Electrons at surfaces of crystalline matter have been widely investigated using photoemission and inversephotoemission spectroscopies. These techniques require samples to be at high vacuum before measurements can be performed. Optical spectroscopies in the visible range of the electromagnetic spectrum provide an alternative means of probing electrons at surfaces without the need for ultrahigh vacuum. They can therefore be used in 'dirty' environments such as semiconductor growth chambers where there are high levels of background gases.
Electronic excitations at surfaces can be distinguished from electronic excitations in bulk matter if the bulk is isotropic (the same in all directions) and the surface is anisotropic (different in two perpendicular directions in the surface). The electric field in a planepolarised light wave points in a definite direction. Measuring the difference in reflectivity of the surface to planepolarised light with the electric field directed along two anisotropic directions in the surface yields a signal which is determined by excitation of electrons at the surface alone. The isotropic bulk electron excitations yield no signal. The technique of reflectance anisotropy spectroscopy (RAS) is therefore a means of probing excitations of electrons localised at surfaces.
Dielectric function of bulk Ge using a hybrid density functional theory approach
Our density functional theory calculations of RAS for a range of well studied and less well understood surfaces shows that experimental RAS signals can be reproduced and attributed to electrons localised at particular atoms at the surface. We are now investigating whether optical spectroscopies of surfaces can be used to identify high levels of specific defects at surfaces such as oxygen or cation vacancies.
The approach that we use for calculating optical spectra of materials is hybrid density functional theory within a Gaussian orbital basis in the Crystal code. Hybrid density functionals allow the generic band gap problem of density functional theory to be corrected by mixing in a fixed proportion of Fock exchange. The Gaussian orbital basis offers a fast calculation method and therefore makes large unit cells accessible. Here is our work on reflectance anisotropy at clean and adsorbatecovered Ge(001) surfaces.

Surface states at the Si(001)c(4x2) surface
RA at clean Si(001) surfaces is mainly caused by dangling bond electrons in surface states localised at surface dimer atoms. It has been extensively studied, both in experiment and numerical calculations. Our hybrid DFT approach applied to the Si(001)c(4x2) surface yields excellent agreement with experimental RA measurements. The figure below shows how much the RA signal from the Si(001) surface depends on dimer order, according to our hybrid DFT calculations.
RA spectra for reconstructed Si(001) surfaces from hybrid DFT calculations
The Si(111) surface forms ordered phases with many simple metal and transition metal adsorbates. We have calculated the RA spectrum of Si(111)(3x1) Li and Ag surfaces and found good agreement with experimental measurements performed by the TCD Surface Physics Group. This work was sponsored by Science Foundation Ireland under grant number RFP/11/PHY/3047.
Recently we have begun to work on optical spectroscopies of oxide surfaces. The anatase TiO_{2}(001) surface reconstructs to form a (4x1) structure in which an extra TiO_{2} row is inserted periodically, as shown below.
Anatase TiO_{2}(001)(4x1) reconstructed surface
The reflectance anisoropy for this surface has been calculated and is shown below. Full details of this calculation are given in our paper in J. Phys. Condens. matter.
This work was sponsored by Science Foundation Ireland under grant number RFP/09/MTR/2295. 