  We observe trion emission from suspended carbon nanotubes where carriers are
introduced electrostatically using field-effect transistor structures. The
trion peak emerges below the $E_{11}$ emission energy at gate voltages that
coincide with the onset of bright exciton quenching. By investigating nanotubes
with various chiralities, we verify that the energy separation between the
bright exciton peak and the trion peak becomes smaller for larger diameter
tubes. Trion binding energies that are significantly larger compared to
surfactant-wrapped carbon nanotubes are obtained, and the difference is
attributed to the reduced dielectric screening in suspended tubes.
