Modulation-doping a correlated electron insulator

Abstract

Correlated electron materials (CEMs) host a rich variety of condensed matter phases. Vanadium dioxide (VO₂) is a prototypical CEM with a temperature-dependent metal-to-insulator (MIT) transition with a concomitant crystal symmetry change. External control of MIT in VO₂-especially without inducing structural changes-has been a long-standing challenge. In this work, we design and synthesize modulation-doped VO₂-based thin film heterostructures that closely emulate a textbook example of filling control in a correlated electron insulator. Using a combination of charge transport, hard X-ray photoelectron spectroscopy, and structural characterization, we show that the insulating state can be doped to achieve carrier densities greater than 5 × 10²¹ cm^-3 without inducing any measurable structural changes. We find that the MIT temperature (T_MIT) continuously decreases with increasing carrier concentration. Remarkably, the insulating state is robust even at doping concentrations as high as ~0.2 e^-/vanadium. Finally, our work reveals modulation-doping as a viable method for electronic control of phase transitions in correlated electron oxides with the potential for use in future devices based on electric-field controlled phase transitions.

Fig. 1. Structure of Modulation-doped VO₂ heterostructures.

a Schematic diagram of the heterostructures used in this work. The thickness of VO₂ is varied while the thicknesses of all the other layers are as mentioned in the schematic. b Schematic energy band diagram for a VO₂/LAO/TiO_2-x heterostructure before and after the junction formation. Electron accumulation is expected based on the known band offsets. The color intensities are chosen to be proportional to expected electron densities for better visualization. E_C, E_V, and E_F indicate the conduction band edge, valence band edge, and Fermi level, respectively. c High-resolution cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image showing abrupt interfaces between TiO₂ substrate and VO₂ film and VO₂ film and the amorphous LAO spacer layer. d Elemental mapping using energy dispersive x-ray spectroscopy (EDS) showing the various layers in the heterostructure. Note that the scales of c and d are different.

Fig. 2. XRD and temperature-dependent electrical transport in VO₂ heterostructures.

a High-resolution θ-2θ XRD spectra for 9.5 nm VO₂ thin film and for VO₂ heterostructures with varying thicknesses. For nomenclature simplicity, we distinguish VO₂ thin films and heterostructures with a VO₂ thickness of ‘t’ as tVO₂ and tVO₂-het, respectively. b Resistance versus temperature plots for the same set of samples as shown in a. Resistance values presented here are normalized to the resistance at 330 K (also see Supplementary Fig. 7). c A comparison of the changes in T_MIT versus the changes in the rutile C-axis lattice parameter (ΔT_MIT vs ΔC_R) for this work and other previously published work using W- and Mo-doping^,, oxygen vacancy doping and strain. The relative changes are compared to the undoped and unstrained states in the case of bulk doping and for strained VO₂, respectively. [also see Supplementary Table 1].

Fig. 3. Carrier concentration-dependent MIT in VO₂ heterostructures.

Plots of temperature-dependent a carrier densities and b carrier mobilities for tVO₂ and tVO₂-het samples as mentioned in the legends. Carrier density in the insulating state increases with decreasing VO₂ thickness while carrier mobility decreases. c A phase diagram from the results in a. The dotted lines connected across the data points are a guide to the eye.

Fig. 4. Transport characteristics of heterostructures as a function of spacer layer thickness.

Schematic representation of quantum mechanical tunneling of charge carrier across the spacer layer for a 2 nm and b 4 nm thicknesses of LAO (t_LAO). ‘Ψ’ is the electronic wave function. The schematics represent a decrease in the transfer of charge carriers from the dopant layer (TiO_2-x layer) to the VO₂ layer as a function of increasing t_LAO. c Resistance-Temperature plots comparing the MIT characteristics of 7.5 nm VO₂ modulation-doped heterostructures employing t_LAO of 2 nm, 4 nm, and 10 nm with the MIT characteristics of a 7.5 nm VO₂ film with a 2 nm LAO cap layer, but without any dopant layer.

Fig. 5. Band bending and core level spectral changes in VO₂ heterostructures.

A comparison of V 2p core-level spectra of modulation-doped VO₂ heterostructures for a the insulating (200 K) and b the metallic states (at 310 K). A clear shift in the V 2p levels is seen in the insulating state spectra but not in the metallic state spectra. Schematics in c and d show the expected band-bending in the modulation-doped heterostructures for the insulating and metallic states respectively. Band-bending is expected in the insulating state and not in the metallic state. Two additional spectral features not seen in VO₂ thin films are labeled P1 and P2.

Fig. 6. Robust MIT in VO₂ at high carrier densities.

A comparison of the V 3d valence band (VB) spectra of modulation-doped VO₂ heterostructures for the insulating (200 K, blue) and metallic states (at 310 K, orange) for different VO₂ film thicknesses of a 7.5 nm VO₂ film and b 7.5 nm, c 4.5 nm, d 3.5 nm, and e 1.5 nm VO₂ heterostructures. There is a clear spectral weight shift across the MIT for all the samples with the insulating state being robust even for the heterostructure with a VO₂ thickness of 1.5 nm, corresponding to carrier doping of ~0.2 e⁻/Vanadium.

Fig. 7. Temperature-dependent X-ray diffractograms of VO₂ thin films and heterostructures.

X-ray diffractograms of a 9.5VO₂, b 9.5VO₂-het, and c 4.5VO₂-het measured in the insulating phase (at 200 K) and the metallic phase (at 320 K) of VO₂. VO₂ ($\overline{4}02$)_M and (002)_R reflections can be clearly distinguished for all the heterostructures studied in this work. The $\left(\overline{4}02\right)$_M peak is the out-of-plane (of the substrate) Bragg reflection in the monoclinic phase of VO₂ while (002)_R is the out-of-plane reflection in the rutile phase. d A comparison of temperature-dependent XRD spectra of the 4.5VO₂-het film measured at 200 K, 280 K, and 320 K. The XRD spectrum measured at 280 K shows rutile phase characteristics like the one measured at 320 K suggesting that VO₂ remains in the rutile phase at 280 K in the 4.5 nm VO₂ heterostructure.