Contact-Free Mapping of Electronic Transport Phenomena of Polar Domains in SrMnO3 Films

Domains in SrMnO3 Films J. Schaab, I. P. Krug, H. Doğanay, J. Hackl, D. M. Gottlob, M. I. Khan, S. Nemšák, L. Maurel, E. Langenberg, P. A. Algarabel, J. A. Pardo, C. M. Schneider, and D. Meier Department of Materials, ETH Zürich, 8093 Zürich, Switzerland Institut für Optik und Atomare Physik, TU Berlin, 10623 Berlin, Germany Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich, 52425 Jülich, Germany Instituto de Nanociencia de Aragón, Universidad de Zaragoza, Mariano Esquillor, 50018 Zaragoza, Spain Instituto de Ciencia de Materiales de Aragón, Universidad de Zaragoza-CSIC, Pedro Cerbuna 12, 50009 Zaragoza, Spain Department of Materials Science and Engineering, Norwegian University of Science and Technology, 7043 Trondheim, Norway Departamento de Ciencia y Tecnología de Materiales y Fluidos, Universidad de Zaragoza, 50018 Zaragoza, Spain (Received 8 December 2015; revised manuscript received 24 March 2016; published 13 May 2016)


I. INTRODUCTION
Domains in ferroic materials exhibit characteristic transport properties that can be controlled by switching the associated order parameter or, more locally, by inducing minute domain-wall movements. Because of the manipulable transport properties, such domains offer great application potential enabling, for instance, reversible control of local rectification currents [1] or nondestructive resistive readout of memory devices [2,3]. Additional functionality arises when the domain walls display electronic properties that are different from the surrounding domains [4], including anomalous photovoltaic effects in the presence of conducting walls [5] and the formation of chargeable nanocapacitors separated by insulating walls [6]. To date, such local electronic transport properties are commonly analyzed by scanning probe microscopy using either conductive atomic force microscopy (cAFM), i.e., two-point conductance measurements, or electrostatic force microscopy (EFM), which allows for contact-free mapping of spatial conductance variations [7]. Because of the applied line-by-line scanning, however, conductance mapping by cAFM and EFM is time consuming with data-acquisition times in the order of minutes. In addition, the spatial resolution is ultimately limited by the diameter of the probe tip (≳30 nm) [8,9]. A promising but largely unexplored pathway for improving these odds is the application of electron microscopy. The sensitivity to local transport phenomena of scanning electron microscopy [10][11][12] and x-ray photoemission electron microscopy [13] has already been shown and first attempts have been made to use these techniques for spatially resolved conductance measurements. A conclusive relation to the local IðVÞ characteristics, however, has not been verified and due to the irradiation of highly energetic electrons in scanning electron microscopy and photons in x-ray photoemission electron microscopy, unwanted irreversible changes in the electronic surface structure may occur. Thus, fast and noninvasive mapping of electronic transport phenomena at the nanoscale is yet to be achieved, gaining even more importance with respect to the future need for adequate monitoring of fabrication processes of envisioned domain-and domain-wall-based nanoelectronics devices.
Here, we demonstrate contact-free nanoscale characterization of electronic transport properties by performing low-energy electron microscopy (LEEM) at variable electron-gun currents. As a model case we investigate strained SrMnO 3 because the system exhibits a unique pattern of polar nanodomains of varying electronic conductance but otherwise uniform structural and electrostatic surface properties. This domain configuration allows for studying transport phenomena without interfering contrasts from unknown topography effects or stationary charges. Based on complementary cAFM and EFM scans we develop a mathematical framework and show that the LEEM experiments on SrMnO 3 can be considered as an inverse IðVÞ measurement: Instead of applying a voltage to the sample, a current I is injected by the electron gun so that a negative voltage V builds up. Since current injection and voltage detection are both realized by the LEEM electron beam, no additional electrical contacts are required. Thus, the current-induced voltage can readily be used for a fast derivation of conductance maps with exposure times of a few milliseconds. Analogous to cAFM, our technique probes the electronic conductance normal to the sample surface, while additional in-plane variations become visible due to the lateral resolution. Our results provide novel insight to the electronic conductance of the new functional material SrMnO 3 and reveal LEEM as a promising tool for fast and noninvasive derivation of conductance maps with nanoscale precision.

II. RESULTS AND DISCUSSION
For our studies, SrMnO 3 epitaxial thin films of 20-nm thickness are grown by pulsed laser deposition on (001)oriented ðLaAlO 3 Þ 0.3 ðSr 2 AlTaO 6 Þ 0.7 (LSAT) substrates with 1.7% tensile strain. Below T C ¼ 400 K the strained films develop a distinct pattern of four domain states with an in-plane polar axis pointing along the h110i directions of the tetragonal unit cell as detailed elsewhere [6]. Most importantly for our study, SrMnO 3 displays well-defined nanodomains of varying conductance at room temperature. Electronic conductance of the domains has been presented in Ref. [6] by cAFM and EFM, but without clarifying the underlying conduction mechanism. To date, the electronic conductance has been addressed only at the bulk level in SrMnO 3 polycrystals and superlattices [14,15] so that additional information about local phenomena and emergent contact resistance in cAFM measurements is highly desirable.
A. Electronic transport probed by scanning probe microscopy We begin our analysis by considering the mechanism responsible for the electronic conductance in our strained SrMnO 3 films. Figure 1 to high current values), reflecting locally structured conductivity that changes abruptly from one domain to the next. Corresponding IðVÞ data, evaluated for three different domains, are presented in Fig. 1(b) and their nonlinearity indicates non-Ohmic behavior. The findings presented in Figs. 1(a) and 1(b) are in qualitative agreement with the literature [6], with the difference being that the current values obtained in this work are about 2 orders of magnitude larger. The latter is indicative of a higher oxygen deficiency, but has no detectable effect on the characteristics of the domain pattern [see Fig. 1(a)].
In order to describe the observed non-Ohmic IðVÞ characteristics in Fig. 1(b), we compare possible transport mechanisms, including thermionic [16][17][18] and Poole-Frenkel emission [19,20], space-charge-limited conduction [21,22], as well as Fowler-Nordheim tunneling [23]. Best fits are achieved assuming the modified thermionic emission model by Simmons [17], which relates the current I to the electric field E according to Here, A eff is the effective contact area, ϕ B is the potential barrier at the metal-insulator (tip-surface) interface, μ is the electron mobility within the bulk, and m Ã =m 0 is the ratio between the effective and the free mass of the electron The electric field under the AFM probe tip can be written as EðVÞ ¼ VfðV; ξÞ with fðV; ξÞ accounting for nonlinearities in the voltage (e.g., built-in potentials) and the electric-field distribution ξ [9,18,24]. By defining I 0 ðTÞ ¼ I 00 T 3=2 exp½−ðϕ B =kTÞ and V −1 0 ¼ β 2 fðV; ξÞ, Eq. (1) then becomes Corresponding fits (solid lines) are presented together with the measured IðVÞ data in Fig. 1(b). The agreement between model and experiment holds for all measured temperatures between room temperature and 315 K (not shown). From the temperature-dependent data an average potential barrier ϕ B can be derived by plotting ln½I 0 ðTÞ=T 3=2 as a function of 1=T [see the inset to Fig. 1(b)]. The data yield ϕ B ¼ 0.27 AE 0.03 eV and no indication of pronounced domain-dependent variations. Based on ϕ B and the fits in Fig. 1(b) a rough estimate of the average electron mobility μ at room temperature can be achieved when assuming a circular tip-surface contact (A eff ¼ πr 2 tip , r tip ¼ 30 nm). In addition, an upper limit for the dielectric constant ϵ can be derived assuming a constant electric field over the film [fðV; ξÞ ¼ 1=d film , d film ¼ 20 nm]. The latter corresponds to a rather drastic but common simplification of the actual electric-field distribution in cAFM [20,25,26]. We note that in our specific case, where the SrMnO 3 film thickness is smaller than the radius of the probe tip, this simplification yields an upper limit for E (E ≈ V=d film > V=r tip ), leading to μ ≈ ð1.4 AE 0.3Þ × 10 −3 cm 2 =ðV sÞ (for m Ã ¼ m 0 ) and ϵ ≤ 490 AE 130. The estimated electron mobility is comparable to perovskite oxides such as CaMnO 3−δ and Ba 0.5 Sr 0.5 TiO 3 where μ is in the order of 10 −2 cm 2 =ðVsÞ and 10 −3 cm 2 =ðV sÞ, respectively [27,28]. The derived upper limit for the dielectric constant ϵ is consistent with frequency-dependent results obtained at low temperature [ϵð1 MHzÞ ¼ 110 at T ¼ 5 K] [29]. Based on the excellent agreement between model and data we thus conclude that the electronic conductance in strained SrMnO 3 is dominated by the interface-controlled and bulk-limited [24,30] transport mechanism described by Eqs. (1) and (2). This implies that the mean free path of the charge carriers in SrMnO 3 is smaller than the thickness of the measured film, i.e., shorter than 20 nm. As a consequence, both the Schottky barrier formed at the tip-surface interface and the mobility of the carriers in the bulk determine the transport behavior [17]. The charge carriers are affected by traps and interface states, which gives rise to additional scattering within the bulk compared to standard Schottky emission [31].
In order to obtain direct evidence for the impact of bulk contributions on the electronic conductance and collect additional information about local variations of the barrier ϕ B , we compare cAFM with complementary EFM measurements as presented in Figs. 1(c)-1(e). The EFM maps of mobile [ Fig. 1(d)] and fixed [ Fig. 1(e)] charges are obtained simultaneously by recording the EFM signals at 2ω and ω, respectively, while scanning in noncontact mode with an ac voltage applied to the tip (ω ¼ 41.3 kHz, U pp ¼ 14 V) [32,33]. The EFMð2ωÞ image in Fig. 1(d) shows the same pattern as probed by cAFM [ Fig. 1(c)], which proves that the intrinsic bulk properties play a significant role for the domain conductance. The simultaneously recorded EFMðωÞ image in Fig. 1(e) reveals a homogeneous electrostatic surface potential. The latter is in agreement with the in-plane orientation of the polar axis in SrMnO 3 and excludes the presence of domain-specific stationary surface charges that may locally alter ϕ B . The EFM data thus corroborate the proposed interface-controlled, bulklimited transport mechanism and the material properties derived based on the cAFM experiments.

B. Current-induced potentials visualized by low-energy electron microscopy
After elaborating the electronic transport mechanism in the strained SrMnO 3 film in terms of conventional scanning probe microscopy methods, we next discuss the potential of LEEM for deriving conductance maps. LEEM is a well-established and explicitly powerful method for characterizing, e.g., the surface structure of metals and semiconductors in real time and with nanoscale resolution (≳2 nm) [34]. More recently, LEEM was applied for the analysis and imaging of domains in ferroic oxides [35][36][37], but the sensitivity of LEEM towards relative, local conductance variations [38,39] has not been explored in detail. In the maybe closest approach, Kautz and co-workers studied the conductivity of in-plane biased graphene based on potentiometry measurements [40]. Their method is particularly strong for measuring variations in the conductance parallel to the surface in electrically conducting materials. In order to expand their approach towards poorly conducting or insulating materials, however, either high in-plane voltages or smaller electrode distances are required, both interfering with the imaging by low-energy electrons. Complementary LEEM measurements probing the out-of-plane conductance, that is normal to the sample surface, are virtually nonexisting. We thus begin with a direct comparison of the spatially resolved LEEM and cAFM data presented in Figs. 2(a) and 2(b). The LEEM data are recorded under ultrahigh vacuum (6 × 10 −10 mbar) at the UE56-1 SGM beam line of the Forschungszentrum Jülich, BESSY-II storage ring, Helmholtz-Zentrum Berlin using a novel type of aberration-corrected electron microscope (SPECS FE-LEEM P90 AC).
Figures 2(a) and 2(b) are taken at the same position and demonstrate that standard reflectivity measurements resolve a domain pattern that qualitatively matches with the cAFM conductance map. The LEEM contrast levels, however, are inverted with respect to cAFM, i.e., in the LEEM image conducting domains are darker than insulating domains. This behavior is consistent with bandstructure-based models relating higher (lower) reflectivity in LEEM to a smaller (larger) number of empty states at the respective kinetic energy [34]. In order to gain more detailed insight, we perform reflectivity measurements with varying kinetic energy of the electrons. The latter is achieved by applying a variable bias voltage to the sample. The results obtained for bias voltages between −8 and þ12 V at a constant electron-gun current I ¼ 1 μA are summarized in Fig. 2(c). Figure 2(c) shows the average normalized electron reflectivity evaluated for the four domains marked in the LEEM image in the inset. For all domains a pronounced steplike drop in electron reflectivity is obtained for increasing bias voltage, indicating the so-called MEM-LEEM transition; that is the transition from the mirror-electron-microscopy (MEM) regime of high reflectivity to the energy range where electrons start impinging onto the surface. Since the nature of the energydependent change in reflectivity is nontrivial, the voltageṼ at which the MEM-LEEM transition occurs is often defined based on the point of inflection between maximum and minimum reflectivity [36,41,42].
For the domains highlighted in the inset to Fig. 2(c) the characteristic voltageṼ shifts by up to ≈5 V. Such local shifts inṼ lead to the strong domain contrasts in LEEM images obtained in the transition region. Typical sources for such shifts in the MEM-LEEM transition are spatial variations in surface topography, surface potential, or surface polarization, with the latter determining the internal and external screening, band bending, and electron affinity at the surface [34,35,37]. Contributions from the aforementioned sources, however, can be excluded based on our scanning-probe-microscopy data, which reveal a homogeneous surface topography with a root mean square roughness of only 0.4 AE 0.1 nm (not shown) and no electrostatic contributions as presented in Fig. 1(e). These findings, in addition to the close relation between the LEEM reflectivity data [ Fig. 2(a)] and cAFM conductance map [ Fig. 2(b)], unambiguously demonstrate that the LEEM contrasts obtained on SrMnO 3 originate from potential differences that relate to variations in conductance G.

C. Conductance maps gained by low-energy electron microscopy
In order to strengthen our conclusion and elaborate the relation between emergent LEEM contrasts and the local conductance we devised an innovative strategy, performing LEEM experiments as a function of the electron-gun current (see Fig. 3). Taking into account that the inelastic mean free path of low-energy electrons in inorganic compounds can reach several nanometers [43], the experiment may be considered as an inverse IðVÞ measurement complementary to the cAFM data in Fig. 1(b): Instead of applying a voltage to the sample, a current I is injected by the electron gun and a negative voltage is built up at the surface of the sample due to the finite electronic conductance of SrMnO 3 . In the LEEM data in Fig. 3(a) the effect is evident from the trend that the MEM-LEEM transition voltageṼ continuously shifts towards higher values with increasing gun current. As we show in Fig. 3(a) this trend, i.e., the current-induced change in voltage, is captured by the transport model of Simmons [Eq. (2)], which enables a quantitative analysis. Since it is the electron-gun current that induces the voltage, however, it is reasonable to use the inverse of Eq. (2) for analyzing the dose-dependent LEEM experiment where W denotes the so-called Lambert-W function [z ¼ WðzÞe WðzÞ , z ∈ C]. Analogous to the transport measurements in terms of cAFM (see Sec. II A), the electric-field distribution and potential barrier are the only experimental input parameters that require additional assumptions. Obviously, these two parameters are not identical for cAFM and LEEM. Nevertheless, when rigorously applying the same approximation, i.e., VðIÞ ¼Ṽ, sample surface and are generated based onṼ values extracted pixel by pixel from reflectivity measurements, as seen in Fig. 2(c). Figures 3(b) and 3(c) reflect that the sensitivity of conductance maps increases with increasing electron-gun currents, which is consistent with Fig. 3(a). The gain in sensitivity, however, coincides with a loss in spatial resolution because higher gun currents yield more pronounced charging effects that reduce the image quality. In general, the conductance resolution can be optimized up to the point at which built-up charges prevent arriving electrons from interacting with the sample and hence cancel the imaging procedure. For the model system SrMnO 3 an electron-gun current of 0.1 μA, for instance, allows for resolving conductance variations ΔG ≈ 30 nA=V with a spatial resolution ≲100 nm.

III. SUMMARY AND CONCLUSION
In summary, by applying cAFM and EFM we demonstrate interface-controlled and bulk-limited transport in strained SrMnO 3 and derive estimates for the potential barrier, electron mobility, and dielectric constant. We then compare the scanning probe results with LEEM measurements and reveal a correlation between the transport behavior and LEEM reflectivity data. This correlation allows for contact-free imaging of current-induced potential variations, i.e., visualizing areas of different conductance based on low-energy electrons with data-acquisition times in the order of a 10-10 2 ms [6]. The applied LEEM reflectivity measurements provide qualitative information with a high spatial resolution that is limited only by the performance of the microscope. Quantitative conductance maps are gained based on LEEM experiments performed at variable electron-gun current. Emergent contrasts are dominated by the dc bulk conductance normal to the sample surface with in-plane variations becoming visible due to the lateral resolution. The application of dosedependent LEEM facilitates noninvasive conductance maps with adjustable sensitivity and spatial resolution and, most importantly, provides access to local IðVÞ characteristics. Our concept relies on surface charging which is a well-known and widespread effect in electron microscopy, occurring in a large variety of functional materials including, e.g., semiconductors, insulators, ferroelectrics, and silicon-based structures. With this, our results foreshadow possible applications in fundamental materials science, such as time-resolved studies of dynamical transport phenomena, but even beyond the basic research sector. The use of electron beams is already common in industry and even waver-sized samples can be characterized automatically and quickly. Moreover, the usage of a single electron beam for both current injection and noninvasive probing can easily be adapted for industrial purposes. Thus, transport measurements by low-energy electrons may be employed for industrial sampling and quality monitoring in nanoelectronics fabrication processes.