  First time-resolved photoemission experiments employing attosecond streaking
of electrons emitted by an XUV pump pulse and probed by a few-cycle NIR pulse
found a time delay of about 100 attoseconds between photoelectrons from the
conduction band and those from the 4f core level of tungsten. We present a
microscopic simulation of the emission time and energy spectra employing a
classical transport theory. Emission spectra and streaking images are well
reproduced. Different contributions to the delayed emission of core electrons
are identified: larger emission depth, slowing down by inelastic scattering
processes, and possibly, energy dependent deviations from the free-electron
dispersion. We find delay times near the lower bound of the experimental data.
