We compute spectrograms and relative time delays for laser-assisted photoemission by single attosecond extreme ultraviolet pulses from valence band (VB) and 2p core levels (CLs) of a Mg(0001) surface within a quantum-mechanical model. Comparing the time-dependent dispersion of photoelectron (PE) wave packets for VB and CL emission, we find striking differences in their dependence on the (i) electron mean free path (MFP) in the solid, (ii) screening of the streaking laser field, and (iii) chirp of the attosecond pulse. The relative photoemission delay between VB and 2p PEs is shown to be sensitive to the electron MFP and screening of the streaking laser field inside the solid. Our model is able to reproduce a recent attosecond-streaking experiment [S. Neppl et al., Phys. Rev. Lett. 109, 087401 (2012)], which reveals no relative streaking time delay between VB and 2p PEs. DOI: 10.1103/PhysRevLett.112.023602 PACS numbers: 42.50.Hz, 42.65.Re, 79.60.-i During the past decade, the combination of either an isolated attosecond extreme ultraviolet (XUV) pulse [1,2] or a train of attosecond XUV pulses [3] with a synchronized delayed femtosecond (fs) near-infrared (NIR) laser pulse has allowed the measurement of apparent photoemission time delays in the laser-assisted XUV photoionization of atoms in the gas phase [2,3] and on solid surfaces [4,5]. Apparent relative photoemission delays are of the order of tens of attoseconds (1 as ¼ 10 −18 s) [2,4] or less [5] and yield information on the (i) primary XUV photoabsorption process, (ii) influence of the NIR-laser field, (iii) residual charge of the target [6], (iv) electronic correlation [7], and (v) collective (plasmonic) excitation processes on the PE propagation [8]. The temporal and spectral structure of both, electron wave packets and attosecond XUV pulses can be characterized based on streaked PE spectra [9,10]. NIR-laser-streaked XUV photoemission thus holds promise to enable the scrutiny of electronic dynamics in atoms and solids with unprecedented time resolution at the natural time scale of the electronic motion in matter [11,12].Compared to gaseous atomic targets, the modeling of photoemission from solids is more challenging due to a complex electronic band structure [4,13,14], elastic and inelastic collisions inside the substrate [15][16][17], the screening of the NIR streaking field inside solids [16,17], and surface and bulk plasmon excitations [8,18]. In a first, proof-of-principles experiment on solids, a relative photoemission delay of Δτ VB−4f ¼ 110 AE 70 as between PEs emitted from the valence band (VB) and 4f core levels (CLs) of a W(110) surface was deduced from streaked PE spectra [4], initiating comprehensive theoretical studies [13][14][15][16][17]19,20]. Employing classical transport theory, the 4f PEs were traced to be slower, originate in deeper layers than VB PEs, and thus need more time to escape through the surface [4,15]. Based on quantum-mechanical calculations, the measured relative time delay Δτ VB−4f was interpreted as a result of the di...