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For the 8-nm barrier sample, we calculate that the energy separation between (Formula presented) and (Formula presented) is 47-52 meV for the bias range over which excited state emission is observed (1780-1850 meV). This is very close to the Γ-point LO phonon energy in AlAs enabling intersubband scattering to be mediated by zone center LO phonon emission. Such intersubband scattering by small wave-vector phonons is expected to be very fast, proceeding over typical time scales of several hundred femtoseconds [R. Ferreira and G. Bastard, Phys. Rev. B 40, 1074 (1989)];
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By contrast, (Formula presented) inequivalent intervalley scattering requires the participation of large-wave-vector acoustic and optical phonons and is expected to take place over time scales longer than a picosecond [S. Zollner, S. Gopalan, and M. Cardona, J. Appl. Phys. 68, 1682 (1990)]. Thus, electrons transferring into (Formula presented) states are expected to remain in the longitudinal X states until (Formula presented) transfer occurs.
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