Angle-resolved photoemission, valence-band dispersionsE(k→), and electron and hole lifetimes for GaAs

Abstract

Accurate valence-band dispersions $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ along the major symmetry directions $\ensuremath{\Gamma}\ensuremath{-}K\ensuremath{-}X$, $\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Delta}\ensuremath{-}X$, and $\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Lambda}\ensuremath{-}L$ have been determined for GaAs using simple angle-resolved photoemission techniques of general utility with synchrotron radiation for $25\ensuremath{\le}h\ensuremath{\nu}\ensuremath{\le}100$ eV. At these photon energies, emission features can be understood within the direct-transition model, and spectral peaks can be classified roughly into two categories: one being those associated with primary cone emission with a lifetime-broadened free-electron-like final-state dispersion, and the other (usually weaker) being those associated with secondary cone-surface umklapp emission which emphasizes valence-band critical points with high state densities. Valence-band dispersions $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ along the $\ensuremath{\Gamma}\ensuremath{-}K\ensuremath{-}X$ symmetry line perpendicular to the surface are determined using normal-emission spectra (primary cone peaks) from the (110) surface at various photon energies. Valence-band dispersions $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ along $\ensuremath{\Gamma}\ensuremath{-}K\ensuremath{-}X$, $\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Delta}\ensuremath{-}X$, and $\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Lambda}\ensuremath{-}L$ symmetry lines parallel to the surface are determined using off-normal emission spectra (primary cone peaks) from the same (110) surface with fixed perpendicular component of the electron momentum $\ensuremath{\hbar}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\perp}}$ at a zone center (extended-zone scheme) and varying parallel component of the electron momentum $\ensuremath{\hbar}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$, which are obtained by suitably varying $h\ensuremath{\nu}$ and emission angles. Experimental valence-band dispersions and critical points are compared with other theoretical and experimental results. Simple formulas are derived to relate the widths of spectral peaks to electron and hole lifetimes. Initial hole lifetimes at valence critical points and typical final electron lifetimes are obtained. The latter yields final-state momentum broadenings (typically \ensuremath{\lesssim} 10% of the Brillouin-zone size) which are consistent with the direct-transition model.