Ultrafast photocurrent measurements are performed on individual carbon nanotube p-i-n photodiodes. The photocurrent response to subpicosecond pulses separated by a variable time delay Δt shows strong photocurrent suppression when two pulses overlap (Δt=0). The picosecond-scale decay time of photocurrent suppression scales inversely with the applied bias V SD, and is twice as long for photon energy above the second subband E 22 as compared to lower energy. The observed photocurrent behavior is well described by an escape time model that accounts for carrier effective mass. © 2012 American Physical Society.