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Heteroepitaxial vertical perovskite hot-electron transistors down to the monolayer limit

Abstract

Two-dimensional heterostructures combined with vertical geometries are candidates to probe and utilize the physical properties of atomically-thin materials. The vertical configuration enables a unique form of hot-carrier spectroscopy as well as atomic-scale devices. Here, we present the room-temperature evolution of heteroepitaxial perovskite hot-electron transistors using a SrRuO3 base down to the monolayer limit (4 Å). As a fundamental electronic probe, we observe an abrupt transition in the hot-electron mean free path as a function of base thickness, coinciding with the thickness-dependent resistive transition. As a path towards devices, we demonstrate the integrated synthesis of perovskite one-dimensional electrical edge contacts using water-soluble and growth-compatible Sr3Al2O6 hard masks. Edge-contacted monolayer-base transistors exhibit on/off ratios reaching 108, complete electrostatic screening by the base manifesting pure hot-electron injection, and excellent scaling of the output current density with device dimensions. These results open new avenues for incorporating emergent phenomena at oxide interfaces and in heterostructures.

Introduction

Along with exfoliated two-dimensional (2D) materials1,2,3,4,5, atomic-scale artificial perovskite oxide heterostructures offer exciting opportunities6,7 for new devices and experimental probes of quantum materials. Specifically, designing vertical architectures incorporating these materials has unique advantages. It effectively utilizes their atomically thin nature by actively setting the channel length to an atomic scale, which would be an enabling pathway for fast electronics8, which is technically challenging in planar devices. More importantly, the perpendicular geometry can diversify functionalities in fundamental studies and applications by integrating layers with a wide range of physical properties in an interface-specific manner. For example, hot-electron transport across interfaces can be used to surpass fundamental thresholds9,10, such as the thermodynamic Shockley–Queisser limit in solar cells. In oxide heterostructures, hot-electron spectroscopy11 would be an invaluable tool to investigate the nanometer scale electronic reconstructions that are often observed at interfaces and in confined geometries7.

In pursuit of this approach, we demonstrate the evolution of a highly robust vertical hot-electron transistor (HET)12 based on perovskite oxide heterostructures down to the monolayer-base limit, consisting of a SrTiO3 emitter (both Nb-doped and undoped), atomically thin SrRuO3 base, and Nb:SrTiO3 (001) collector (Fig. 1; see the Methods section).

Results

Heterostructure fabrication and junction characteristics

In device operation, hot electrons are injected out-of-plane across the forward-biased base–emitter (BE) junction, traverse the grounded base, and are collected across the reverse-biased base–collector (BC) junction. We first focus on devices with conventional laterally staggered surface contacts. The heteroepitaxial trilayer shows epitaxial and atomically flat surface topographies with the perovskite step-and-terrace structure of the underlying substrate, as seen by atomic force microscopy (AFM) and reflection high-energy electron diffraction (RHEED) patterns (Fig. 2a–e). Accordingly, both interfaces form Schottky junctions following the thermionic emission model, evident from the rectifying current-voltage characteristics with constant Schottky barrier height ϕ and ideality factor η near unity down to the monolayer limit (Fig. 2f, g). This is remarkable considering that only a single unit cell (u.c.) of SrRuO3 (4 Å) is responsible for the Schottky junction formation at both interfaces.

Electrical characteristics of variable thickness SrRuO3 HETs

The common-base and common-emitter output characteristics of these devices show clear transconductance down to the monolayer limit (Fig. 3a–d). As the base becomes thinner, more hot electrons overcome ϕBC due to less scattering in the base; accordingly, the collector current density JC increases exponentially (Fig. 3b, inset). In general, an atomically thin base could be prone to the formation of pinhole and edge defects which electrostatically couple the emitter and the collector via a semiconducting channel, inducing permeable-base transistor operation13,14 governed by the drift-diffusive transport of Fermi-level electrons, as opposed to hot-electron transport. To rule out this possibility, we demonstrate that the metal base in our HETs completely screens the electric field and electrically isolates the emitter and the collector, by the measurement of constant voltage feedback curves (Fig. 3a–c).

The common-base transfer characteristics further corroborate this complete screening in the base by showing that the VEB required for the onset of JC is independent of VCB (Fig. 3f). Considering the Thomas–Fermi screening length LTF of 2 Å in SrRuO3 at both interfaces, it is significant that the transistor still operates as a pure HET with only a single u.c. of SrRuO3. The monolayer common-base current gain α 0.12 and common-emitter current gain β 0.14 follow the expected relation β = α/(1–α). After optimizing the processing conditions, our devices show 100% HET yield with exceptionally high stability and reproducibility for >100 devices examined (Fig. 3e). This is in contrast to prior work using a manganite base with low HET yield and dominantly permeable-base devices14. We attribute this important difference to the perfect registry of SrRuO3 with the underlying substrate; namely, the common Sr cation throughout the trilayer, with interfaces free of polar electrostatic boundary conditions15,16.

Probing the fundamental characteristics of hot electrons

The extremely high reliability of these HETs allows the experimental determination of hot-electron parameters, which were not previously accessible due to low yield and device-to-device fluctuations14. As shown in Fig. 4a–c, we observe the systematic thickness-dependent evolution of α over a wide range of 7 orders of magnitude. Note that these devices were optimized for stability, not output current density, by incorporating a thick undoped SrTiO3 emitter (Fig. 1). This avoided the growth-to-growth carrier density fluctuations of doped SrTiO3, which would obscure the intrinsic response for thicker SrRuO3. The exponential trend of α can be parametrized by the hot-electron mean free path λH as12

$$\alpha = \left\{ {\begin{array}{*{20}{c}} {\alpha _0 \times {\mathrm{exp}}(-t/\lambda _{{\mathrm{H,I}}}),} & {t \le 3\ {\mathrm{u.c.}}} \\ {\alpha _0 \times {\mathrm{exp}}(-3 \ {\mathrm{u.c.}}/\lambda _{{\mathrm{H,I}}}) \times {\mathrm{exp}}[-(t-3\ {\mathrm{u.c.}})/\lambda _{{\mathrm{H,B}}}],} & {t \, \, > \, \, 3 \ {\mathrm{u.c.}}} \end{array}} \right.,$$
(1)

where t is the SrRuO3 thickness, α0 is α extrapolated to t = 0 u.c., and λH,B (λH,I) is the bulk (interfacial) hot-electron mean free path. The fact that α fits very well the exponential form self-consistently confirms HET operation, and highlights the ability to control SrRuO3 thickness on the atomic level. These results indicate that SrRuO3 is homogeneous with λH,I 0.3 ± 0.01 u.c. up to 3 u.c. However, two distinct regions exist for thicker SrRuO3: the interfacial region with λH,I, and the ‘bulk’ region away from the interface with λH,B 1.4 ± 0.03 u.c., in good correspondence to recent studies using ballistic electron emission microscopy across the vacuum/SrRuO3 interface17.

The abrupt transition in λH at 3 u.c. is quite reminiscent of the commonly observed resistivity transition for ultrathin SrRuO318,19,20,21. While there are some variations in the observed critical thickness, and debate on its origin, we see the same transition in our films. Figure 4c shows the thickness-dependent evolution of the room-temperature in-plane conductivity for identically grown samples on an undoped substrate. Notably, for 3 u.c. and below, the temperature dependence is insulating, while for 4 u.c. and above, increasingly bulk-like metallic temperature dependence is observed (Fig. 4d, inset).

From a fundamental perspective, λH has a rather interesting comparison to that for conventional transport, λF, the Fermi-electron mean free path. λF can be estimated from the resistivity ρ, which can be expressed via Boltzmann transport as $$\rho = 3{\uppi}^2\hbar /q^2k_{\mathrm{F}}^2\lambda _{\mathrm{F}}$$, where ħ is the reduced Planck’s constant, q is the elementary charge, and kF is the Fermi wave vector22. Figure 4d shows the deduced thickness-dependent λF at room temperature. As previously noted, the smooth decrease of λF down to 4 u.c. arises from enhanced surface/interface scattering20. Even in the atomistically clean limit, surface/interface scattering impacts the in-plane transport of ultrathin films23, including diffuse scattering at step edges, whereby λF can be expressed in terms of t using Matthiessen’s rule as $${\mathrm{1}}/\lambda _{\mathrm{F}} = 1/\lambda _{{\mathrm{F,B}}} + 1/t_0t$$, where λF,B is the bulk Fermi-electron mean free path, and t0 is the surface/interface scattering constant. Estimating λF,B as λF for t = 60 u.c., λF fits well this functional form down to 4 u.c. but then drastically decreases in the thinner films with insulating temperature dependence.

As has been previously emphasized, the extremely short λF,B (300 K)  0.6 u.c. in SrRuO3 is highly inconsistent with coherent transport in conventional metals22,24, and this ‘badly metallic’ behavior is a characteristic feature of strongly correlated metals under much current investigation25. Here we find that λH,B exceeds our estimate for λF,B by a factor of 2.3 (Fig. 4d). This enhancement could originate from Ru 4d electrons effectively screening the inelastic electron–electron scattering of hot electrons26. Note that λH,B can be isolated from surface/interface scattering, as indicated by its constant thickness dependence above the sharp transition between 3 u.c. and 4 u.c.—this is a unique advantage of these thickness-dependent hot-electron experiments, enabling a direct measure of fundamental scattering mechanisms without surface/interface contributions. The surprising enhancement of λH,B with respect to λF,B suggests that further hot-electron spectroscopic studies of strongly correlated metals would provide valuable insights in this relatively unexplored regime.

Perovskite one-dimensional electrical edge contacts

We turn now to considerations relevant for the potential development of monolayer heterostructures for practical devices. While there are several important issues that need to be addressed, a central obstacle is the low output current density in the HETs presented thus far (JC μA cm−2). Two significant contributions are the high emitter resistance introduced via thick undoped SrTiO3 (needed for device stability investigating the thick-base regime, but which limits hot-electron injection), and the in-plane base series resistance arising from the laterally staggered contact geometry, which becomes increasingly dominant in the monolayer limit. In order to address these issues, we can thin down and dope the emitter, which readily improves the emitter resistance by orders of magnitude15,27,28. Furthermore, we demonstrate here the synthesis of a perovskite one-dimensional electrical edge contact, in analogy to that recently developed for 2D materials29, using a water-soluble and growth-compatible Sr3Al2O6 hard mask layer30 (Fig. 5a; see the Methods section). The Sr3Al2O6 layer not only bypasses aggressive lift-off processes, but also is stable at high growth temperatures and oxidizing conditions, allowing for the corresponding growth of the perovskite edge contact.

As a result, the monolayer-base devices improved significantly: JC increased by 5 orders of magnitude; on/off current ratios reached 100,000,000; and α increased threefold to 0.35, with a corresponding enhancement of β to 0.54 (Fig. 5). Pure HET operation is evident from the voltage feedback curves and the transfer characteristics as discussed previously (Fig. 5b, d). Most importantly, we find that JC self-consistently scales with the residual base resistance underneath the emitter as 1/RE (RE is the emitter radius)31, which is very favorable to device downscaling (Fig. 5g). This confirms that the perovskite edge contact effectively minimizes the base series resistance by placing the contact at the edge of the monolayer base/emitter interface, and should enable high current density in sub-micron devices. Furthermore, the edge contact method developed here should be broadly useful for a wide range of oxide heterostructure devices.

Methods

Heterostructure fabrication and device processing

The heteroepitaxial trilayer was fabricated using pulsed laser deposition with a 248 nm KrF excimer laser using TiO2-terminated Nb:SrTiO3 (001) substrates (0.01 wt% Nb dopant concentration). SrRuO3 base (1 u.c. to 15 u.c.) was grown in 100 mTorr O2. The base thickness was controlled on the atomic scale by monitoring the in situ RHEED oscillations, where one oscillation corresponds to a single u.c. Coherent RHEED oscillations throughout the growth indicate high quality layer-by-layer growth of the SrRuO3. In particular, the growth of SrRuO3 is interrupted every 4 u.c. for thicker films so that the adatoms on the surface can sufficiently rearrange, and preserve the step-and-terrace structure of the underlying substrate, as indicated by the RHEED intensity recovery right after the interruption (Fig. 2a). This preservation of the step-and-terrace structure is especially critical for SrRuO3, because it has been otherwise reported to adversely affect the transport properties20. A 60 nm-thick SrTiO3 emitter was consecutively grown through a rectangular template mask in 1 mTorr O2. The substrate temperature was 700 °C during the entire growth. The SrRuO3/SrTiO3 (001) heterostructure was fabricated under the same growth conditions. The SrTiO3/SrRuO3/Nb:SrTiO3 (001) trilayer was then Ar-ion etched into rectangular shapes, and annealed in 760 Torr O2 at 350 °C for 6 h to fill oxygen vacancies generated by Ar-ion etching. Rectangular Au and Al electrodes were deposited using e-beam evaporation on the base and emitter, respectively. Indium was ultrasonically soldered onto the collector. These electrodes form Ohmic contacts to each layer.

Perovskite one-dimensional electrical edge contact

30 nm-thick Nb:SrTiO3 (0.05 wt% Nb dopant concentration)/monolayer SrRuO3/Nb:SrTiO3 (001) heteroepitaxial trilayer was grown using the same substrates and growth conditions as noted above (the emitter was grown without the use of a template mask). The key step is the growth of a water-soluble and growth-compatible Sr3Al2O6 hard mask layer on the trilayer. The Sr3Al2O6 hard mask layer bypasses aggressive lift-off processes and also serves as a mask during Ar-ion etching and perovskite edge contact regrowth processes involving high growth temperatures and oxidizing conditions. A 180 nm-thick Sr3Al2O6 hard mask layer30 was grown in lithographically patterned circular shapes in 5 × 10−6 Torr O2 at room temperature, and capped with a 60 nm-thick SrTiO3 grown in 1 mTorr O2 at room temperature to enhance its stability in the air. The trilayer covered with the Sr3Al2O6 hard mask layer in circular shapes was Ar-ion etched to expose the edge of the monolayer base and annealed in 760 Torr O2 at 350 °C for 6 h. A 30 nm-thick SrRuO3 edge contact was consecutively grown in 100 mTorr O2 at 700 °C. The entire structure was then immersed into room-temperature filtered de-ionized water to dissolve the Sr3Al2O6 hard mask layer. For device isolation, the trilayer was Ar-ion etched into larger circular shapes and annealed in 760 Torr O2 at 350 °C for 6 h. Electrodes were deposited on each layer as noted above.

Characterization

AFM images were acquired in tapping mode. All electrical measurements of the device were performed using a semiconductor parameter analyzer in DC mode at room temperature in ambient conditions. The in-plane transport measurements were conducted in a four-point geometry with Au contacts for SrRuO3 films.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

This work was supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract no. DE-AC02-76SF00515. Work on the one-dimensional electrical edge contact was supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4415.

Author information

Authors

Contributions

B.S.Y.K. performed the device fabrication, measurements, and data analysis. Y.H., T.Y., and H.Y.H. assisted with the planning, measurements, and analysis of the study. B.S.Y.K. wrote the manuscript, with input from all authors.

Corresponding authors

Correspondence to Brian S. Y. Kim or Harold Y. Hwang.

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The authors declare no competing interests.

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Kim, B.S.Y., Hikita, Y., Yajima, T. et al. Heteroepitaxial vertical perovskite hot-electron transistors down to the monolayer limit. Nat Commun 10, 5312 (2019). https://doi.org/10.1038/s41467-019-13290-3

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• DOI: https://doi.org/10.1038/s41467-019-13290-3

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