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This work presents a novel synthesis process for locally growing carbon nanotubes on specific surface area using micro-machined heaters in a room temperature quartz tube. The temperature difference between the heating area (~600 degC) and the bulk silicon substrate (200 degC) is about 400 degC. Therefore, this process is compatible with on-chip microelectronics. The detailed micro-heater fabrication processes are presented. CNTs were synthesized using a chemical vapor deposition technique by varying the supplied power of the micro-heaters. Patterned iron film (10 nm) is used as the catalyst. We have demonstrated the capability of growing aligned carbon nanotube bundles with an average length of 75 mum and diameter of 30 mum by using this heater. The CNT growth rate was about 5 mum/min and the whole CNT synthesis can be completed within half an hour. This effective and rapid process facilitates the integration of carbon nanotubes in localized area within a larger-scale system.