In-Gap States and Band-Like Transport in Memristive Devices

The creation of point defects in matter can profoundly affect the physical and chemical properties of materials. If appropriately controlled, these modifications can be exploited in applications promising advanced and novel functionalities. Redox-based memristive devices – one of the most attractive emerging memory technologies – provide one of the most striking examples for the potential exploitation of defects. Applying an external electric field to an initially insulating oxide layer is known to induce a non-volatile, voltage-history dependent switching between a low resistance state and a high resistance state, also named memristive device. This switching occurs through the creation and annihilation of the so-called conductive filaments, which are generated at the nanoscale by assembly of donor-type point defects such as oxygen vacancies.
To date, the exact relationship between concentration and nanoscale distribution of defects within the filament on the one hand and the electronic transport properties of the devices on the other hand is still elusive. Due to limitations in sensitivity or spatial resolution of most characterization methods, the electronic structure of conductive filaments has not yet been characterized in detail. However, this knowledge is crucially needed as input for the development of electronic transport models with high predictive power.
With this in mind, we characterized the electronic structure of epitaxial SrTiO_3-­x -based memristive devices and compare it to that of single crystalline SrTiO_3-­x. To gain access to the defect states in the band gap, we employed soft X-ray resonant photoelectron spectroscopy (RESPES), which allows element-specific measurement of valence and defect levels of SrTiO_3-­x through resonant emission when the excitation energy corresponds to an absorption edge. The measurements were carried out in a photoelectron emission microscope (PEEM) setup at the Nanospectroscopy beamline of Elettra synchrotron laboratory, enabling us to spatially resolve the filament in the memristive device and presenting the first report of spatially resolved RESPES, a powerful tool to map the electronic structure of small features. 
In a first step, we investigated the spectroscopic fingerprint of oxygen vacancies in SrTiO_3-­x single crystals formed upon irradiation with an intense soft X-ray beam in ultra-high vacuum. We probed the occupied part of the electronic states near the Fermi energy using laterally-averaged RESPES. To this end, the valence band and the possibly occupied states within the band gap were mapped as a function of photon energy near the Ti L absorption edge (Figure 1 a-b). Interestingly, we find occupied states of Ti 3d character between the Fermi energy and the valence band for the reduced case (light blue/green spots at photon energies ~458.9 eV and ~464.1 eV in Figure 1a)), which are absent in the oxidized case (Figure 1b)), suggesting that they are caused by the existence of oxygen vacancies. These in-gap states have relative maxima at ~0.31 eV and ~1.11 eV below the conduction band (Figure 1c-d)), and the photon energies at which they are observed indicate that these states are of Ti³⁺e_g character. These energy levels can be interpreted as the defect states for singly and doubly charged oxygen vacancies. Combined with the relative position of the Fermi level, these states are the key features of the electronic structure induced by a high density of oxygen vacancies in SrTiO_3-­x.

Figure 1.  RESPES analysis of SrTiO_3-x single crystals. (a) RESPES map measured under reducing conditions. (b) RESPES map measured under oxidizing conditions and Ti L edge for reference. In both cases, second order light was subtracted from the RESPES map.  (c) Valence band spectra at a photon energy of 463.3 eV. (d) Zoom-in for the valence band spectrum in reducing conditions.

In order to gain access to the electronic structure of the conductive filament, we recorded PEEM images of the SrTiO_3-­xdevice near the Ti 3p core level and identified a well pronounced filament within the device area (Figure 2 a)). The conductive filament corresponds to reduced SrTiO_3-­xwith up to 30 % Ti³⁺, while the surrounding device area is composed almost entirely of Ti⁴⁺(Figure 2 a) and b)). We mapped the valence band region in real space at a photon energy of 463.3 eV, an energy at which we could detect the in-gap states induced by the oxygen vacancies in the single crystalline reference. Again, we observe a clear contrast in the region of the conductive filament for the energies corresponding to the in-gap states (Figure 2(c)). Extracting spectra from the filament and the surrounding region reveals that only the former exhibits significant weight of the in-gap states in the spectra (Figure 2 d)), whereas no in-gap states can be detected for the surrounding area. The in-gap states lie at the same energy positions compared to the valence band maximum as found for the reduced single crystalline reference (Figure 1d), indicating they are caused by the presence of oxygen vacancies.

In order to clarify how these in-gap states influence the current transport in our device, we used the experimentally determined positions of the in-gap states to simulate the band diagram shown in Figure 2 e) and the electronic current transport for the device applying single-band transport theory. We self-consistently solved a coupled equation system of Poisson equation, charge conservation law and current transport equation based on the gradient of the quasi-Fermi-level. The simulated temperature dependence of the current density-voltage curves nicely fit our experimental data. Hence, we can describe the electronic transport in forward direction as band-like transport of thermally excited electrons in the conduction band within the SrTiO_3-­x bulk, which are injected into the SrTiO_3-­x from the Nb:STO electrode, and direct tunneling through the Schottky depletion region close to the Pt interface. The in-gap states within the SrTiO_3-­x remain almost completely filled, as their energetic position is located well below the Fermi-energy (Figure 2e)).  Therefore, a significant contribution from hopping conduction or trap-assisted tunneling through defects states can be disregarded which, however, has been often discussed as underlying transport mechanism in conductive filaments.Rather than contributing to the conduction directly, the defect levels affect the overall band structure, enabling the injection of mobile carriers from the Nb:STO into the conduction band of SrTiO_3-x, which then dominates the transport in the Nb:STO-STO-Pt devices.

Figure 2. (a) Ti³⁺ map based on the Ti 3p_3/2 spectrum. (b) Ti 2p _3/2 spectra for the filament and the surrounding. (c) Spatial map of the in-gap state distribution. (d) Valence band spectrum extracted from the filament at a photon energy of 463.3 eV with a fit of the valence band maximum and the in-gap states (red lines). (e) Band diagram of the device calculated based on the position of the in-gap states. The blue line shows the conduction band and the dashed green lines shows position of the defect states obtained by PEEM in respect to the conduction band 

This research was conducted by the following research team:

Christoph Baeumer¹, Carsten Funck², Andrea Locatelli³, Tevfik Onur Menteş³, Francesca Genuzio³, Thomas Heisig¹, Felix Hensling¹, Nicolas Raab¹, Claus M. Schneider¹, Stephan Menzel¹, Rainer Waser^1,2, Regina Dittmann¹

¹ Peter Gruenberg Institute, Forschungszentrum Juelich GmbH and JARA-FIT, 52425 Juelich, Germany 
² Institute for Electronic Materials, IWE2, RWTH Aachen University, 52074 Aachen, Germany;
³ Elettra-Sincrotrone, S.C.p.A, S.S 14 - km 163.5 in AREA Science Park, 34149 Basovizza, Trieste, Italy

Contact persons:

Christoph Bäumer, e-mail: c.baeumer@fz-juelich.de
Regina Dittmann, email: r.dittmann@fz-juelich.de