A method for making a carbon nanotube-based device is provided. A substrate with a shadow mask layer formed thereon is provided, to define an unmasked surface area on the substrate. The substrate is rotated around an axis. A catalyst layer including at least one catalyst block is formed on the unmasked surface area of the substrate. A thickness of the at least one catalyst block is decreased gradually from a first end thereof to an opposite second end thereof, and somewhere the at least one catalyst block having a region with a thickness proximal or equal to an optimum thickness at which carbon nanotubes growing fastest. A carbon source gas is introduced. At least one carbon nanotube array extending from the catalyst layer using a chemical vapor deposition process is formed. The at least one carbon nanotube array is arc-shaped, and bend in a direction of deviating from the region.