A planar-type single electron transistor (SET) was fabricated by the atomic force microscopy (AFM) nano-oxidation process. The fabricated SET showed the Coulomb oscillation characteristic with the period of about 2 V at room temperature. From the three-dimensional simulation, it is found out that the smaller the SET island size, the smaller the tunnel junction capacitance, and the tunnel junction capacitance shows a weak dependence on the tunnel junction width. Using the analytical model, the reason for this weak dependence was clarified.