The interfaces between two condensed phases often exhibit emergent physical properties that can lead to new physics and novel device applications, and are the subject of intense study in many disciplines. We here apply novel experimental and theoretical techniques to the characterization of one such interesting interface system: the two-dimensional electron gas (2DEG) formed in multilayers consisting of SrTiO$_3$ (STO) and GdTiO$_3$ (GTO). This system has been the subject of multiple studies recently and shown to exhibit very high carrier charge densities and ferromagnetic effects, among other intriguing properties. We have studied a 2DEG-forming multilayer of the form [6 unit cells STO/3 unit cells of GTO]$_{20}$ using a unique array of photoemission techniques including soft and hard x-ray excitation, soft x-ray angle-resolved photoemission, core-level spectroscopy, resonant excitation, and standing-wave effects, as well as theoretical calculations of the electronic structure at several levels and of the actual photoemission process. Standing-wave measurements below and above a strong resonance have been introduced as a powerful method for studying the 2DEG depth distribution. We have thus characterized the spatial and momentum properties of this 2DEG with unprecedented detail, determining via depth-distribution measurements that it is spread throughout the 6 u.c. layer of STO, and measuring the momentum dispersion of its states. The experimental results are supported in several ways by theory, leading to a much more complete picture of the nature of this 2DEG, and suggesting that oxygen vacancies are not the origin of it. Similar multi-technique photoemission studies of such states at buried interfaces, combined with comparable theory, will be a very fruitful future approach for exploring and modifying the fascinating world of buried-interface physics and chemistry.
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