A capacitor of a memory device is formed on a semiconductor substrate having transistors thereon. A mold layer having holes defined therein is formed on the semiconductor substrate. A catalytic metal layer is formed proximate to a bottom boundary of each hole. Reaction gas is fed to the catalytic metal layer to form carbon nanotubes via a catalytic reaction of the reaction gas by the catalytic metal layer. After forming a lower electrode layer proximate to the bottom boundary and sidewall of each hole and over the carbon nanotubes, a dielectric layer is deposited over the lower electrode layer. Upper electrodes are formed on the dielectric layer to form capacitors electrically connected to the transistors.