## 1 Introduction  
The availability of attosecond extreme-ultraviolet (EUV) pulses enabled access to electron dynamics on their natural time scales [1; 2; 3]. This progress in laser technology opened up the new research field of attosecond science [4]. Photoionization and photoemission dynamics are studied in various systems, ranging from atoms [5; 6; 7] and molecules (for a review, see Reference [8]) to condensed matter systems like solid surfaces [9; 10; 11; 12] and nanoparticles [13]. Moreover, in this context, fundamental questions arise regarding the role and concept of time in quantum mechanics [14; 15]. Experimental access to relative delay in solid-state photoemission between different initial states triggered various theoretical approaches to understand these phenomena. Since a comprehensive ab initio many-body theory of this process is still missing, various approaches were taken to tackle different aspects of these phenomena. Among others, there are ballistic approaches [16; 17; 18] as well as approaches including influences of the crystal lattice [19; 20]. Aspects like inelastic mean free path, or excited state lifetime, respectively [18], electron-hole interaction [16], infrared (IR) field screening [21; 22], final-state effects [20; 23], coupling between Coulomb potential and light field [6; 24; 25], and intra-atomic Eisenbud-Wigner-Smith (EWS) delays [10] have also been recently investigated. The key to attosecond laser pulses is the energy upconversion of an ultrashort few-cycle near-infrared laser pulse (IR) to shorter wavelengths in the EUV regime via the high harmonic generation (HHG) process [26; 27]. Typically, an attosecond EUV burst is used to excite electrons from a bound core level or valence state into the continuum. To obtain temporal resolution, photoelectrons are probed by the fundamental IR pulse. Here, the most important techniques are the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) [2; 28], and attosecond streaking spectroscopy [29]. The main difference between these techniques is that RABBITT uses an attosecond pulse train (APT) to excite photoelectrons, while streaking spectroscopy is based on excitation with a single-attosecond pulse (SAP). In both cases, the time delay between the EUV and IR pulse is varied to obtain an energy- and time-resolved spectrogram. The photoemission process can be envisioned as follows: The EUV pulse (train) excites a wave packet from an initial state \(\Phi_{0}(z)\) into a final state inside the material (Figure 1). However, because of the different time structure and corresponding EUV energy spectrum, the generated electron-wave packets exhibit different momentum or kinetic-energy distributions. In a streaking experiment, excitation with a single-attosecond pulse led to broad excitation-energy distribution in the order of several eV (Figure 1a), whereas in RABBITT the femtosecond envelope of the APT resulted in a highly modulated distribution that exhibited rather narrow spectral features (Figure 1b). Because of the HHG process, these spectral features are separated by twice the fundamental photon energy. In both cases, the so-generated continuum electron wave packet \(\Phi(z)\) propagates towards the surface. Note that the part of the wave packet that propagates into the bulk is irrelevant for the simulations considered here and is therefore not shown in Figure 1. If the wave packet was excited by a single-attosecond pulse, a single electron wave packet travels to the surface. In case of excitation by an APT, a train of electron pulses moves toward the surface, where they are emitted into the vacuum. Figure 1: Principle of **(a)** as-streaking and **(b)** reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) at solid surfaces: Initial state \(\Phi_{0}(z)\) is excited into the continuum by a single-attosecond extreme-ultraviolet (EUV) pulse (green) or by an attosecond pulse train (red), respectively.