Photoemission Spectroscopy (also known as Photoelectron Spectroscopy, PES) probes the energy levels of electrons, or more in general, the nature of chemical bonding and electron motion in a substance. PES is based on the Photoelectric Effect, which means that when light impinging on a surface is absorbed it induces the emission of electrons. Together with the related Auger spectroscopy, the PES technique is commonly referred as Electron Spectroscopy for Chemical Analysis (ESCA) and was pioneered by Swedish physicist Kai Siegbahn.


The electronic transitions are selected by tuning the energy of the incident radiation (a). The electrons bring information via the Kinetic Energy, the direction of the momentum (the angle between the impinging radiation and emitted electrons, and their angle with the surface) and spin (b). The basic relation is $E_k=h\nu-\Phi-E_b$, with $\Phi$ the work function, $\nu$ the light frequency, and $E_b$ the binding energy. Photoelectrons suffer elastic/inelastic scattering when leaving the sample. The escape depth in solids is only few Ångström. This sometimes makes it problematic to separate surface and bulk contributions. In an atom excited by X rays, the main structures in the spectrum are due to photoelectrons. There are however also other peaks, of similar width but different energy, unrelated to incident photons, due to Auger recombination (c). In a proper theoretical formulation, PES and the Auger recombination should be treated on equal footing as a single coherent process.
In a theory of energy and angle resolved photoemission, a basic quantity of interest is the spectral function $A(q,E)=-\frac{1}{\pi}\frac{Im \Sigma(q,E)}{[E-\epsilon_q-Re\Sigma(q,E)]^2+Im\Sigma(q,E)^2}$, where $\epsilon_q$ is the one-body part and $\Sigma(q,E)$ accounts for the self-energy corrections. The quantity $A(q,E)$, to be compared to experimental PES spectra, is computed at the ab-initio level, and incorporates the information about the electronic energy bands, about the effects of correlation between electrons, the structure of the Fermi surface, the role of lattice vibrations (and in a more general form) about spin ordering.
Traditional radiation sources are X-ray (XPS) and ultraviolet radiation (UPS). The use of synchrotron radiation has made such division somewhat conventional. In synchrotron sources the photon energy can be chosen continuously over a wide energy range. Other qualities of synchrotron light are high brightness and intensity, tunable polarization, the feasibility of short time-scale, time-resolved experiments.
A comparison between theory and experiment for the KL$_{23}$V Auger spectra of Na/Al(111). For such a system, the different Na adsorption geometries, on changing the adatom fractional coverage and the substrate growth temperature, are known.

Panel (a): The Na (√3×√3) R30º phase (1/3 ML). Calculated (solid line) and measured (red circles) KL$_{23}$V Auger profiles. The calculated curve, normalized to the experimental data, is obtained convolving the Auger rate with a Lorentzian with half width equal to 0.42 eV for the core hole lifetime and a Gaussian for nominal instrumental broadening. The measured one is shown after background subtraction. Panel (b): the Na 2×2 phase (1/2 ML). Calculated (solid line) and measured (blue circles) KL$_{23}$V Auger profiles. The calculated curve is obtained as in panel(a), but summing the contributions from the two inequivalent Na atoms.
The experimental and theoretical KL$_{23}$V spectra show a remarkable agreement. For the 1/3 ML, in panel a), both theoretical and experimental spectra display a main feature of the same shape and intensity. On the other hand, to fit the experiments for the 1/2 ML phase, it is necessary to sum up the contributions of the two theoretical spectra obtained from the inner and outer inequivalent Na atoms. The best fit was obtained by shifting the Auger spectrum of the outer atom by -0.5 eV, and assigning a weight of 3/8 to the outer Na atom signal and 5/8 to the inner one. The weight ratio between the two Na components is in agreement with the analysis of the relative height of the XPS signal. It is interesting to note that this result suggests a different population for the Na atoms in the two inequivalent sites.(after M. I. Trioni, S. Caravati, G. P. Brivio, L. Floreano, F. Bruno, and A. Morgante , Physical Review Letters 93, 206802 (2004)

Theoretical calculations of Angle-Resolved PhotoEmission Spectra can achieve a very high level of accuracy, even for complex materials. In the figure, experimental measurements are compared against different theoretical predictions for bulk Cu$_2$O, a rather complicated material containing d-electrons. The levels of theory employed here are the standard Local-Density Approximation, the GW method, and the "self-consistent GW" (SCGW). In the panel a), the experimental spectrum is compared with the calculated density-of-states within the SCGW. The panel b) provides angle-resolved experimental data as a color plot in the background. The different levels of theoretical treatment, going from the simplest, LDA (grey lines), to GW (black lines) and self-consistent GW (red diamonds) show a consistent improvement when increasing the complexity of the calculations. The SCGW results show a quantitative level of accuracy (after F. Bruneval et al., Phys. Rev. Lett. 97, 267601 (2006) ).

The full three-dimensional dispersion of the $\pi$-bands of graphite measured with angle-resolved photoemission spectroscopy (ARPES) and compared to first-principles calculations. The figures a) and b) are cuts through the H point along the k$_y$ direction, whereas the figures c) and d) are equi-energy contours of the photoemission intensity around the KH axis. The red lines represent the density functional theory (LDA) band structure that underestimates the slope of the bands and the trigonal warping effect. Including electron-electron correlation on the level of the GW approximation (blue lines) renormalizes the Fermi velocity by more than 17%, and yields remarkable improvement with the experiments (A. Grüneis, C. Attaccalite et al. Phys. Rev. Lett. 100, 037601 (2008) )

The PES of vapor-phase C60, as measured by Canton et al. [1] and by Bruhwiler et al. [2], compared with calculation based on a Lanczos determination of the Green's function of the hole created in the highest occupied molecular orbital, and taking into account its interaction with the molecular vibrational modes. The calculation takes the vibrational frequencies and electron-vibration couplings from the ab-initio determination of Ref. [3], and samples randomly the thermal population of the initial molecular vibrational states at the experimental temperature T=800 K. All spectra are shifted to have the main peak at zero energy. The two main structures reflect the 0-vibron and 1-vibron lines of the two high-frequency Hg modes below 200 meV, and suffer a blue shift characteristic of the dynamical Jahn-Teller effect due to the degenerate orbital state of the hole. The broad global nature of the spectrum is mostly related to many-vibration incoherent excitations of the strongly-coupled low-energy Hg mode (after N. Manini et al., Phys. Rev. Lett. 91, 196402 (2003) ) .
[1] P. Bruhwiler et al., Chem. Phys. Lett. 279, 85 (1997).
[2] S. E. Canton et al., Phys. Rev. Lett. 89, 045502 (2002).
[3] N. Manini et al., Philos. Mag. B 81, 793 (2001).
The photoelectric effect, in which electrons are emitted from matter after absorption of light, is a quantum phenomenon, discovered by Heinrich Rudolf Hertz in 1887. The theoretical description by Albert Einstein in 1905 was a major boost to the promotion of the quantum concept of wave-particle duality of light. Accordingly, light is absorbed in quanta (photons). Increasing the beam intensity increases the number of photons, and the number of electrons emitted. The energy of the emitted electrons depends on the photon energy, but not on the light intensity. All of the energy from one photon must be absorbed; part is spent to free the electron from the atom, whilst the rest goes into the electron's kinetic energy as a free particle.