Magneto-transport study of top- and back-gated LaAlO₃/SrTiO₃ heterostructures Open Access

The two-dimensional electron liquid (2DEL) present at the interface between the insulating oxides LaAlO₃ (LAO) and SrTiO₃ (STO) exhibits several fascinating properties, including superconductivity and a large spin-orbit coupling.¹ It has also attracted much attention in the context of device applications following the realization of field-effect transistors and devices with nanoscale dimensions.^2–6 

The large electric permittivity of the STO substrate, especially at low temperatures, facilitates tuning of the 2DEL properties by an electric field effect in back gate transistors.² This back gate configuration allows considerable control of multiple parameters of the 2DEL such as the superconducting critical temperature, spin-orbit interaction, carrier density, and mobility.^7–12 Additionally, it might simultaneously change the confinement of the 2DEL.^8,13,14 This confinement modifies the bulk STO electronic structure and leads to an orbital ordering with light d_xy and heavy d_xz/d_yz sub-bands.^15,16 Recently, there has been growing interest in employing top electrodes in gating experiments of LAO/STO devices,^17–21,38 as LAO has a large band gap and reasonably large dielectric constant.²² The transistor operation of a top-gated LAO/STO device was demonstrated with an on-off switch of the conductivity using less than 1 V.³ However, the responses of the 2DEL to top and back gate can be different: a first comparison revealed, indeed, a different modulation of the mobility by the two approaches.¹⁸ 

In this paper, we present a systematic study of transport properties of top- and back-gated LAO/STO heterostructures in the presence of a perpendicular magnetic field. Electric field effect tuning is achieved by using the LAO film and STO substrate as top and back gate dielectrics respectively. Large tunability in resistance, carrier density and magneto-resistance were observed in both configurations. The top-gate approach shows reversible tuning with voltage sweeping, contrary to back gate.^7,14 Top and back gates affect the mobility differently, back gate being more effective to boost it. The evolution of the weak-localization/weak-antilocalization behavior is also extracted from the magneto-transport data. This allows us to study inelastic and spin-orbit magnetic fields for constant carrier densities achieved by a combined use of top and bottom gates. We try to link the differences in the response of the 2DEL to the confining potential shape and to the multi-band conduction.

The Hall bars are defined by pre-depositing an amorphous STO layer as a hard mask.⁵ Structures down to 25 μm in width are realized by optical lithography. Subsequently, epitaxial LAO films are deposited on TiO₂-terminated STO (001)-oriented single crystals by pulsed laser deposition in an oxygen pressure of 8 × 10⁻⁵ Torr at 800 °C or 830 °C and annealed in 0.2 bars of oxygen at 520 °C for an hour as documented elsewhere.^7,23 After growth, ex-situ sputtered Pt is used for the top gate and Au films are sputtered on the backside of the substrate for the back gate electrodes. A schematic of a device with a top and back gate is displayed in Figure 1(a). Figure 1(b) shows an optical image of a typical Hall bar structure with sputtered Pt film as the top gate. Measurements are carried out keeping the leakage current from the top electrode below 1 nA, much smaller than the channel current (typically in the range 0.1–1 μA). Transport data presented here below were obtained measuring a sample grown at 830 °C with 15 unit cells (u.c.) thick crystalline LAO in a perpendicular magnetic field configuration. Samples with thickness in the range 10–17 u.c. and channel width in the range 25–100 μm were also fabricated and tested: they all show comparable transport properties.

Capacitance characterization with an AC voltage of 10 mV at 200 Hz demonstrates good capacitor behavior (small loss tangent and negligible leakage current) of top-gated devices prepared in this fashion.²⁴ We consistently observe an effective dielectric constant (ϵ_eff) for the Pt/LAO/2DEL capacitor smaller than the bulk value, which is possibly due to interfacial effects.²⁵ Moreover, this interfacial effect might be the reason for the weak dependence of ϵ_eff on temperature as shown in Figure 1(c) (bulk LAO has a temperature independent dielectric constant). ϵ_eff has little dependence on the top gate voltage V_TG as shown in Figure 1(d). We also do not observe in the investigated V_BG range substantial changes in the capacitance when we modulate the 2DEL carrier density using back gate.²⁶ 

Figure 2 compares the low temperature resistance behavior sweeping the gate voltages from the top (panel (a)) and from the back (panel (b)).²⁷ For top gate voltages V_TG, the tuning of the sheet resistance R_S is reversible. We note the modulation of R_S is about 40%, the V_TG range being set to avoid leakage across the LAO layer. For back gate voltages V_BG, a large history dependent behavior manifests in R_S when V_BG is first swept upwards and then downwards. In this geometry, from the as-grown state, R_S first decreases and then saturates for a wide range of V_BG (red curve in panel (b)). If we stop increasing V_BG (at $V BG max =50$ V as in panel (b)) and reverse the sweeping direction, we observe that the resistance increases strongly (blue curve), deviating from the upward sweep. Then, as long as V_BG is kept below $V BG max$⁠, the sweeps are reversible (the resistance moves along the blue curve). In this configuration, extremely high resistance states can be achieved. If V_BG exceeds $V BG max$⁠, the resistance remains constant in the upward sweep (green curve); however, the new reversible behavior is shifted to higher voltages (purple curve). This “forming process” of the resistance state suggests that many added electrons spill out of the quantum well and go into trapped states.¹⁴ 

To build a more comprehensive understanding of the different effects of V_TG and V_BG, we investigate the magneto-transport properties of the 2DEL using both gates. The data are displayed in Figure 3: in the left panels, the measurements are performed at various V_TG while V_BG is maintained fixed, and vice versa for the right panels. We observe that the changes in R_S induced by sweeping V_TG or V_BG are quite comparable, but on a completely different voltage range. Figures 3(c)–3(f) display the Hall resistance R_xy as a function of magnetic field for different values of V_TG and V_BG: we observe an evolution from linear to non-linear behavior pointing to a transition from single to multiple band conduction.^11,28,29 Since correctly extracting the total carrier density n_2D from a non-linear R_xy is generally difficult, the modulation of the total carrier density δn_2D is calculated using a parallel plate capacitor model. For the top gate, using ϵ_eff = 12, we obtain a change in n_2D that agrees with the estimation from the variation of the Hall coefficient with V_TG when R_xy is linear in field (see Figure 3(c)). For the back gate, δn_2D is obtained by the capacitor measurement as a function of V_BG.⁷ These δn_2D modulations are plotted as top axes in panels (a) and (b). Now comparing the change in R_S versus δn_2D for the two gates, we see that the same R_S modulation is achieved by top gate with a variation in n_2D that is roughly twice that obtained with the back gate.

This different response of R_S to the top and back gates, as well as the evolution of the Hall effect, may suggest distinct effects of the two gates on the confining potential and hence on the sub-band structure. Self-consistent calculations using a Schrödinger-Poisson approach show that a pure increase in carrier density results in a stronger confinement.^30,31 Modeling of back gate transistors⁸ and analysis of back gate voltage sweeps¹⁴ indicate that positive voltages increase the confinement width (weaker confinement) of the 2DEL; as a consequence, the energy splitting between the lower energy d_xy — and lower mobility — and higher energy d_xz/d_yz — and higher mobility — bands should be reduced.

In order to highlight the difference between the two gate approaches, we plot the mobility μ as a function of the carrier density in Figure 4 for top (panel (a)) and back (panel (b)) gate voltage sweeps. n_2D is estimated from the linear Hall effect and the carrier change induced by the capacitor effect, and μ is defined as σ(0)/n_2De, where e is the electron charge and σ(0) is the zero-field conductance; μ calculated in this fashion is therefore an effective mobility. In the same graphs, we use a color code to indicate the degree of non-linearity observed in the Hall resistance $Δ R x y ′ / R x y ′ ( 0 ) =| R x y ′ ( 7 . 5 T ) − R x y ′ ( 0 T ) |/ R x y ′ (0 T)$⁠, $R x y ′$ being the derivative ∂R/∂B at a given field. For single band conduction, $Δ R x y ′ / R x y ′ ( 0 )$ is zero (represented as blue) while for multi-band conduction, it becomes non-zero (represented as yellow/red). The mobility curves in Figure 4(a) show that top gate sweeps result in a strong modulation of n_2D and a smaller change in μ. When we change the back gate voltage, we notice a sharp increase in the carrier mobility: this is more evident in panel (b) where mobility is strongly enhanced by back gate voltages for a small variation in the carrier density. We also observe that, concomitant with the increase in μ, the Hall resistance becomes non-linear, suggesting that a second band with high mobility comes into play.^{11,15,16,28,29}

A possible scenario to understand the response of the transport properties to the field-effect tuning relates the effect of the two gates to the confining potential. As discussed above, a deconfinement of the 2DEL would reduce the d_xy versus d_xz/d_yz band splitting, this energy becoming negative in bulk STO.³² Along with this effect, carriers could be transferred to the more mobile band, resulting in higher mobility and non-linear Hall resistance. On the other hand, if electrons are more confined, the energy splitting should increase, and a shift in the Fermi level would mainly induce an increase in n_2D with little change in μ.

We finally explore the effect of top and back gates on the spin-orbit interaction of the system. We fit the magneto-conductance curves using the Maekawa-Fukuyama formula³³ and extract the inelastic field B_i and the spin-orbit field B_so for different sets of V_TG and V_BG.³⁴ Figure 5 shows the evolution of B_i and B_so as a function of n_2D. We observe that for each V_TG the back-gate tuning results in an effective modulation of B_so, in agreement with previous studies on the spin-orbit interaction.^9,29 While B_i seems to be determined mainly by n_2D, B_so should be more sensitive to the modification of the confining potential. To get further insight into the evolution of B_so upon gate tuning, in the inset of Figure 5, we plot B_so versus V_BG for the three carrier densities indicated by the shaded areas in the main panel of the figure. For the plot, V_BG is chosen as the “tuning parameter” as it should affect the electron confining potential most and hence the strength of the spin-orbit interaction, although probably in a complex way.^11,35–37 The data plotted in the inset show that the spin-orbit coupling can be tuned at constant n_2D and suggest that V_BG is indeed modifying the confinement of the 2DEL.

To conclude, we present a systematic study of the effects of top and back gate on LAO/STO heterostructures. The detailed characterization reveals differences between the evolution of R_S, R_xy and magneto-conductance using the two approaches. The observation for the back gate of a forming process and the strong enhancement of the electron mobility suggest that positive back gate deconfines the 2DEL: on one side some electrons are trapped deep in the STO; on the other side, the contribution from d_xz/d_yz states becomes more significant. The control of the electronic properties of the 2DEL using both gates, as demonstrated here, allows the spin-orbit strength to be tuned at fixed carrier densities and opens new opportunities to realize transistors where mobility and carrier density are tuned independently.

We acknowledge Pavlo Zubko for useful experimental advice and Marc Gabay for enlightening discussions. We thank M. Lopes and S. C. Müller for the technical assistance. This research was supported by the Swiss National Science Foundation through the NCCR MaNEP and Division II and has received funding from the European Research Council under the European Unions Seventh Framework Programme (No. FP7/20072013) / ERC Grant Agreement No. 319286 (Q-MAC).