Continuous-wave spectroscopy of femtosecond carrier scattering in GaAs

We show that cw luminescence spectroscopy of the cascade of electrons in the conduction band of III-V compound semiconductors relaxing by LO-phonon emission yields information on the band structure, on electron-phonon, electron-electron, and intervalley scattering rates, and on impurity levels at higher-conduction-band minima in III-V compound semiconductors. The luminescence emitted by electrons recombining with holes on acceptors shows a series of up to nine very pronounced peaks directly measuring the steady-state distribution of electrons, while they cascade to the bottom of the conduction band in a few hundred femtoseconds. We determine the lifetime broadening by comparing the high-resolution cw hot-electron luminescence spectra with theoretical line shapes, calculated using a double-δ-function k-space integration, 16×16 k⋅p band structure, and transition-matrix elements in the dipole model. We determine an electron–LO-phonon scattering time of ${\tau }_{\mathrm{LO}}$=(132±10) fs, and Γ→L scattering times between ${\tau }_{\Gamma \to L}$=150 and 200 fs. We obtain $D_{\Gamma \to L}$=(9.5±1.5)×${10}^8$ eV/cm for the related deformation potential. We show how temperature-dependent scattering times, and electron-density–dependent scattering (i.e., electron-electron scattering) can be studied with the same method. Thus, we measure ultrafast processes by cw luminescence spectroscopy which are too fast or too weak for the sensitivity of present-day femtosecond spectroscopy. Unlike experiments using ultrashort laser pulses, the present method can study ultrafast (femtosecond) relaxation processes under low and high carrier concentration and with high spectral resolution.