A method for manufacturing carbon nanotubes with an integrally attached outer graphitic layer is disclosed. The graphitic layer improves the ability to handle and manipulate the nanometer size nanotube device in various applications, such as a probe tip in scanning probe microscopes and optical microscopes, or as an electron emitting device. A thermal chemical vapor deposition reactor is the preferred reaction vessel in which a transition metal catalyst with an inert gas, hydrogen gas and a carbon-containing gas mixture are heated at various temperatures in a range between 500 C. and 1000 C. with gases and temperatures being adjusted periodically during the reaction times required to grow the nanotube core and subsequently grow the desired outer graphitic layer.