## Final Activity Report Summary - PENSATO (Photo-emission of nanostructures: simulation, application, tool)

The main goal of the present project has been the description of photo-emission. In these experiments, radiation (light, X-rays) is shone on the sample which causes the emission of electrons. The latter so-called photo-electrons are collected and their energy and momentum are determined. These quantities yield information on the electronic states in the material, which in turn provides extremely useful information on the atomic structure of the samples.

For the description of photo-emission, it is necessary to take the excitation into account. As the electron is removed from the sample, the others will relax. Therefore, a many-particle theory is needed. The relaxation of the other electrons screens the generated hole.

This screening is the most difficult part of the description of photo-emission. It is given by the dielectric matrix which in turn is closely connected to the dielectric function, i.e. the frequency-dependent refractive index and the absorption spectrum. Therefore, we investigated the dielectric matrix starting from the available approximations within time-dependent density-functional theory (TDDFT). To this end, state-of-the-art experiments have been performed in collaboration with the beamline ID16 of the ESRF. The striking result was that for semi-conductors for any non-zero momentum transfer, both the electron energy loss function and the dielectric function are given with predictive quality by the adiabatic local-density approximation (ALDA) once lifetime effects are included. Moreover, our results showed that a strong mixing due to short-range interaction effects occurs for the transitions between single-particle states.

The off-diagonal elements of the dielectric matrix connect components of perturbation and total field of different wavelengths. The calculation of the spectra involves an inversion of this matrix. Therefore, all the elements of the inverse matrix contribute to each element of the matrix.

The influence of these off-diagonal terms, generally referred to as local-field effects because it is caused by the inhomogeneity of the material on the atomic scale, can in certain cases be very strong. We have, therefore, carried out explicit measurements of the off-diagonal terms in order to complete our investigation.

Following these advances (published in PRL and included in the 2008 Scientific Highlights of the European Synchrotron Radiation Facility) we are now able to calculate the dielectric matrix and the dielectric function for semiconductors with high accuracy. Together with certain technical developments (calculation of the so-called spectral function) this enables now the calculation of photo-emission spectra of a high quality, for which preliminary results exist.

A very important point in all theoretical work is the collaboration with experiment. Due to our close collaboration with the beamline ID16 at the synchrotron in Grenoble, we have been able to fine-tune the investigations which helped greatly in finding the correct interpretations of the measured data.

Another problem was to understand major deviations between theory and experiment for momentum transfer close to Bragg reflections. We have been able to show that local field effects cause an anomalous angular dependence of the spectra in these regions of momentum transfer. New experiments are planned to confirm this prediction.

The target systems of our research are nanostructures, for they show behaviour different from the corresponding bulk materials. In order to include the effects of nanostructuration, we investigate the influence of confinement (i.e. the size effect in very small structures) on the electronic screening in nanocrystals. The results of this part of our work are extremely important for the main project, the calculation of photo-emission spectra, because they help to include the correct screening in the calculations.

In conclusion, we have carried out important steps towards a complete and accurate description of photo-emission spectra. The exciting and important results of the electronic screening have led to the establishment of this topic as an independent line of research in our group.

For the description of photo-emission, it is necessary to take the excitation into account. As the electron is removed from the sample, the others will relax. Therefore, a many-particle theory is needed. The relaxation of the other electrons screens the generated hole.

This screening is the most difficult part of the description of photo-emission. It is given by the dielectric matrix which in turn is closely connected to the dielectric function, i.e. the frequency-dependent refractive index and the absorption spectrum. Therefore, we investigated the dielectric matrix starting from the available approximations within time-dependent density-functional theory (TDDFT). To this end, state-of-the-art experiments have been performed in collaboration with the beamline ID16 of the ESRF. The striking result was that for semi-conductors for any non-zero momentum transfer, both the electron energy loss function and the dielectric function are given with predictive quality by the adiabatic local-density approximation (ALDA) once lifetime effects are included. Moreover, our results showed that a strong mixing due to short-range interaction effects occurs for the transitions between single-particle states.

The off-diagonal elements of the dielectric matrix connect components of perturbation and total field of different wavelengths. The calculation of the spectra involves an inversion of this matrix. Therefore, all the elements of the inverse matrix contribute to each element of the matrix.

The influence of these off-diagonal terms, generally referred to as local-field effects because it is caused by the inhomogeneity of the material on the atomic scale, can in certain cases be very strong. We have, therefore, carried out explicit measurements of the off-diagonal terms in order to complete our investigation.

Following these advances (published in PRL and included in the 2008 Scientific Highlights of the European Synchrotron Radiation Facility) we are now able to calculate the dielectric matrix and the dielectric function for semiconductors with high accuracy. Together with certain technical developments (calculation of the so-called spectral function) this enables now the calculation of photo-emission spectra of a high quality, for which preliminary results exist.

A very important point in all theoretical work is the collaboration with experiment. Due to our close collaboration with the beamline ID16 at the synchrotron in Grenoble, we have been able to fine-tune the investigations which helped greatly in finding the correct interpretations of the measured data.

Another problem was to understand major deviations between theory and experiment for momentum transfer close to Bragg reflections. We have been able to show that local field effects cause an anomalous angular dependence of the spectra in these regions of momentum transfer. New experiments are planned to confirm this prediction.

The target systems of our research are nanostructures, for they show behaviour different from the corresponding bulk materials. In order to include the effects of nanostructuration, we investigate the influence of confinement (i.e. the size effect in very small structures) on the electronic screening in nanocrystals. The results of this part of our work are extremely important for the main project, the calculation of photo-emission spectra, because they help to include the correct screening in the calculations.

In conclusion, we have carried out important steps towards a complete and accurate description of photo-emission spectra. The exciting and important results of the electronic screening have led to the establishment of this topic as an independent line of research in our group.