Introduction

In quantum well (QW) heterostructures, the probability of quantum mechanical tunnelling depends on the available quantized states at both the originating and the receiving sides of the junction. Therefore, the tunnelling current is usually not a monotonically increasing function with respect to the external bias. In particular, quantized resonant states can form in a QW between the two barriers, and can give rise to an interesting tunnelling behaviour, so called, resonant tunnelling (RT). Here, the energy of the wavefunctions with discrete levels can shift and align by applying an external bias (Fig. 1)1,2. When properly aligned, the tunnelling current peaks, exhibiting a negative differential resistance (NDR) just above the resonant bias (VR). Such an intriguing NDR behaviour can be exploited in various devices such as tunnel diodes and RT transistors. More importantly, the RT phenomena offer unique insight into electrical transport properties of materials, such as localized defect states, collective electronic excitations and QW band structures. Up to date, NDR and accompanying RT behaviours have been studied mostly in Si-based or III–V compound semiconductors1,2,3,4,5. Excellent crystalline quality of the conventional semiconductors and actual realization of two-dimensional (2D) heterostructures with nanometre thick barrier layers enabled the observation of the RT behaviour.

Figure 1: Resonant tunnelling from a quantum oxide superlattice.
figure 1

(a) Schematic diagram of a δ-doped quantum oxide superlattice. The δ-doped La layer creates a 2D electron gas within the layer forming a quantum well structure. (b,c) Calculated potential wells (thin black lines) and probability functions of finding electrons (thick lines), i.e., absolute square of wavefunction, at their corresponding energy levels. At V=0 (b) the wavefunctions with the same energy levels are aligned for each quantum well. When V>0 the position of wavefunctions are shifted and no longer aligned. At V=VR (c) the ground state wavefunction of a quantum well becomes aligned with the first excited state wavefunction in the adjacent quantum well, allowing a large tunnelling current to flow across the superlattice junction. The dotted line indicates the electric field, which corresponds to VR=1.23 V for the whole superlattice.

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On the basis of recent advances in oxide thin-film synthesis, precision design of complex oxide thin films and heterostructures by pulsed laser epitaxy (PLE) or molecular beam epitaxy at the atomic scale has become available6,7,8. Indeed, many previous studies demonstrated emergent physical phenomena in conjunction with the quantum mechanical tunnelling in transition metal oxide (TMO)-based tunnel junctions, utilizing the exotic properties, including superconductivity9, magnetoresistance10,11, electroresistance12,13 and multiferroicity14. The strong coupling among charge, spin, lattice and orbital degrees of freedom has been investigated in terms of the various tunnelling behaviours, such as Josephson effect and spin-polarized tunnelling. More recently, a large electroresistance was also observed in ferroelectric tunnel junctions12. The tunnelling current across the ferroelectric layer is found to be efficiently controlled by not only the polarization direction, but also, more importantly, the interfacial electronic phase of the electrode layers13. Unfortunately, however, a clear RT behaviour has not been experimentally realized in TMO heterostructures.

Although a clear RT behaviour has not been widely explored with TMOs, the NDR behaviour itself has been reported in various complex oxide junction structures15,16,17,18. In particular, non-volatile resistance switching (RS) in TMO-based heterostructures has attracted scientific attention for developing next-generation memory devices based on memristors19,20,21. In typical RS devices, the electric resistance of a junction can be modulated by applying external bias, and the device can have two (or more) resistance states, that is, a high-resistance state (HRS) and a low-resistance state (LRS). The switching from a LRS to a HRS usually accompanies a NDR behaviour, as the amount of current decreases on increasing the bias above the switching voltage.

In the following, we investigate the junction transport property of a QW superlattice (SL) precisely designed by inserting atomically thin LaTiO3 (LTO) between SrTiO3 (STO) barrier layers. A clear RT behaviour with NDR is observed. Moreover, as oxide heterostructures can reveal RS, we further propose that the combination of RS with NDR is an efficient way to maximize the resistance ratio between the HRS and LRS in oxide QW heterostructures.

Results

Precision design of oxide quantum heterostructures

To realize a TMO QW heterostructure, a La δ-doped STO SL with atomically sharp interfaces was fabricated22. We believe that a sample with an excellent crystalline quality is highly necessary for the observation of the quantum resonant behaviour in TMOs. Therefore, we epitaxially grew a high quality [LTO1/STO6]10 SL with minimized defect states using our atomic scale synthesis capability6,8. Detailed information on the sample growth by PLE and experimental detail, as well as the excellent crystallinity of our SL is demonstrated in the Methods and Supplementary Fig. 1.

A schematic drawing of the SL structure is shown in Fig. 1a. It should be noted that La δ doping creates a 2D electron gas (2DEG) with high-density conducting carriers at the interface (0.5 electrons per unit cell), due to the leakage of the 3d1 electrons in La3+Ti3+O2−3 into the 3d0 states in Sr2+Ti4+O2−3 (refs 8, 23, 24, 25). The partial 3d electrons, or the distribution of the Ti3+ ions are confined around the LTO layer with the QW width of a few (5–6) unit cells23,26. On the other hand, it has been shown that the STO layer remains largely insulating and can serve as a barrier layer if the thickness is larger than three unit cells (u.c.)23,26. Therefore, the 2DEG formed at the interface can be considered as a QW with a thickness of a few nanometres, as shown in Fig. 1b. While many previous studies have focused on the in-plane electronic transport behaviours of such a 2DEG in titanate-based oxide heterostructures25,27,28, little is known about the out-of-plane junction properties29. In addition, unlike typical RT devices composed of tens of nanometres-thick semiconductor QWs, the tunnelling in our devices occurs through only an atomically thin layer, the fundamental lattice unit, providing a promising outlook for an ultrafast transit time.

Nonlinear current–voltage characteristics

Figure 2 shows the junction current–voltage characteristics of the TMO QWs at various temperatures. At room temperature, a weak hysteresis curve, which manifests the typical bipolar RS behaviour, was observed. The two different resistance states could be achieved by switching the polarity of the bias voltage. Indeed, the memory characteristics have been confirmed to show a typical RS behaviour. In general, understanding the switching mechanisms is a major challenge in achieving better non-volatile memory performance. To explain the bipolar RS phenomenon, various electric field polarity-dependent models, including ion migration19, Mott transition30 and formation of Schottky barrier31,32,33, have been suggested. In particular, the Schottky barrier formed at the interface has been identified to trigger the RS behaviour for Nb:STO-based junctions31,33. More specifically, changes in the Schottky barrier by either a charge trap at the defect states or oxygen migration due to applied bias voltage has been frequently attributed for the bipolar RS behaviour31,32,34. Similar mechanism, if not the same, seems to play a major role in our SL as well. As a qualitatively similar bipolar RS behaviour was also observed for a Pt/Nb:STO junction (inset of Fig. 2a), we believe that the RS behaviour originates mainly from the interface between the SL and Nb:STO.

Figure 2: Resonant tunnelling and negative differential resistance.
figure 2

(a) Temperature-dependent I(V) characteristics of a superlattice revealing a resonant tunnelling feature superimposed with the resistance switching. The arrows indicate the direction of voltage sweep. The inset shows a similar temperature-dependent current as a function of voltage for a bare Nb:SrTiO3 substrate. (b) Differential curves (dI/dV) for the same data.

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As temperature decreases, the overall current level increases for both voltage polarities, and the RS becomes more distinct with a larger discrepancy between the LRS and HRS. Such temperature-dependent increase of the current level can be attributed to the largely enhanced carrier mobility and dielectric constant of STO at low temperatures25. In particular, similar temperature-dependence of the current level for the Pt/Nb:STO junction (inset of Fig. 2a) suggests that the bottom electrode Nb:STO is largely responsible for the increasing current level with decreasing temperature. At T<∼220 K, an interesting transport behaviour starts to develop at ∼1.2 V while maintaining the overall bipolar RS feature of our SL. A clear and smooth NDR behaviour is then observed by further ramping up the voltage to the positive bias direction. It should be noted that such a smooth peak in I(V) curve is significantly different from the usual abrupt NDR features observed for conventional RS in TMOs. For general RS (for both bipolar and unipolar), the current level drops immediately when the switching occurs from a LRS to a HRS, in stark contrast to what we observe here. Moreover, a further increase in the current above the clear peak feature in I(V) curve was observed, which has never been reported for conventional RS, to the best of our knowledge. These characteristic features signify that the origin of NDR in our QW SLs is fundamentally different from that of the conventional RS often observed in oxide thin films.

It is also important to point out that the NDR behaviour uniquely originates from the TMO QW structure. I(V) curves for a Pt/Nb:STO junction as a function of temperature shown in the inset of Fig. 2a represent only a typical bipolar RS behaviour of Nb:STO junctions. While similar RS behaviours have been observed for various Nb:STO-based junctions as discussed previously32,33, the smooth peak feature and clear NDR behaviour were absent, indicating that the deliberately designed TMO SL with QWs is indeed responsible for the unique feature. Moreover, on differentiating the I(V) curves of the SLs as shown in Fig. 2b, we indeed find two clear zero-crossing points for T<200 K. This result again indicates that the NDR is a consequence of the resonant states formed inside the QWs, rather than associated with the conventional RS. Observation of NDR only at lower temperature possibly due to the reduced phonon scattering further confirms the RT behaviour.

Theoretical calculations on resonant tunnelling

To verify that the NDR behaviour indeed originates from RT, we have performed a theoretical analysis by taking into account the band gap, effective mass and dielectric constant (ɛr) of the TMO heterostructure (see Methods section for detail). Among these parameters, ɛr of an oxide heterostructure with 2DEGs has not been widely studied. However, it is expected that the creation of interfacial charges would drastically reduce the ɛr value of the highly dielectric STO. As this change leads to a significant modification in the dielectric screening of the conducting carriers, we focus here on the effect of ɛr. Figure 3 shows the evolution of energy levels of the quantized states and VR for [LTO1/STO6]10 SL as a function of ɛr. The quantized energy levels show the values in the absence of external electric field. The actual potential wells and wavefunctions within the well with corresponding energy levels are represented in Fig. 1b for ɛr=100. As ɛr increases, the well becomes shallower, weakening the quantum confinement—that is, both the energy difference between the states and the number of confined states are reduced upon the increase of ɛr. For ɛr≤100, the well is deep enough to accommodate three confined states (ground, first and second excited states) within the QW, while only two confined states are possible for ɛr>100 (Fig. 3a). On the basis of the energy level separation and the QW geometry, we can calculate VR as a function of ɛr (Fig. 3b). As ɛr increases, a smaller VR is expected because of the smaller energy difference between the ground and first excited states. For ɛr=100, VR=1.23 V is needed to induce RT between the ground and first excited states in the deliberately designed oxide SL, as shown in Fig. 1c. The theoretical calculation implies that it would be rather difficult to observe a well-defined higher order peak in the tunnelling current. The confinement of the second excited state is only possible for ɛr<100 ideally. Even then, the state becomes easily unbound by applying a small electric field. Practically, the overall high current level makes it impossible to observe clear high-voltage features. Especially, the current substantially increased to a very high level at low temperature and the current compliance set to prevent thermal damage of the oxide QW obscures the peak feature. (We noted some temperature fluctuation near the lowest temperature due to the Joule heating, but the I(V) characteristic was highly stable and reproducible.)

Figure 3: Theoretical calculation of the confined energy levels and VR in an oxide quantum well structure.
figure 3

Effect of ɛr on (a) energy levels of confined electrons in the quantum wells without an external electric field and (b) VR in a [(LaTiO3)1/(SrTiO3)6]10 oxide superlattice. When ɛr=100, we obtain a single resonant condition at VR=∼1.23 V, which is consistent with the experimental result.

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Discussion

It should be noted that the RT behaviour is observed for the positive bias only, which can be attributed to the asymmetric sample geometry and resultant current profile. The current level for the negative bias is too large (for both HRS and LRS), possibly hindering the observation of the NDR behaviour. In addition, the current reaches to the compliance limit much faster, which makes it even more difficult to observe the NDR behaviour for the negative bias. Finally, the I(V) characteristic of our oxide device is remarkably similar to that from a SiO2/Si resonant tunnelling diode,4 strongly supporting that the NDR behaviour is based on RT in our TMO heterostructure.

We note that a few previous studies on TMO junctions claimed an observation of resonant states16,35. These reports indicated that resonant states could be formed with VR on the order of 0.1–1.0 V due to defects or impurity states. The observations are based on the chemical doping, that is, oxygen vacancies in SrTiO3−δ and Mn doping into SrRuO3 (SrRu0.95Mn0.05O3) for Pt/SrTiO3−δ and SrRu0.95Mn0.05O3/Nb:STO interfaces, respectively. On the other hand, our discovery of clear RT is based on a deliberately designed TMO QW SL, which might provide an unprecedented opportunity to develop novel tunnelling oxide electronic devices.

The observation of RT behaviour further provides quantitative information useful for understanding the physics of RT phenomena and insight for technological applications. We note that such a quantitative analysis could not be conducted on TMO QWs, as RT behaviour has never been observed previously. As the RT lifetime (τRT) is important to understand the tunnelling behaviour of electrons through the TMO QW, we have computed τRT using the energy uncertainty condition at the energy corresponding to the RT, that is, τRT=ħ/2ΔE, where ħ=h/2π, h is the Planck’s constant and ΔE is the half width at half maximum of the resonant peak36. Due to the broad feature of the resonance peak (∼1 eV) for our TMO QW, we obtain a rather small τRT value (∼0.7 fs), which is orders of magnitude smaller than that obtained in semiconductor QWs36. This value is also rather small compared with the traverse lifetime across the tunnelling barrier, and therefore, strong coherence is not expected in the complex oxide QWs. In fact, the small τRT in our QW SL is expected as such a heterostructure has a rather small relaxation time (τμ=∼42.4 fs)24 of the charge carriers, which is also orders of magnitude smaller than those obtained from conventional semiconductors, due possibly to strong correlation37. In addition, the peak-to-valley current ratio (PVCR) and the peak current density (PCD) of our TMO-based RT diode are about 1.3 and 120 A cm−2, respectively, at the lowest temperature (4 K). PVCR is rather small compared with that of conventional semiconductor RT diodes where the typical value is >3 at room temperature. On the other hand, PCD of semiconductor RT diodes span seven orders of magnitude from tens of mA cm−2 to hundreds of kA cm−2. Therefore, the PCD value we have measured from our TMO RT device is within the range of the semiconductor-based RT diodes.

The RT behaviour in our oxide QW SL enhances yet another advantageous functionality, which is unique to the TMOs. Indeed, the resistance ratio between the HRS and LRS is observed to be largely enhanced due to the RT feature. Figure 4 shows the junction resistance of the HRS and LRS measured at 0.5 and –0.5 V, respectively, as a function of temperature. The inset shows the resistance plot as a function of applied bias voltage. The difference between the HRS and LRS resistance increased with decreasing temperature. Below 150 K, we observed the ON/OFF ratio to be larger than 105, while it was slightly larger than 10 at room temperature. Typically, the ON/OFF ratio for bipolar RS is about 102, much smaller than that for unipolar RS. The completely different temperature-dependent behaviour of the resistance (HRS shows insulating behaviour while LRS shows metallic temperature-dependent behaviour) mainly due to the RT feature greatly enhances the ON/OFF ratio. Below 120 K, the compliance current played a role, somewhat decreasing the HRS resistance value (empty symbols in red). Nevertheless, we could still observe a large resistance ratio (∼105) with an increasing trend towards the lowest temperature we employed. Undoubtedly, such a large enhancement in the resistance ratio stems from the RT behaviour of the QW SL. The drastically enhanced tunnelling probability near the resonant bias voltage substantially decreased the resistance of the LRS near VR. The dip feature for the resistance value at ∼1 V for the LRS shown in the inset of Fig. 4 clearly signifies the enhanced tunnelling probability.

Figure 4: Temperature-dependent resistance switching.
figure 4

The resistance values for high- and low-resistance states (that is, ON and OFF) at −0.5 and 0.5 V are summarized as red and blue filled symbols, respectively. The empty symbols denote the resistance values for high-resistance states at −0.5 V with partial switching due to the compliance current limit. The inset shows the temperature-dependent resistance as a function of applied voltage. See the legend in Fig. 2 for temperature indexing.

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In summary, we have observed an intriguing NDR feature in a SrTiO3/LaTiO3/SrTiO3 QW superlattice at low temperatures. The NDR behaviour is attributed to a resonant tunnelling occurring through the deliberately designed oxide QWs. In particular, because of the existence of the resonant tunnelling, a largely enhanced ON/OFF ratio has been achieved in the bipolar resistance switching, which occurs at the interface between the heterostructure and metallic substrate. Our study also demonstrates the potential of oxide heterostructures for a quantum mechanical behaviour that has been thought to be possible only in conventional semiconductor heterostructures. Thus, we believe that the discovery of resonant tunnelling through oxide-based QWs can lay down a stepping stone to oxide electronics.

Methods

Sample fabrication

A [(LaTiO3)1/(SrTiO3)6]10 SL sample was fabricated at 700 °C in 10−5 torr of oxygen partial pressure using pulsed laser epitaxy. A KrF excimer laser (λ=248 nm) with a laser fluence of ∼1 J cm−2 was used for ablation of a single crystal STO and a sintered La2Ti2O7 target. An atomically flat TiO2 layer terminated (001) Nb-doped STO (0.05 wt%) single crystal buffered with 10 u.c. of STO was used as a substrate. The 10 u.c. STO buffer layer was used to ensure a good surface and interface quality of the oxide QW. The growth process was monitored using reflection high-energy electron diffraction (RHEED), ensuring the layer-by-layer growth. Supplementary Fig. 1a shows an oscillation of the RHEED specular spot intensity as a function of growth time. Six u.c. layers of STO and one u.c. layer of LTO were consecutively deposited. The in situ RHEED pattern along the [100] direction of the substrate before the SL growth (Supplementary Fig. 1b) is clearly maintained even after the growth (Supplementary Fig. 1c), indicating an optimized 2D layer-by-layer growth. The surface topographic image by atomic force microscopy (the background of Supplementary Fig. 1d) also presents a well-conserved ∼0.4 nm high step-and-terrace structure of the substrate even after the deposition of the SL, indicating atomically well-defined surface and interface. After the growth, the SL sample was in situ post-annealed for 10 min at the growth temperature in a relatively high-oxygen pressure ambience (10−2 torr) and then cooled in the same pressure to fully compensate potential oxygen vacancies. We note that the low-pressure growth and subsequent post-annealing are necessary steps for the growth of the perovskite LaTiO3, as it has a very narrow growth window for oxygen pressure. The growth at higher oxygen pressure results in La2Ti2O7 or impurity phases. X-ray diffraction θ–2θ scan demonstrated that the designed SL structure was realized (Supplementary Fig. 1d). Excellent crystallinity was confirmed from the rocking curve scan as shown in Supplementary Fig. 1e (for example, 006 peak of the SL). The full-width-at-half-maximum value was comparable to that of the Nb-doped substrate. Reciprocal space mapping around the 114 Nb:STO substrate reflection confirms the fully-strained SL sample (Supplementary Fig. 1f).

Electrical characterization

The top electrode Pt (∼300 μm in diameter) was patterned by RF sputtering on top of the sample surface using a shadow mask. External bias was applied to the Nb:STO substrate, which served as the bottom electrode. The temperature-dependent current–voltage (I(V)) curve was measured using a physical property measurement system (Quantum Design Inc.) with a source measure unit (Kethley 236). The current compliance (0.1 A) and the maximum sweep voltage value (−2 to 4 V) were set to prevent the device from damaging.

Theoretical calculation

The shape of electrostatic potential (Fig. 1b) induced by La δ-doping in STO was obtained by solving the Poisson and the Schrödinger equation self-consistently, without any electric field applied. The self-consistent calculations were performed iteratively using Broyden’s second method until the convergence of the electrostatic potential is reached.38 An external electric field was then applied to obtain envelope wavefunctions and energy levels of electrons (Fig. 1c). We examined ɛr values of STO in the range of 10–103, (note, while ɛr of bulk STO at low temperature is known to be very large, ɛr strongly varies with the electric field, temperature and sample geometry) and effective mass of 4.4 (out-of-plane band effective mass of STO) was used for the calculations39.

Additional information

How to cite this article: Choi, W.S. et al. Resonant tunnelling in a quantum oxide superlattice. Nat. Commun. 6:7424 doi: 10.1038/ncomms8424 (2015).