We present a combined resonant soft X-ray reflectivity and electric transport study of LaAlO ₃/SrTiO ₃ field effect devices. The depth profiles with atomic layer resolution that are obtained from the resonant reflectivity reveal a pronounced temperature dependence of the two-dimensional electron liquid at the LaAlO ₃/SrTiO ₃ interface. At room temperature the corresponding electrons are located close to the interface, extending down to 4 unit cells into the SrTiO ₃ substrate. Upon cooling, however, these interface electrons assume a bimodal depth distribution: They spread out deeper into the SrTiO ₃ and split into two distinct parts, namely one close to the interface with a thickness of about 4 unit cells and another centered around 9 unit cells from the interface. The results are consistent with theoretical predictions based on oxygen vacancies at the surface of the LaAlO ₃ film and support the notion of a complex interplay between structural and electronic degrees of freedom.