The current invention provides methods of fabricating a capacitive micromachined ultrasonic transducer (CMUT) that includes oxidizing a substrate to form an oxide layer on a surface of the substrate having an oxidation-enabling material, depositing and patterning an oxidation-blocking layer to form a post region and a cavity region on the substrate surface and remove the oxidation-blocking layer and oxide layer at the post region. The invention further includes thermally oxidizing the substrate to grow one or more oxide posts from the post region, where the post defines the vertical critical dimension of the device, and bonding a membrane layer onto the post to form a membrane of the device. A maximum allowed second oxidation thickness t2 can be determined, that is partially based on a desired step height and a device size, and a first oxidation thickness t1 can be determined that is partially based on the determined thickness t2.