Dielectric collapse at the LaAlO3/SrTiO3 (001) heterointerface under applied electric field

The fascinating interfacial transport properties at the LaAlO3/SrTiO3 heterointerface have led to intense investigations of this oxide system. Exploiting the large dielectric constant of SrTiO3 at low temperatures, tunability in the interfacial conductivity over a wide range has been demonstrated using a back-gate device geometry. In order to understand the effect of back-gating, it is crucial to assess the interface band structure and its evolution with external bias. In this study, we report measurements of the gate-bias dependent interface band alignment, especially the confining potential profile, at the conducting LaAlO3/SrTiO3 (001) heterointerface using soft and hard x-ray photoemission spectroscopy in conjunction with detailed model simulations. Depth-profiling analysis incorporating the electric field dependent dielectric constant in SrTiO3 reveals that a significant potential drop on the SrTiO3 side of the interface occurs within ~2 nm of the interface under negative gate-bias. These results demonstrate gate control of the collapse of the dielectric permittivity at the interface, and explain the dramatic loss of electron mobility with back-gate depletion.

. Notable in this system is the dramatic tunability of the interfacial conductivity using external electric fields, attracting considerable attention for fundamental studies, as well as device applications 18,19 . The application of a back-gate voltage V g tunes multiple parameters in the system simultaneously, including the superconducting transition temperature, the carrier density, the Hall mobility and the confining electric field 3,18,[20][21][22][23] . In order to understand how these changes are inter-related, especially the dramatic loss of Hall mobility with back-gate depletion 20 , knowledge of the band alignment and potential profile changes with gating is essential.
In this study, we analyze the depth profile of the potential on the SrTiO 3 side of LaAlO 3 /SrTiO 3 (001) heterojunctions using synchrotron radiation PES for various V g . A schematic of the experimental setup is shown in Fig. 1

Results
Photoemission core-level spectroscopy of LaAlO 3 /SrTiO 3 . The measured Ti 2p core-level spectra of the LaAlO 3 /SrTiO 3 heterostructures at V g = 0 V and a bare SrTiO 3 (001) substrate are shown in Fig. 2. The characteristic probing depth λ, based on the theoretical study of Tanuma et al. 25 , was tuned by changing the irradiation photon energy (hν) and the photoelectron emission angle (θ) with respect to the surface normal. hν was 1.2 keV (λ = 2.0 nm for θ = 0 degree) and 7.9 keV (λ = 10 nm for θ = 0 degree), θ was varied from 0 to 80 degrees (also see Fig. 1). The Ti 2p core-level spectra from the LaAlO 3 /SrTiO 3 sample are shifted towards more positive relative binding energy from that of the bare SrTiO 3 substrate with no observable Ti 3+ component, as previously found 17 . As the probing depth becomes shallower (λ < 10 nm), no significant peak shift or broadening characteristic to potential variation, was observed within the experimental resolution of 50 meV. These results together with the gate-tunable transport properties 20 imply that the potential profile varies on the scale of 10 nm or more in the SrTiO 3 from the LaAlO 3 /SrTiO 3 heterointerface. By assuming that all carriers detected from Hall effect under no applied bias (n 2D ~2 × 10 13 cm −2 ) reside within 0.4 nm of SrTiO 3 surface and fully contribute to the Ti 3+ signal, the estimated total volume of Ti 3+ is still below its practical detection limit of 2~3 at. %. Moreover, the possible carrier distribution, which is interrelated with the potential profile, experimentally prohibits the observation of any Ti 3+ states present. Figure 3 show the measured Ti 2p core-levels using (a) SX-PES and (b) HAX-PES with −100 V ≤ V g ≤ 100 V. For all V g , the gate leakage current through the SrTiO 3 during the PES measurements was less than 10 nA. The binding energy of the SrTiO 3 core-level spectra were normalized to those of the LaAlO 3 spectra, which minimizes possible artifacts from the PES measurements, such as fluctuations of the photon energy. For negative V g , the Ti 2p core-level first shifts to more positive relative binding energy from V g = 0 V before saturating at +0.1~+0.2 eV in the case of SX-PES, while it remains unchanged for the HAX-PES. Both SX-PES and HAX-PES measurements show no Ti 2p core-level shift for positive V g . Similar results were also obtained in the Sr 3d core-level measurements. The change of the Ti 2p core-level peak position are plotted as a function of V g in Fig. 3(c) and (d), showing a total energy shift ~+0.15 eV for V g < 0 V for the SX-PES without any hysteresis.
Qualitatively we can examine these results by considering the simultaneous tuning of the sheet carrier density and the potential profile due to the application of negative V g . Considering the SrTiO 3 substrate as a capacitor dielectric between the back gate contact and the interface conducting layer, V g < 0 V corresponds to depletion of carriers at the interface resulting in a downward shift of the Fermi energy (E F ) towards the conduction band bottom. At the same time however the band-bending is enhanced by the gating. This shifts the center of the electron distribution closer to the interface. For fixed sheet carrier density, n 2D , the increased confinement shifts E F upwards in energy, opposite to the effect of depletion. Since the SX-PES Ti 2p core-level shifts to higher binding energy for V g < 0 V the band-bending induced upshift in E F is dominant. Indeed the dielectric constant of SrTiO 3 at room temperature ε r (T = 300 K)~350, gives a total carrier density change of ~2 × 10 10 cm −2 for V g = −50 V. This is just 0.14% of the measured total Hall sheet carrier density in this sample 20 . The magnitude of the energy shift clearly depends on the probing depth of the PES measurement compared to the characteristic length scale of the confinement potential narrowing. Hence the lack of an observable shift in the HAX-PES data suggests that the most significant changes in the confining potential occur in the topmost layers of the SrTiO 3 .
Self-consistent simulation for the core-level spectra and potential profile. In order to quantitatively analyze these scenarios, we simulated the potential profile in SrTiO 3 as a function of the depth (z) from the interface based on a modified Thomas-Fermi screening model, using the PES data to constrain the results. The scheme of self-consistent calculation is as follows: for a trial potential Φ(z), the carrier density profile n(z) is calculated using is the density of states at electron energy  from the conduction band minimum which is calculated via 16 , and f( ) is the Fermi-Dirac function. Following ref. 16, we use the three-dimensional form of the density of states. The potential is obtained by solving Poisson's equation ε 0 is the vacuum permittivity, ε r () is the electric field () dependent relative permittivity of bulk SrTiO 3 , and e 0 is the elemental charge. Here, we assumed other sources of charge, e.g. holes, extrinsic donors and acceptors, are negligible. Equations (1) and (2) were solved self-consistently with a convergence criterion of 0.01% throughout the whole depth region. For each V g , the two boundary conditions used are Φ(z = 0) and | ∂Φ ∂ z z ( ) z=∞ . The former is equal to the energy shift of the Ti 2p core-level peak position in the SX-PES spectra at the appropriate V g 24 , and the latter is 0 V/m and 1 × 10 5 V/m, for V g = 0 and −50 V respectively, given the 0.5 mm SrTiO 3 substrate thickness. In order to compare the experimentally obtained spectra with our model, we introduce an evaluation function known as the core-level intensity spectrum I(E). This is generally computed according to where C(E) represents a core-level spectrum described by a Voigt function peaked at E 0 , which in this case we set to zero as we are interested only in the relative change in the spectrum at different V g , not in the absolute value of E 0 24 . The final best fit result is determined by minimizing the sum of the squares of the difference between the measured and calculated forms of the I(E) for both the SX-PES and HAX-PES measurements.
The electric field () dependent local nonlinear permittivity of SrTiO 3 , ε r (, z), must be considered as discussed in previous reports 16,20,26 . First we attempted to utilize the reported form of ε r () in our simulation (Fig. 4(c) inset) 27 . However when n 2D was constrained to the measured value from Hall effect 20 , satisfactory agreement with the PES spectra was not possible. Even allowing n 2D to be a free parameter (allowing for the possibility of localized charge not contributing to the Hall measurement), no value could reasonably fit the spectra and other features such as the core-level shift in Fig. 3(c) (see supplementary materials). The key point is that the reported bulk form of ε r () did not accurately reproduce the nonlinearity of the dielectric permittivity inferred from the data.
As an alternative, we then assumed a smoothly varying dielectric constant as a function of distance from the interface ε r (z) for V g = 0 and −50 V, based on a simple sigmoid function, which was used as a physically reasonable qualitative form. The self-consistently solved potential and carrier density profiles are shown in Fig. 4(a) and (b). Here the errors of the simulated parameters were estimated with a threshold of 3% increase in the total squared error from the minimum value, except for the error in Φ(0) which was directly taken from the experimental error in the PES spectra. The comparison between the experimental spectra (open symbols) and the best-fit simulated spectra (solid lines) from the obtained potential profiles are shown in Fig. 4(d) and (e). Good agreement is observed for both the SX-PES and HAX-PES data. The main panel of Fig. 4(c) shows the best fit ε r (z) for V g = 0 and −50 V in these simulations, and the insets of Fig. 4(c) shows the extracted ε r ().
From these simulations, close to the interface, we find a relatively abrupt potential shift of ~0.15 eV inside the SrTiO 3 for V g = −50 V compared to V g = 0 V. As shown in the inset of Fig. 4(a), the potential crosses E F around z = 6 nm and 2 nm for V g = 0 and −50 V, the former is in good agreement with previous experimental and theoretical estimates of the electron gas thickness being < 10 nm 13, 15, 16, 28, 29 .

Discussion
Experimentally a significant change of the potential around the interface occurred only for V g < 0 V, and not V g > 0 V. Based on these calculation results, we can explain this asymmetry by considering the magnitude of  around z = 0. For V g = 0 V,  is not large enough to significantly reduce ε r , and positive V g only tends to decrease the interfacial electric field. The resultant changes in the band-bending and position of E F are therefore relatively small and below the PES resolution. This is in stark contrast to the case of V g < 0 V, where  = z ( 0) is large enough to reduce ε r , which self-consistently enhances the confinement leading to significant changes in the potential which are measurable by SX-PES.
Quantitatively, the collapse of ε r with  obtained in the analysis above is more rapid than reported for non-doped SrTiO 3 16, 30-32 and Nb doped SrTiO 3

27
; the latter being somewhat more strongly affected for a given  than the former one. This has important implications for calculations of electron accumulation layers in any  Fig. 4(c). Solid line is calculated by fitting the extracted form of ε r () in the inset of Fig. 4(c) using a sigmoid function. SrTiO 3 -based heterostructure. We note that our self-consistent approach is the same as the one of Copie et al., who utilized the literature form of ε r () 16 . The ε r () relationship reported by Yamamoto et al. 27 has also been successfully used to model the depletion layer in metal/SrTiO 3 Schottky junctions 33 . An important difference between the Schottky depletion layer and the LaAlO 3 /SrTiO 3 is the existence of free electrons in the latter, which can screen applied electric fields in addition to the lattice polarization which is the only possibility in the former. Indeed, a recent theoretical study has noted the interplay between electron density changes and lattice polarization 34 . In order to clarify these points, direct microscopic investigations of the lattice polarization with gate voltage are essential. Noting the large changes in potential over just a few lattice parameters, the failure of the prior experimental measurements of ε r () to capture our data likely reflect the need to explicitly consider ε r on short length scales, and include nonlocal effects 35,36 . In this sense, our model employing ε r (z) is one of the approximations implicitly incorporating the effect of k-dependence of ε r . Despite the flexibility in the functional form of ε r , an abrupt drop in the potential at the interface is an essential feature required to reproduce our spectroscopic results.
Finally we note the intriguing point that when the electric displacement field D() is calculated using the new functional form of ε r (),  is multi-valued for 0.02 ≤ D ≤ 0.08 Cm −2 , as shown in Fig. 4(f). Although the underlying physics and effects of such an electrostatic instability are currently not clear, it is possible that the presence of multiple metastable dielectric states in SrTiO 3 close to the interface could induce local structural phase transitions 37 and associated effects in resistive switching properties 38 , in addition to creating an unstable potential profile at the interface. The collapse of ε r around the interface, simultaneously enhancing the electron confinement and impurity scattering, especially at low temperatures, explains the substantial decrease in the mobility 20 and enhanced localization 37 that has been previously observed for back-gating. The strong contrast with top-gating 39 suggests that this nonlinear dielectric response provides new device switching approaches in oxide heterostructures.

Methods
The LaAlO 3 /SrTiO 3 was fabricated on TiO 2 -terminated SrTiO 3 (001) substrates by pulsed laser deposition as described elsewhere 20 . During LaAlO 3 depositions, the substrate was kept at a temperature of 800 °C, and the ambient oxygen pressure was maintained at 1 × 10 −5 Torr. The LaAlO 3 thickness is 10 unit cells (~4 nm), which is the identical sample used in our previous transport study using back-gate 20 . SX-PES and HAX-PES synchrotron radiation measurements were carried out under applied V g at beamline BL2C of the Photon Factory, KEK, Japan and beamline BL47XU of SPring-8, Japan, respectively. The SX-PES and HAX-PES spectra were recorded using a Scienta SES-2002 electron energy analyzer, and a Scienta R-4000 electron energy analyzer, respectively. All PES measurements were performed at room temperature. A schematic of the experimental setup is shown in Fig. 1. V g was applied from the back of the 0.5 mm thick SrTiO 3 substrate during the PES measurements, with the LaAlO 3 / SrTiO 3 interface grounded using Al wire bonding via a gold-coated copper plate. The back of the SrTiO 3 substrate was electrically contacted to this copper plate using silver epoxy.