An ultimate pressure of the order of 10(-12) Torr using a turbomolecular pump was realized. The ultimate pressure of a turbomolecular pump with magnetic bearings is mainly limited by outgassing from heat generation of the rotor. The rotor temperature in operation is about 60-degrees-C due to eddy-current loss in the magnetic suspensions. The rotor temperature was measured by thermovideo camera through an optical window. To reduce thermal outgassing of the rotor, the rotor must be cooled by radiation. The lower half of the rotor and the opposite stators were coated with SiO2 to a thickness of about 10 mum. This ceramic surface has high emissivity and good thermal heat exchange. The suspended rotor temperature during operation then dropped to about 25-degrees-C. Also, the SiO2 coating enabled the rotor to be baked with more efficiency. The upper half of the rotor and the stators, and aluminum alloy housing were finished using a clean machining method known as the EL process, which helped reduce outgassing. These processes were applied by Seiko-Seik and Osaka Vacuum. Ultimate pressure of the turbomolecular pumps with turbobacking were of the order of 10(-12) Torr, measured by a Leybold extractor gauge; best pressure was less than 2 X 10(-12) Torr.