High sensitivity variable-temperature infrared nanoscopy of conducting oxide interfaces

TL;DR

This study demonstrates that scattering-type near-field optical microscopy can non-invasively and with high spatial resolution probe the local transport properties of conducting oxide interfaces over a wide temperature range, revealing detailed electronic behavior.

Contribution

The paper introduces a novel application of near-field optical microscopy for quantitative, high-resolution analysis of 2D electron systems at buried oxide interfaces across broad temperatures.

Findings

Near-field optical phase is highly sensitive to 2DES transport properties.

Modeling links optical signals to plasmon-phonon interactions and electron transport.

Spatial imaging of nano-channels demonstrates technique's resolution and applicability.

Abstract

Probing the local transport properties of two-dimensional electron systems (2DES) confined at buried interfaces requires a non-invasive technique with a high spatial resolution operating in a broad temperature range. In this paper, we investigate the scattering-type scanning near field optical microscopy as a tool for studying the conducting LaAlO3/SrTiO3 interface from room temperature down to 6 K. We show that the near-field optical signal, in particular its phase component, is highly sensitive to the transport properties of the electron system present at the interface. Our modelling reveals that such sensitivity originates from the interaction of the AFM tip with coupled plasmon-phonon modes with a small penetration depth. The model allows us to quantitatively correlate changes in the optical signal with the variation of the 2DES transport properties induced by cooling and by electrostatic gating. To probe the spatial resolution of the technique, we image conducting nano-channels written in insulating heterostructures with a voltage-biased tip of an atomic force microscope.

Equations

$${ϵ}_{\text{2DES}}={ϵ}_{\text{STO}}-\frac{n_{\text{3D}}{e}^2}{m^{\ast }{ϵ}_0({\omega }^2+\text{i}\omega {\tau }^{-1})},$$

Full text

Two-dimensional electron systems (2DES) at oxide interfacesoh2004 ; ths2006 ; zubko2011interface offer a unique playground combining the physics of strong electronic correlations, typical of complex oxides, with quantum confinement induced by the finite thickness of the 2DES. This particular setting, being different from the one of semiconductor heterostructures regarding the symmetry of the electronic states, the carrier effective masses and other physical quantities, has been predicted to display novel phenomena. The experimental observation of a negative electronic compressibility for LaAlO3/SrTiO3 (LAO/STO) interfacesli_very_2011 as well as the evolution of the superconducting critical temperature upon gate tuningrtc2007 ; cgr2008 ; valentinis2017modulation have been interpreted as manifestations of such unique entanglement. This environment can also promote the coexistence of multiple electronic phasesAriando2011electronic . For instance, it was predicted that, in the presence of a Rashba-type spin-orbit interaction, whose relevance for the LAO/STO interface has been revealed in magnetotransportshalom2010tuning ; cgg2010 and spin-charge conversion experimentslesne2016highly ; chauleau2016efficient , the 2D correlated electron system undergoes an electronic phase separation with an intrinsically inhomogeneous charge distributioncaprara_intrinsic_2012 . Visualizing such effects remains challenging: it requires a local probe with nanometer-scale resolution capable of imaging the dynamic electric response of the 2DES. In this regard, optical probes are particularly interesting tools to investigate the electron dynamicsdrk2010 ; nucara2018infrared . In the far-field approach they, however, lack the spatial resolution, limited by the wavelength, which is the order of microns to millimeters in the infrared range used to detect the Drude response of the conduction electrons.

The rapidly developing technique of scattering-type scanning near-field optical microscopy (s-SNOM)kh2004 ; ohh2006 overcomes such limitation and allows the investigation of the amplitude and phase of the optical response with the resolution of 10-20 nm. This approach rests on the near-field interaction of the sample surface with a metal-coated atomic force microscope (AFM) tip illuminated by an infrared laser: the back-scattered light, recorded as a function of the tip position, brings information of the surface conductivity. Used to study local optical propertieshillenbrand2002phonon ; huber2008terahertz ; huth2011infrared ; PostNicklate2018 and plasmon modes in metallic nanostructuresevd2008 ; saa2011 ; aan2013 and two dimensional materialsfrg2013 ; fab2011 ; cba2012 ; fra2012 ; wlg2015 ; dml2015 , this approach has been also applied to oxide materials ldd2017 ; lewin2018nanospectroscopy . In particular, Cheng et al ldd2017 found that the presence of the 2DES at the LAO/STO interfaces can be detected using a room-temperature s-SNOM, opening new horizons for non-invasive near-field optical studies of the oxide interfaces. However, only the near-field amplitude was presented, without information about the phase component, and the authors argued that the increase of the near-field amplitude is a signature of a higher metallicity. Moreover, no systematic wavelength dependence was shown. As we show here, the 2DES-related amplitude change can be either positive or negative, depending on the wavelength and temperature.

Recently, a possibility to do s-SNOM measurements at low temperature has been demonstrated yang2013cryogenic ; mcleod2017nanotextured ; lang2018infrared , with a great potential for studying complex phenomena in strongly correlated electron systems. Here we employ a cryogenic s-SNOM system (cryo-SNOM, neaspec GmbH) to study the near-field response of LAO/STO heterostructures in the range of wavelengths from 9.3 to 10.7 $\upmu$m (CO2 laser) from room temperature to 6 K. We demonstrate that both the amplitude and the phase of the back-scattered optical signal are sensitive to the presence of the 2DES at the LAO/STO interface. We consider a physical model of the near-field response arising from the formation of coupled plasmon-phonon modes at the interface. This model describes the wavelength dependence of the near-field signal and explains its temperature and field-effect evolution due to the variation of the charge mobility and density. Finally, we demonstrate that 160-190 nm wide conducting channels electrically created by an AFM tip can be detected in an insulating background, illustrating the high spatial resolution and high sensitivity of this technique applied to oxide interfaces.

Results

s-SNOM imaging of LAO/STO interface at room temperature

LAO/STO heterostructures are prepared by pulsed laser deposition as described in the Methods. In order to identify the near-field signature of the 2DES, an insulating reference region is created on the crystalline STO (c-STO) substrate by depositing, using photolithography, an amorphous STO (a-STO) layer of 5-15 nm prior to the LAO growth. During the s-SNOM measurements the AFM is operated in tapping mode with an oscillation amplitude of about 60 nm and the detected signal is demodulated at a higher harmonic $n$ of the tapping frequency in order to suppress the far-field contribution to the backscatteringohh2006 . The tip is grounded to reduce the possible electrostatic interaction with the sample. Interferometric detection allows measuring of both amplitude $s_{n}$ and phase $\phi_{n}$ of the near field signal $s_{n}\textrm{exp}(\textrm{i}\phi_{n})$ (in this work we use n=3). Figure 1 presents s-SNOM measurements at room temperature on two samples with a LAO layer thickness of 2 and 8 unit cells (u.c.), which is respectively below and above the threshold value (4 u.c.) for the formation of the conducting interfaceths2006 . Notably, the laser wavelength used in the experiment, $\lambda_{0}$= 10.7 $\upmu$m (935 cm*-1*), corresponds to a photon energy above the optical phonons in STO and LAO.

In the first sample (Figure 1a), there is essentially no difference between the near-field signal (both in amplitude and phase) measured in the two insulating regions. In the second sample (b), the amplitude and phase contrasts between the conducting and insulating (reference) regions are remarkably strong: $s_{3}/s_{\textrm{3,ref}}$=131 $\%$ and $\phi_{3}-\phi_{\textrm{3,ref}}$=0.36 rad, where $s_{\textrm{3,ref}}$ and $\phi_{\textrm{3,ref}}$ are the reference values. The striking difference between the near field images of the two samples proves that the contrast is due to the presence of the conducting 2DES. We note that not only the amplitudeldd2017 but also the phase is a sensitive probe of the conducting electrons. These quantities are measured independently from each other and therefore bring complementary information.

Theoretical model

In order to understand the physical origin of the strong sensitivity of s-SNOM signal to the presence of the 2DES, we calculate the dispersion of the surface phonon-plasmon polaritons in the LAO/STO interface with and without 2DES for the in-plane momenta $q$ relevant for this experiment. In simulations, we use the optical dielectric functions of insulating LAO and STO extracted from previous far-field measurementszhang1994infrared ; van2010charge (Supplementary Note 1). They can be parameterized by a series of Lorentzians corresponding to optically active phonon modes (Supplementray Table 1 and Supplementray Table 2). Furthermore, considering the weak near-field contrast between the amorphous and crystalline STO (Supplementary Note 2), for simplicity we ignore a possible small difference between the dielectric functions of a-STO and c-STO in the infrared range. We model the dielectric function of the 2DES as the sum of insulating STO and of a Drude componentdrk2010 ; lewin2018nanospectroscopy :

[TABLE]

where $\omega$ is the photon frequency, $m^{*}$ is the effective mass, $\epsilon_{0}$ is the vacuum permittivity, $n_{\textrm{3D}}$ is the three dimensional carrier density, $\tau^{-1}=\frac{e}{m^{*}\mu}$ is the scattering rate ($e$ is the elementary charge and $\mu$ is the optical carrier mobility). Based on the results of ab-initio calculationsson2009density and previous infrared measurementsdrk2010 , we use an exponential density distribution in the 2DES $n_{\textrm{3D}}(z)=n_{\textrm{2D}}/z_{0}\cdot\textrm{exp}(-z/z_{0})$ with the decay length $z_{0}$=2 nm, where the integrated 2D carrier density $n_{\textrm{2D}}=8\times 10^{13}$ cm*-2* is taken from transport experimentscrg2010 . For the effective mass, we adopt the value $m^{*}=3.2m_{e}$drk2010 . As it was noticed in previous infrared spectroscopy measurementsdrk2010 ; lewin2018nanospectroscopy , a much lower value for the mobility has to be used in the Drude model in doped strontium titanate to describe the data in the mid-infrared range, as compared to zero frequency transport experiments. This is related to the enhancement of the scattering rate due to electron-phonon interactionvan2008electron ; drk2010 ; devreese2010many .

Figure 2a-c presents the imaginary part of the calculated reflection coefficient $r_{\textrm{p}}(q,\omega)$ (Supplementary Note 3) for a bulk STO covered with 2 nm of LAO without a 2DES (a) and hosting a 2DES (b,c) with two values of the optical carrier mobility of 10 cm2V*-1s-1* and 2 cm2V*-1s-1* respectively. In the first case, one can observe various surface phonon-polariton modes showing a weak dispersion due to a hybridization between the optical phonons in STO and LAO. The closest to our spectral range is the mode at 736 cm*-1* (marked as STO+LAO), which involves the highest-frequency optical phonons of both STO and LAO. The main effect of the presence of the 2DES (Figure 2b) is the splitting of the STO+LAO mode into two branches. The lower one (labelled as LAO) does not disperse and originates from the LAO phonon. The upper one (called 2DES+STO) disperses strongly and is due to a plasmon mode in the 2DES, which is electromagnetically coupled to the phonon mode in STO. The interaction with the phonon sets the upper plasmon branch high enough in energy to affect our measurement. Due to this coupling, the dispersion does not have the canonical $q^{1/2}$ expected for a 2D electron gasstern1967polarizability ; nakayama1974theory . Interestingly, when the optical mobility is decreased to a rather small value of 2 cm2V*-1s-1* (Figure 2c), the dispersion of the STO+2DES branch becomes weaker, but the splitting remains visible. In Figure 2d the real and imaginary parts of $r_{\textrm{p}}$ are shown at the optical momentum $q_{\textrm{opt}}$, where the tip-sample coupling functionfab2011 (dashed curves in Figure 2a-c) has a maximum. One can see that for both mobility values the presence of the plasmon mode influences significantly the reflection coefficient, especially its imaginary part, even though the mode frequency is below the optical range accessible with our laser (green region).

Based on the calculated $r_{\textrm{p}}(q,\omega)$, we simulated the s-SNOM spectra (Figure 2e) for the three cases using a standard point-dipole model for the sample-tip interactionfab2011 ; aizpurua2008substrate (Supplementary Note 4). By comparison, one can see the influence of the 2DES on the near-field signal. Our calculations therefore explain the contrast observed in Figure 1b as due to the appearance of a coupled plasmon-phonon mode. Interestingly, in the experimental spectral range the near-field phase in the presence of the 2DES is always above that of the non-conducting interface (the reference), showing a systematic increase with the mobility and decrease with the frequency. On the other hand, the amplitude shows a less systematic behavior.

Temperature and frequency dependent s-SNOM measurements

A direct way to test the theoretical prediction for the dependence of the optical response on the mobility is to measure the temperature evolution of the near-field signal of the 2DES. Electrical DC transport measurementsoh2004 ; crg2010 reveal a dramatic increase of the carrier mobility and only a small decrease of the carrier density upon cooling. Figure 3a displays the temperature evolution of the amplitude and phase measured at three wavelengths, 9.3 $\upmu$m (1075 cm*-1*), 10.2 $\upmu$m (980 cm*-1*) and 10.7 $\upmu$m (935 cm*-1*). The corresponding near-field images at 6, 100 and 250 K are shown in Supplementary Note 5. In agreement with the calculations, the phase contrast is larger for the lowest frequency of light for any temperature. As the sample is cooled down, the near-field phase increases, reaching almost 1 rad at 6 K for the 10.7 $\upmu$m wavelength. At the same time, the near-field amplitude decreases.

To compare the temperature dependence of the s-SNOM signals with the model, we compute the near-field response as a function of the optical mobility $\mu$, while keeping all other parameters constant. In particular, in the frequency range of our experiment, the dielectric functions of STO and LAO do not change significantly with temperaturezhang1994infrared ; van2010charge . In Figure 3b we show the calculated amplitude and phase contrasts for the three experimental wavelengths as a function of the mobility logarithmically decreasing from 10 to 1 cm2V*-1s-1*. Such scale is used to accommodate the large increase of the DC mobility upon coolingoh2004 ; crg2010 while taking into account the mentioned decrease of the mobility in the infrared range. A comparison with the experimental results confirms that the model correctly captures the thermal evolution of the amplitude and the phase signals at all studied frequencies. Notably the experimental values of the phase contrast are reproduced quantitatively by the calculations. The frequency dependence of the near-field amplitude and phase contrasts is shown in Figure 3c for three selected values of $\mu$ (2, 5 and 10 cm2V*-1s-1*). By plotting on the same graph the measured values at 300 K and 6 K for the three laser wavelengths we find a good agreement between the model and the experiment. This allows us to estimate that the optical mobility increases from $\sim$2 cm2V*-1s-1* at room temperature to $\sim$10 cm2V*-1s-1* at 6 K. In Supplementary Note 6 we show that the curves in Figure 3b are robust with respect to a reasonable variation of the carrier density, the decay depth $z_{0}$ and the AFM parameters.

Electrical tuning of the near-field response

At low temperatures, electrostatic back-gating through the STO allows modulating the electrical properties of the 2DESshalom2010tuning ; fete2014magnetotransport . A field-effect device based on a LAO/STO heterostructure with 5 u.c. of LAO is sketched in Figure 4a. The DC sheet resistance (Figure 4b, top) continuously increases as $V_{\textrm{G}}$ is tuned from zero towards negative values. This occurs due to a simultaneous decrease of the carrier density and mobility, as we determine from a separate Hall-effect measurement (Figure 4b, bottom). Concomitantly the near-field response, measured at $\lambda_{0}=$10.7 $\upmu$m (Figure 4c,d), shows a loss of contrast between the conducting and the reference regions. One can see that while the amplitude changes by only 5 $\%$, the phase decreases by more than a factor of 2 when $V_{\textrm{G}}$ is swept from 0 to -60 V.

The strong modulation of the phase and the weak variation of the amplitude with gating can be understood within the model described above. In Figure 4e we present a simulation where we use the experimentally determined gate-voltage dependence of the carrier density (Figure 4b) and the optical mobility by dividing the DC mobility by a factor of 20 in order to obtain reasonable LT optical mobility at $V_{\textrm{G}}=0$. One can see that both trends are qualitatively reproduced. The small change of the amplitude is due to the opposite effect of the mobility and density on $s_{3}$ (see Supplementary Figure 5). On the other hand, the decrease of both carrier density and mobility suppresses the near-field phase. This naturally explains the profound decrease of $\phi_{3}$ with the gate and corroborates our previous conclusion that the near-field contrast originates from the 2DES.

Near-field imaging of AFM-written conducting wires

Having demonstrated the sensitivity of the optical near-field technique to the electrical properties of the conducting layer, we investigate the capability of this approach to detect conducting regions at the nanoscale. To this purpose, we define nano-conducting channels in insulating heterostructures consisting of 3 u.c. of LAO on STO by applying a voltage bias to an AFM tipcen2008nanoscale ; cen2009oxide . The conducting lines have widths ranging from tens to hundreds of nanometers, depending on the tip bias. The heterostructures used in these experiments are grown as described in the Methods and the writing canvas is prepared as described in previous worksboselli2016characterization . The wires are written using a MFP-3D Infinity AFM (Asylum Research-Oxford Instruments) in contact mode with a tip bias of 9 V and a scanning speed of 300 nm/s. Figure 5a shows s-SNOM images of two parallel conducting channels at room temperature. The conducting wires are clearly seen both in the amplitude and the phase images while the topographic AFM images (shown in Supplementary Figure 6) do not reveal any structures at the wire positions. Albeit the absolute contrast is weak, a perpendicular line cut (Figure 5b) nicely reveals the profile of the wires. Fitting the peaks with Lorentzians yields the full width at half maximum (FWHM) of 160-190 nm, which is reasonably close to an estimate ($\sim$120 nm) using the cutting method on a similar sample (Supplementary Note 7).

According to our simulation (Figure 5c), one expects an experimentally detectable near-field contrast for carrier densities above 1012 cm*-2*. By comparing the measurements with the calculations, we find that the optical signal of the wires is well reproduced considering a carrier density of $\sim 1\times$1013 cm*-2* and a carrier mobility ranging from 0.5 to 1 cm2V*-1s-1*, which is close to the optical mobility values found at room temperature in Figure 3. The lower value of the carrier density in the written wires as compared to regular conducting oxide interfacecrg2010 is reasonable, taking into account that the s-SNOM measurements were performed about 80 minutes after the writing and that the conductivity of these devices at room temperature decreases in timebi2010water . In the future, one can envision the use of cryo-SNOM to freeze the written patterns immediately and conserve them long enough to perform a complete characterization.

Discussion

The high sensitivity of the near-field signal to the parameters of the conducting interface is at first unexpected, since the Drude conductivity in the 2DES induces only a tiny change to the far-field infrared properties, such as the reflectivity and ellipsometric anglesdrk2010 ; yazdi2016infrared ; nucara2018infrared . To qualitatively explain this striking difference, one should consider that the penetration depth of the far-field infrared radiation is of the order of tens to hundreds of microns, while the evanescent surface waves excited by the AFM tip in the s-SNOM experiment decay inside the material at distances comparable to the 2DES thickness. Therefore, whereas the far-field optical properties are dominated by the insulating strontium titanate, the near-field response is strongly influenced by the interface conductivity. The theoretical model developed here explains this effect quantitatively and moreover predicts the correct frequency, temperature and gate-voltage dependence of the near-field amplitude and the phase. In particular, we notice a rather systematic variation of the phase with respect to these parameters, making it a useful observable for mapping the 2DES. Moreover, we demonstrate that a higher amplitude does not necessarily signal a higher sample metallicity as suggested in Ref.ldd2017 . We believe that the use of more realistic treatments for the sample tip-interaction, such as the finite-dipole model cvitkovic2007analytical ; hauer2012quasi and extending the range of wavelengths will allow in the future the direct extraction of the 2DES parameters from the SNOM data.

Our study reveals the central role of the plasmon-phonon coupling in the oxide interfaces. While coupled surface phonon-plasmon modes were widely studied in conventional semiconductorsrichter1984coupled , in the oxide interfaces they have been not explored so far, with an exception of the $q\sim 0$ Berreman mode observed in the far field infrared spectradrk2010 ; yazdi2016infrared ; nucara2018infrared . A related physical phenomenon is a clear observation of a huge decrease of the optical mobility above the phonon frequency as compared to the DC value, even though the absolute value of the optical mobility may be somewhat affected by the limited precision of the point-dipole model. Importantly, this observation is made here entirely on the basis of near-field measurements. This means that the electron-phonon interaction van2008electron ; devreese2010many ; van2010charge is as efficient for the scattering of the surface phonon-plasmon modes as for the polaronic absorption at zero momentum.

While a high sensitivity of the near-field signal is important, the key advantage of s-SNOM over conventional optical techniques is a nanoscale spatial resolution. In the present case s-SNOM offers nanoscale imaging of the local metallicity linked to the carrier concentration and optical mobility. Here we exploit it for contactless near-field imaging of AFM-written conducting nanowires in the LAO/STO interface embedded in an insulating background. The ability to visualize buried nanoscale conducting structures shows clearly the usefulness of this technique for the development of oxide interface based electronics. It complements other non-invasive techniques such as piezoresponse force microscopy (PFM) huang2013direct , microwave impedance microscopy (MIM) jiang2017direct , scanning SQUID microscopy kalisky2013locally and scanning single-electron transistor (SET) microscopy honig2013local by offering nanoscale information about infrared optical response. We foresee that the use of this local optical probe, in combination with cryogenic performance and electrostatic gating, will provide important information on the possible phase separation and charge inhomogeneities due to ferroelectric domain wallskalisky2013locally ; honig2013local ; frenkel2017imaging , metal-insulator transitions and other emergent phenomena in a large family of 2D oxide interfaceshwang2012emergent ; pai2018physics .

Methods

Sample preparation

The LAO/STO heterostructures were grown by pulsed laser deposition (PLD) on TiO2-terminated (001) oriented commercial STO substrates (CrysTec GmbH). The samples were prepared in two steps: first a pattern was defined with the photoresist on the substrates by photolithography and a layer of amorphous STO (a-STO) was deposited at room temperature in an atmosphere of 10*-4* mbar of O2 using a laser fluence of 0.6 J cm*-2* and a repetition rate of 1 Hz. After the removal of the photoresist that protected selected regions of the bare substrate from the deposition of a-STO, we grew the LAO films using the same experimental conditions but keeping the substrate at 800 *∘*C. After the growth, the samples were annealed in-situ for 1h at 550 *∘*C in an oxygen pressure of 200 mbar and cooled down to room temperature in the same atmosphere. The thickness of the LAO layer was monitored by reflection high energy electron diffraction (RHEED). The backside of one sample was covered with gold in order to realize a field-effect device.