Direct imaging of LaAlO 3 / SrTiO 3 nanostructures using piezoresponse force microscopy

The interface between LaAlO3 and TiO2-terminated SrTiO3 can be switched between metastable conductive and insulating states using a conductive atomic force microscope probe. Determination of the nanoscale dimensions has previously required a destructive readout (e.g., local restoration of an insulating state). Here it is shown that high-resolution non-destructive imaging of conductive nanostructures can be achieved using a specific piezoresponse force microscopy (PFM) technique. Images of conductive and insulating nanoscale features are achieved with feature sizes as small as 30 nm. The measured nanowire width from PFM is well correlated with those obtained from nanowire erasure.

Oxides heterointerfaces exhibit a wealth of physical properties with the potential to be controlled at nanoscale dimensions.In particular, the interface between two insulating perovskite oxide semiconductors, LaAlO 3 and TiO 2 -terminated SrTiO 3 , exhibits unique properties including conductivity, 1, 2 magnetism, 3 superconductivity, [4][5][6][7][8] and spin-orbit coupling. 9, 10LaAlO 3 /SrTiO 3 heterostructures undergo an interfacial insulator-to-metal transition as a function of LaAlO 3 layer thickness. 2At or below a critical thickness of three unit cells (u.c.) of LaAlO 3 the interface is insulating, while at or above 4 u.c. the interface is conducting.For films grown near the critical thickness, the metal-insulator transition can be locally and reversibly controlled at room temperature with a voltage-biased conductive atomic force microscope (c-AFM) tip. 11The writing process is performed with a positively biased c-AFM tip that locally induces interfacial conductivity; nanostructures are locally "erased"-restored to an insulating state-using a negatively biased c-AFM tip.
This convenient and non-volatile c-AFM lithography approach allows customized oxide nanodevices such as field-effect transistors, 12,13 photo detectors, 14 nanoscale THz sources and detectors, 15 electron rectifiers, 16 and single-electron transistors. 179][20] One challenge in characterizing the dimensions of oxide nanostructures created by c-AFM lithography is that the conductive nanostructures embedded at the interface show no measurable topographic features to gauge their lateral dimensions.Measurement of the structure size has so far only been available by using a destructive erasure process. 11In addition, this erasure measurement only measures the size locally where the nanowire was cut.
To address these issues, it is desirable to develop methods capable of high-resolution, nondestructive imaging of the nanostructures.One reported experiment for imaging the c-AFM written structures used electric force microscopy (EFM). 21The reported spatial resolution, of order 100 nm, is roughly an order of magnitude larger than what is obtained by erasure experiments.Other experimental techniques used to characterize other properties of the LaAlO 3 /SrTiO 3 heterostructures, for example, scanning superconducting quantum interference device (SQUID) microscopy, are capable of imaging magnetic order with micron-scale resolution. 8Cross-sectional scanning tunneling microscopy (XSTM) and cross-sectional c-AFM have demonstrated the confinement of the conducting interface along the growth direction. 22,23 tructural probes such as transmission electron microscopy (TEM) have confirmed interface structural reconstructions, 24,25 but are not suitable for imaging of conductive nanostructures because of the sensitivity to irradiation.
Here, a specific piezoforce microscopy (PFM) technique is used to characterize electronic nanostructures formed at the LaAlO 3 /SrTiO 3 interface.7][28] The details of the growth condition are reported in Refs.29 and 30.The LaAlO 3 /SrTiO 3 system possesses an effective piezoelectric tensor element d e f f 33 that varies linearly with carrier density. 28The piezoelectric response is used to image the carrier density in nanostructures created by c-AFM lithography at the LaAlO 3 /SrTiO 3 interface.Further experiments confirm that the size of nanostructures can be controlled by tuning the lithography parameters (e.g., tip bias voltage or speed).PFM imaging results are consistent with the scenario that the piezoresponse arises due to the carrier-mediated lattice distortion at the interface.
The PFM experimental set-up is illustrated in Figure 1.In the first part of the experiment, a conducting region is created by c-AFM lithography.A c-AFM tip is placed in contact with the top LaAlO 3 surface, for purposes of c-AFM lithography, topography, and PFM imaging.The back gate of the sample is grounded (V bg = 0 V).The c-AFM tip is electrically biased during c-AFM lithography and electrically isolated for PFM imaging.For the PFM experiments, an ac voltage V ac cos(2π f t) is applied to two Au electrodes that electrically contact the interface.The induced piezoresponse is measured through the vertical deflection of the AFM cantilever and detected using a lock-in amplifier at reference frequency f, which is adjusted for resonant enhancement.All experiments are carried out under ambient conditions at room temperature.
This PFM imaging technique can be used to visualize a single nanowire created by c-AFM lithography (Figure 2).Prior to creation of the nanowire, "virtual electrodes" are created by raster scanning a rectangular-shaped area that overlaps each of the two adjacent Au electrodes with V ti p = 8 V. Then a conducting nanowire is created between the two "virtual electrodes" with writing parameters V ti p = 8 V and moving speed v ti p = 600 nm/s.To compare the wire width measured from PFM method with the wire width measured from the erasing process, the wire is cut at the middle by moving the tip perpendicular to the nanowire with V ti p = −8 V and speed v ti p = 10 nm/s (Figure 2(a)).The formation of this conducting nanowire and the cutting are confirmed by monitoring the conductance during the writing with 0.1 V source voltage.The conductance drop profile versus position can be fit to the functional form G(x) = G 0 − G 1 tanh (x/h); the wire width is found to be  8 nm as the full-width at half-maximum (FWHM) of the differential conductance profile dG(x)/dx (Figure 2(b)).
After the c-AFM lithography, an ac voltage V ac cos (2π f t) with amplitude V ac = 0.5 V is applied to these two Au electrodes.Frequency tuning is performed to track the resonant frequency f r before taking PFM images.The excitation voltage amplitude is held at V ac = 0.5 V and the frequency f is fixed at f r during the PFM image scan.During all the PFM imaging presented here, the resonant frequency f r is in the range between 275 kHz and 300 kHz for the Pt coated tip we used.
PFM imaging at the contact resonance frequency helps to improve the signal-to-noise ratio, but reliable quantitative imaging suffers from possible frequency shifts and quality-factor variations that can take place due to changes in elastic modulus or damping. 31In the PFM imaging presented here, the large PFM signal amplitude contrast is not due to resonance frequency shift.In our previous PFM study, resonance frequency shift under dc bias sweeping is less than 1 kHz. 28y scanning over the area in which the nanowire was written, a PFM amplitude image of the cut single nanowire is observed (Figure 2  (Figure 2(e)).The result yields a FWHM of 32 nm.This analysis is repeated along the nanowire (Figure 2(f)), yielding an average wire width of 33 ± 3 nm.
In c-AFM lithography, the dimensions of the nanostructures produced are influenced by various lithography parameters (e.g., V ti p , v ti p ), environmental factors such as the relative humidity, 32 as well as other uncontrolled sample and/or canvas variations.Keeping the controllable parameters fixed, and working with a single canvas, it is possible to examine how the PFM imaging depends on the writing speed.Five parallel wires, each separated by 200 nm, are created with a fixed tip voltage V ti p = 10 V at writing speeds 200 nm/s, 400 nm/s, 600 nm/s, 800 nm/s, and 1000 nm/s (Figure 3(a)).The temperature and relative humidity are controlled stable at 72 • F and 34%, respectively.The wires are then cut in the center by using V ti p = −8 V and moving the tip perpendicularly to the wires at speed v ti p = 10 nm/s.The PFM amplitude image of these five parallel wires is shown in Figure 3(b).As with all of the other nanowire images, no topographic features or crosstalk is observed in the PFM images by comparing the AFM topography image of the same area (Figure 3(a), inset).Small features in the PFM images might be due to sample inhomogeneity.The wire widths are measured by fitting the horizontal profile extracted by averaging over the entire imaging region (Figure 3(c)).This data set shows a consistent trend that for a fixed writing voltage the wire width decreases with increasing writing speed.
The same analysis can be used to measure the insulating gap width from the PFM image (Figure 3(d)).For each wire, the vertical PFM amplitude profile is extracted by averaging the wire region.A linear background is subtracted, which mainly comes from the slow decay of the  nanowires under ambient environmental conditions. 32This decay is probably the reason for the change in amplitude from the upper and lower half of the PFM image (Figure 3(b)), since this PFM image is scanned from top to bottom.The wire written at v ti p = 200 nm/s does not show an obvious gap in the middle as can be seen in the PFM image.The wire written at v ti p = 600 nm/s shows a relatively large gap size from the Gaussian fitting and the gap is also difficult to discern in the PFM image.A possible reason is that after the cutting and before the PFM imaging a frequency tuning is performed at the image center that is also the center of the 10 V, 600 nm/s written wire.Some tuning-induced PFM features can obscure the cutting gap and make the fitting inaccurate.The gap sizes for the wires written at 400 nm/s, 800 nm/s, and 1000 nm/s demonstrate that with all other conditions kept the same, higher lithography writing speeds tend to produce wider insulating gaps.
Generally, the width obtained from PFM measurements is larger than from the erasure method.Most likely, this discrepancy is due to intrinsic resolution for PFM imaging.To help establish a clear relationship between the two available methodologies, the two methods were compared under various writing speeds and tip voltages.Figure 4 plots the nanowire width obtained by cutting the nanowire (W fit ) versus the value measured by PFM (W PFM ).A linear fit yields W f it = 1.02 × W P F M − 25.6 nm.The offset between the non-destructive PFM imaging and the destructive erasure-based method (25 nm) is typical of the spatial resolution reported for other piezoelectric thin film materials. 33n this class of materials, there are several possible mechanisms that can give rise to such an observed electromechanical response.Ferroelectric layers are known to give rise to PFM signals 34 and addition of a LaAlO 3 overlayer results in ferroelectric-like structural distortions in SrTiO 3. 24, 25, 35, 36   In addition there are electrochemical processes that should be considered.During c-AFM lithography, surface charging as well as ionic dynamics, both at the surface and in the bulk, 26,[37][38][39] can take place.This process, alone or coupled with electrostrictive effects of LaAlO 3 layer, 40 can also lead to a measurable PFM response.In previous studies on the electromechanical response of LaAlO 3 /SrTiO 3 using PFM 26 or electrochemical strain microscopy (ESM), 37 the ac excitation voltage is usually applied on the tip.In that case, surface charging and/or oxygen vacancy formation or migration can produce a PFM response.In the experiments reported here, the tip is biased only while creating nanostructures.After the c-AFM lithography procedure, the tip is electrically isolated during PFM imaging.In this regard, it is challenging to imagine a scenario involving electrically induced oxygen vacancy migration or electrostriction in the LaAlO 3 layer plays a significant role in the observed piezoresponse.Here we propose that the carrier density modulation at the interface, not a direct piezoelectric response, can also produce the PFM response.To further illustrate this, the PFM imaging setup is modified so that instead of grounding the back of the SrTiO 3 substrate, a nearby centrally located electrode is grounded instead (Figure 5(a)).A single nanowire and a side gate, located 1000 nm away from the nanowire, are both created with V ti p = 10 V.The nanowire is not cut for this experiment, and the side gate is electrically grounded.An ac voltage V ac = 0.5 V at resonant frequency is applied to the both ends of the single wire; therefore, there is no net current running through the wire.Both the tip and the back gate are electrically floated during the PFM imaging scan.Under these conditions, the applied ac voltage only induces fields within the interface itself, with no electric field applied across the LaAlO 3 film or SrTiO 3 substrate.
These PFM imaging results provide evidence in favor of a carrier-mediated lattice distortion as the primary mechanism for our PFM response, and are consistent with a number of prior experimental and theoretical investigations.Previous experimental studies demonstrated a positive correlation between the carrier density at the conducting interface and the lattice contraction of LaAlO 3 film along c-axis. 41,42 attice distortion was also directly observed at the SrTiO 3 layer near the interface using transmission electron microscopy 24 as well as by various x-ray techniques. 35,43,44 Te lattice distortions at the interface can even result in a biaxial strain and a strain gradient that may induce ferroelectric 45 and flexoelectric 46 polarization in SrTiO 3 layer near the interface.First-principles studies identified a connection between lattice polarization of LaAlO 3 layer and the interface metalinsulator transition. 47The charge density is mainly distributed in the subbands of Ti 3d orbitals at the interface. 48,49 he interfacial lattice distortion is strongly related to the carrier density due to Jahn-Teller effect. 35,44,50 Lrge ferroelectric-like distortions of the TiO 6 octahedra, which substantially affect the Ti d-electron density, are reported in a theoretical study for LaTiO 3 /SrTiO 3 superlattices. 51n summary, a specific PFM technique has been used to provide high-resolution and nondestructive imaging of conductive nanostructures created by c-AFM lithography at the LaAlO 3 /SrTiO 3 interface.These high-resolution PFM images of the nanodevices help to confirm the nanoscale dimensions which are important for further investigations.For example, in transport measurements performed on LaAlO 3 /SrTiO 3 , the transport channel typically involves nanowire segments created by c-AFM lithography.Correctly measuring the nanowire width can provide important information to help understand the transport properties.The PFM images consistently show a sub-50 nm width and are well correlated with prior method involving nanowire erasure.The width of a single wire is measured as small as 30 nm before deconvolution.Influence of various c-AFM lithography parameters on the dimensions of nanostructures is also investigated by the PFM imaging.The PFM imaging results are consistent with a carrier-mediated lattice distortion at the LaAlO 3 /SrTiO 3 interface as the likely origin of the piezoresponse.

FIG. 1 .
FIG. 1. Schematic of the experimental set-up.(a) During c-AFM lithography, the tip is biased and a lock-in amplifier can be connected to monitor the 2-terminal conductance while a nanowire is created (green line).(b) During PFM imaging, the tip is electrically isolated and an ac voltage V ac is applied to two Au electrodes that make contact to the LAO/STO interface.The vertical deflection of the tip is measured by a lock-in amplifier.

FIG. 2 .
FIG. 2. PFM imaging of single nanowire.(a) Lithography schematic based on an AFM topography image: green areas are written with V ti p = 8 V while red areas are erased with V ti p = −8 V. (b) Estimation of the wire width by fitting the conductance drop curve.(c) PFM amplitude image of the structure shown in Figure 2(a).Solid line is the Gaussian fitting and its FWHM is indicated.(d) DC IV curves of the structure before and after PFM imaging.(e) PFM amplitude of the dashed line shown in Figure 2(c).(f) Wire width distribution as a function of y axis.
(c)).The dc current-voltage (IV) curves of the structure before and after taking the PFM image are also measured (Figure 2(d)).The two IV curves are highly overlapping, indicating that the PFM process is non-destructive.The nanowire width is obtained by fitting a line cut (Figure 2(c), dashed line) of the PFM amplitude signal to a Gaussian function This article is copyrighted as indicated in the article.Reuse of AIP content is subject to the terms at: http://aplmaterials.aip.org/about/rights_and_permissionsDownloaded to IP: 128.104.194.31On: Mon, 13 Jul 2015 18:49:12

FIG. 3 .
FIG. 3. PFM imaging of five parallel nanowires.(a) Lithography schematic based on an AFM topography image: five wires, separated by 200 nm, are written at speeds of 200 nm/s, 400 nm/s, 600 nm/s, 800 nm/s, and 1000 nm/s with V ti p = 10 V; the wires are then cut in the middle using V ti p = −8 V at speed v ti p = 10 nm/s.Inset: topography image of the same area as Figure 3(b).(b) PFM amplitude image of the five parallel wires.(c) PFM amplitude vs. x axis after averaging the whole PFM imaging area.Solid line is the Gaussian fitting and FWHM is indicated.(d) PFM amplitude vs. y axis of five nanowires after subtracting a linear background term.Curves are offset for better view.Solid line is the Gaussian fitting to the curve with the same color and its FWHM is shown.

FIG. 4 .
FIG. 4. Wire width calculated from fitting the conductance drop curve (W fit ) versus the wire width directly measured from the PFM image (W PFM ) under various conditions.Linear fitting (black line) yields W f it = 1.02 × W P F M − 25.6 nm.

FIG. 5 .
FIG. 5. PFM imaging of a nanowire near a grounded side gate.(a) Lithography and PFM imaging schematic.The same ac voltage with amplitude V ac = 0.5 V is applied to both ends of the nanowire and the center gate is grounded.(b) PFM amplitude image of the wire.Both the tip and back gate are electrically isolated.