PHYSICAL REVIEW B 93, 245124 (2016) Origin and distribution of charge carriers in LaAlO 3 -SrTiO 3 oxide heterostructures in the high carrier density limit Sumanta Mukherjee and Banabir Pal Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru 560012, India Debraj Choudhury Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru 560012, India and Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India Indranil Sarkar and Wolfgang Drube Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22607 Hamburg, Germany Mihaela Gorgoi Helmholtz Zentrum Berlin f ¨ ur Materialien und Energie GmbH, Albert Einstein Straße 15, 12489 Berlin, Germany Olof Karis Department of Physics and Astronomy, Box 516, 75120 Uppsala, Sweden H. Takagi Department of Physics, University of Tokyo, Tokyo 113-0033, Japan and Max-Plank-Institute for Solid State Research, Stuttgart 70569, Germany Jobu Matsuno RIKEN Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan D. D. Sarma * Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru 560012, India; Department of Physics and Astronomy, Box 516, 75120 Uppsala, Sweden; and Council of Scientific and Industrial Research - Network of Institutes for Solar Energy (CSIR-NISE), New Delhi 110001, India (Received 14 May 2015; revised manuscript received 28 April 2016; published 10 June 2016) Using hard x-ray photoelectron spectroscopy with variable photon energy (2–8 keV), we address the distribution of charge carriers in the prototypical LaAlO 3 (LAO) and SrTiO 3 (STO) oxide heterostructures with high carrier densities (10 17 cm −2 ). Our results demonstrate the presence of two distinct charge distributions in this system: one tied to the interface with a ∼1-nm width and ∼2–5 × 10 14 -cm −2 carrier concentration, while the other appears distributed nearly homogeneously through the bulk of STO corresponding to a much larger carrier contribution. Our results also establish bimodal oxygen vacancies, namely on top of LAO and throughout STO, quantitatively establishing these as the origin of the observed bimodal depth distribution of charge carriers in these highly doped sample. DOI: 10.1103/PhysRevB.93.245124 I. INTRODUCTION The presence of highly mobile two-dimensional electron gas (2DEG) [1,2] at the interface of two insulating, diamagnetic oxides LaAlO 3 (LAO) and SrTiO 3 (STO) has opened up a new field of research [3,4]. Despite many reports on remarkable properties of this apparently simple oxide interface [2,5–11] the appropriate description of this interface has remained controversial [1,12–23]. Even the very central question, whether a single type of charge carriers is responsible for all these, at times, apparently mutually exclusive properties [8,22], has not found a satisfactory * Also at Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru 560064, India; sarma@sscu.iisc.ernet.in answer. In its simplest generic form, the increasing polar field in the overlayer LAO with an increasing thickness can be compensated by the transfer of half an electron per formula unit from the topmost layer of LAO to the topmost TiO 2 layer of STO at the interface [1,12]; this implies the existence of a two-dimensional electron gas with a density of 3.28×10 14 cm −2 at the interface. Extensive first-principles calculations suggest a typical thickness of ∼2 nm for the thus formed 2DEG [24,25]. It is also understood now that the polar discontinuity across the interface of LAO-STO heterostructures can be resolved by a combination of various electronic and atomic reconstructions as well as vacancies, thereby leading to a wide range of electron densities vary- ing from 10 12 –10 17 cm −2 , with significant changes in the transport and magnetic properties [2,4,7]. Moreover, many estimates [1,5,10,11,17,26–30] of the thickness of the 2DEG 2469-9950/2016/93(24)/245124(8) 245124-1 ©2016 American Physical Society