The multifaceted properties of oxides make them attractive

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1 pubs.acs.org/nanolett Anomalous High Mobility in LaAlO 3 /SrTiO 3 Nanowires Patrick Irvin, Joshua P. Veazey, Guanglei Cheng, Shicheng Lu, Chung-Wung Bark, Sangwoo Ryu, Chang-Beom Eom, and Jeremy Levy*, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States ABSTRACT: Nanoscale control of the metal insulator transition at the interface between LaAlO 3 and SrTiO 3 provides a pathway for reconfigurable, oxide-based nanoelectronics. Four-terminal transport measurements of LaAlO 3 /SrTiO 3 nanowires at room temperature (T = 300 K) reveal an equivalent 2D Hall mobility greatly surpassing that of bulk SrTiO 3 and approaching that of n-type Si nanowires of comparable dimensions. This large enhancement of mobility is relevant for roomtemperature device applications. KEYWORDS: LaAlO 3 /SrTiO 3, 2DEG, mobility, nanowire The multifaceted properties of oxides make them attractive platforms for new classes of electronics. 1,2 Oxide heterostructures formed from insulating LaAlO 3 and SrTiO 3 exhibit emergent conducting behavior 3,4 with a controllable metal insulator transition. 5 Diverse phenomena have been observed at the interface such as magnetism, 4 superconductivity, 6,7 and strong spin orbit coupling, 8,9 all of which are promising for the development of multifunctional devices formed from this one material system. Despite the diverse functionality of this system, the relatively low room-temperature mobility of SrTiO 3 and LaAlO 3 /SrTiO 3 heterostructures (6 cm 2 /(V s)) has tempered enthusiasm for applications. Mobility enhancement has long provided a key pathway leading to novel physics and device applications. Improvements in the carrier mobility of Si-based and GaAs-based heterostructures enabled two of the most important fundamental discoveries in solid-state physics: the integer and fractional quantum Hall effects. 10,11 Improvements in the mobility of MgZnO/ZnO heterostructures have resulted in these quantum effects being seen in oxides for the first time. 12,13 The lowtemperature mobility of SrTiO 3 has also increased tremendously in recent years through a variety of growth strategies, including delta doping, 14 chemical beam epitaxy, 15 and strain engineering. 16 Similarly, the low-temperature mobility of SrTiO 3 -based heterostructures has been enhanced by modulation doping, 17 fractional doping, 18 and optimizing of growth conditions. 19 LaAlO 3 /SrTiO 3 has a low-temperature mobility typically on the order of 1000 cm 2 /(V s) and has been reported to be as high as 6500 cm 2 /(V s) (refs 17 and 19). However, none of these growth strategies have resulted in an increase in the room-temperature mobility, and the mobilities of all oxide-based semiconductors are still quite low at room temperature compared to silicon (μ Si = 1400 cm 2 /(V s)). The mobility of the n-type LaAlO 3 /SrTiO 3 interface at room temperature is identical to that of bulk n-type SrTiO 3. The LaAlO 3 /SrTiO 3 interface can be reversibly controlled with high precision (<10 nm) using conductive atomic-force microscope (c-afm) lithography 20 to make a variety of multifunctional devices including transistors, 21 single-electron transistors, 22 rectifying diodes, 23 and photodetectors. 24 Here we describe four-terminal transport measurements on LaAlO 3 / SrTiO 3 nanowires to evaluate their mobility compared to 2D LaAlO 3 /SrTiO 3 and bulk SrTiO 3. LaAlO 3 /SrTiO 3 heterostructures are grown using pulsed laser deposition using one of two growth methods (LTHP, 550 C and 10 3 mbar O 2 ; HTLP, 750 C and mbar O 2 ). 25,26 For each growth method, three unit cells of LaAlO 3 are deposited on TiO 2 - terminated SrTiO 3 substrates, resulting in an insulating interface. The interface is contacted electrically by depositing gold in lithographically defined areas that are etched below the LaAlO 3 /SrTiO 3 interface. Contact pads typically have greater than 1 GΩ isolation. Nanowires are formed using c-afm lithography (Figure 1a). A positively-biased AFM tip in contact with the LaAlO 3 surface deposits positive charge on the surface, 27,28 resulting in nanoscale modulation-doping of the interface. The c-afm lithography is reversible; a negatively-biased AFM tip will remove the surface charge and restore the insulating state. The sharpness with which a nanowire can be erased is also used to measure the nanowire width. 20 The width of a nanowire is determined by moving a negatively biased tip perpendicularly across the nanowire while monitoring the conductance G. The change in conductance is fit to a function of the form G(x) = Received: September 10, 2012 Revised: December 15, 2012 Published: January 10, American Chemical Society 364

2 Nano s Figure 1. (a) c-afm lithography is used to write a nanoscale device at the interface between LaAlO 3 and SrTiO 3. (b) Schematic arrangement of a six terminal Hall cross device. (c,d) Longitudinal and Hall resistances of a six terminal Hall cross, device H8 (w = 20 nm). (e) Electrode arrangement for van der Pauw transport measurements. (f,g) Longitudinal and Hall resistance in van der Pauw geometry of device vdp3 (w = 500 nm). G 0 + G 1 x + G 2 tanh(x/h)+g 3 x tanh(x/h); the width is defined to be the full width at half-maximum of the deconvolved differential (dg/dx)* 1 (ref 20). In this, we present data from two types of devices: nanowire Hall crosses and twodimensional squares with various sizes. The results described here come from a total of 16 distinct devices (9 Hall crosses and 7 squares); these devices were written on 5 distinct thin films (see Table 1 for a device summary). For sake of comparison, 2D mobility measurements are also shown for a 14 uc LaAlO 3 /SrTiO 3 heterostructure measured in the van der Pauw geometry. Two dimensional properties of the 3 unit cell interface samples are explored by writing square-shaped conducting areas with width w = nm and performing measurements in the van der Pauw geometry (Figure 1e). Nanowire transport characteristics are determined by writing five or six-terminal Hall crosses. A schematic of a six-terminal configuration is illustrated in Figure 1b. The Hall crosses have channel widths w ranging between 10 and 100 nm and lengths L ranging between 1.2 and 8 μm. The narrowest structures (w = 10 nm) are written with a single trace, as illustrated in Figure 1a. Wider structures are created by raster scanning the c-afm tip to form a rectangular-shaped structure with the desired width. Four-terminal and two-terminal resistance curves are acquired by sourcing a voltage V ab between electrodes a and b and measuring, using two lock-in amplifiers, both the resulting current i ab and the voltage difference V cd between electrodes c and d. The differential resistance R ab,cd = V cd /i ab yields either the longitudinal (R xx ) or transverse Hall (R H ) resistance. Figure 1b illustrates a typical setup. The fourterminal longitudinal resistance R xx R AD,BC is measured with a true differential amplifier with 1 TΩ input impedance. At room temperature R xx typically ranges between 10 kω and 1 MΩ depending on geometrical and other factors. The transverse ( Hall ) resistance R H R AB,CF is simultaneously measured by monitoring the voltage between electrodes B and F. R xx and R H are measured as a function of out-of-plane magnetic field B Table 1. Sample Summary a room temperature low temperature device name sample name growth type L (nm) w (nm) μ H (cm 2 /(V s)) n s (10 13 cm 2 ) T (K) μ H (cm 2 /(V s)) n s (10 13 cm 2 ) 2D LTHP, 14 uc vdp N LTHP, 3 uc vdp N LTHP, 3 uc vdp N LTHP, 3 uc vdp N LTHP, 3 uc vdp O HTLP, 3 uc vdp O HTLP, 3 uc vdp O HTLP, 3 uc H N LTHP, 3 uc H E LTHP, 3 uc , H E LTHP, 3 uc H C LTHP, 3 uc H H LTHP, 3 uc , H H LTHP, 3 uc , H I HTLP, 3 uc H I HTLP, 3 uc H G HTLP, 3 uc a Growth type, channel length (L), and width (w) are identified for each sample. Equivalent 2D Hall mobility (μ H ) and sheet carrier density (n s ) are shown at room temperature (300 K) and for several samples at low temperature. LTHP: 550 C, P O mbar. HTLP: 780 C, P O mbar. 365

3 Nano s in order to calculate the sheet carrier density n s = (1/e)(ΔB/ ΔR H ), where e is the electron charge. The quantity ΔB/ΔR H is found by performing a linear fit tor H (B). The equivalent 2D Hall mobility ( mobility ) is calculated using the expression μ H = (1/en s R xx )(L/w). Typical R xx and R H versus B curves are shown in Figure 1c,d. Over the time that it takes to sweep the magnetic field, R xx exhibits a slight (<0.4%) increase that is typical of LaAlO 3 / SrTiO 3 -based nanowires. 28 Slight changes in R H between forward and backward sweeps are also observed, and these slight differences are accounted for by symmetrizing the forward and backward-swept data collection sets. At room temperature, R H is found to be a highly linear function of B over the range 9 to 9 T; for the purpose of extracting the mobility it is sufficient to scan over the range ±1 T. The Hall offset resistance is generally quite small, typically <0.1% of the longitudinal resistance. The Hall offset resistance R H (0) observed in Device H8 (Figure 1d) can be converted to an equivalent longitudinal shift between the terminals on opposite sides of the channel δx =(R H (0)/R xx )L 0.5 nm, smaller than the nanowire width. Figure 1f,g shows R xx and R H versus B for device vdp3 (w = 500 nm). The room-temperature sheet carrier density and mobility of several nanowire devices are shown in Figures 2a,b. Devices have characteristic widths ranging from 10 nm to 1 μm. These graphs summarize the mobility and carrier density for both Hall cross and van der Pauw geometries. The van der Pauw devices (vdp2 vdp8) are generally in good agreement with the 14 uc 2D control sample: regardless of width, all exhibit a room temperature mobility of approximately 6 7 cm 2 /(V s). Among the Hall cross devices, however, even the widest structure, Device H7 with a main channel width w H7 = 125 nm, displays a modest increase in mobility to μ H7 =25cm 2 /(V s). This trend continues as mobility further increases as w is reduced. Nanowires with w = 10 nm exhibit the largest mobility enhancements. The five devices with w = 10 nm have mobilities that range between 15 and 60 times (average 25 times) that of bulk SrTiO 3 at room temperature. Mobility enhancements are observed in samples grown using both HTLP and LTHP growth conditions, with μ HTLP = 210 cm 2 /(V s), and μ LTHP = 90 cm 2 /(V s), implying that the effect is not principally related to growth conditions. Temperature-dependent transport properties of representative devices are shown in Figure 3, showing that mobility Figure 3. Equivalent 2D Hall mobility is measured as a function of temperature. Symbols are data points, lines are guides to the eye. A 1/ T 2 line is shown for comparison. Inset shows the four-terminal resistance R xx plotted versus two-terminal resistance R 2t, parametrized by temperature for devices H5 and H6. Also shown is the fourterminal resistance R xx (b) and sheet carrier density n S (c) as a function of temperature for devices H5 and H6. Figure 2. (a) Equivalent 2D Hall mobility and (b) carrier density are plotted as a function of wire width at room temperature. Open symbols represent measurements in the Hall geometry; closed symbols are taken in the van der Pauw geometry. enhancements relative to the 2D LaAlO 3 /SrTiO 3 interface persist to low temperature. While the mobility of the 2D device scales as T 2 over the temperature range K, similar to bulk n-type SrTiO 3 (ref 29), the mobility of Devices H5 and H6 clearly deviates from this power-law scaling, changing much more rapidly with temperature over the same range. Device H6 reaches a maximum mobility of more than cm 2 /(V s) at 20 K before decreasing slightly at lower temperatures. This nonmonotonic behavior is correlated with resistance changes and a breakdown of scaling between the two-terminal (R 2t = R AD,AD ) and four-terminal resistances (Figure 3a, inset). R xx and 366

4 Nano s n S for devices H5 and H6 are plotted as a function of temperature in Figure 3b,c, respectively. A third, wider Hall bar, H1, also shows an enhanced mobility at low temperatures. The observed enhancement of carrier mobility in nanowire devices stands in contrast to what is typically observed in semiconductors. The room-temperature mobility of bulk silicon (1400 cm 2 /(V s)) is reduced when formed into a nanowire geometry (e.g., cm 2 /(V s) for ref 30); surface passivation can help restore but does not enhance the mobility. 31 Significant increases in carrier mobility with decreasing cross section have not (to our knowledge) been reported for silicon or III V semiconductor nanowires. There are several factors that may help to explain the observed mobility enhancement. First, one may consider the c- AFM lithography technique. Conductivity at the LaAlO 3 / SrTiO 3 interface is controlled by placement of positive charges on the top LaAlO 3 surface. 27,28 This type of surface modulation doping can reduce scattering from charged impurities, as with III V semiconductor heterostructures. However, square devices created by c-afm do not exhibit an enhanced mobility at room temperature, ruling out modulation doping as the principal mechanism. Another factor that must be considered relates to the consequences of an inhomogeneous carrier density, which can sometimes lead to an apparent mobility enhancement. 32 Measured carrier densities for the w =10nm devices are found to vary between and cm 2 and are generally comparable to what is measured for 2D LaAlO 3 /SrTiO 3. In addition, nanoscale inhomogeneities on the scale of these devices are predicted to result in an overall lower mobility. 32 The variation in mobility observed for the narrowest nanowires (w = 10 nm) suggests that there is a hidden variable closely coupled to the enhancement mechanism. The mobility enhancement of devices created on HTLP-grown samples is somewhat higher as compared to LTHP samples. However, variations among the HTLP devices are themselves large, implying that the overall room-temperature mobility enhancements are not growth-related. Above room temperature, the dominant source of scattering in doped SrTiO 3 is scattering from LO phonons, 33 whose energies correspond to 674 and 1151 K. In the temperature range K, the T 2 dependence appears to be consistent with Landau Pomeranchuk scattering, 34,35 a phonon-mediated electron electron interaction also observed in bulk n-type SrTiO A predicted breakdown of T 2 scaling in one dimension 36 could point toward an explanation of the results presented here. As noted previously, the room-temperature mobility of 1D and 2D devices begin to diverge near 100 nm. We also note that the temperature dependence of mobility also shows different behavior when comparing 1D and 2D devices: 2D follows a T 2 dependence, while the mobility of 1D devices changes much more rapidly. The method used to determine the width of oxide nanowires could systematically underestimate the width by a factor of 2, but not 25. Typical variations for the nanowire width for a given sample and set of writing conditions are 20%. It is apparent however that the 1D (Hall cross) and 2D (van der Pauw) devices show very different physics. 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