than any other conditions, the thicknesses of the unreacted $TiO_x$ layer get decreased. From these results, it was concluded that the $TiO_x$ blocking layer caused a degradation of piezoelectric properties and a research for the condition of pure $TiO_2$ (without blocking layer) onto the bottom electrode is needed for the potential application of FRAM and probe based data storage devices.