Enhanced current density and asymmetry of metal–insulator–metal diodes based on self-assembly of Pt nanoparticles

Rectification underlies a wide range of technologies such as storage capacitors, wireless communication, high-speed switching, and energy harvesting. Direct conversion of free-propagation electromagnetic waves into direct currents using rectification has attracted considerable attention. By combining the antenna and rectifying diode, rectenna devices can perform as photoelectric conversion systems for a wide range of applications, such as infrared (IR) radiation rectification,^1,2 IR detection,^3–5 and IR imaging.^6,7 Optical rectennas, as a class of nanoscale devices, are being increasingly considered to harvest light from visible to IR range.^8,9 Metal–insulator–metal (MIM) tunnel diodes are strong candidates for use as rectifiers in optical rectennas owing to their high-speed response toward ultra-fast pole changes within the optical frequency range of visible to IR frequencies. Owing to the tunneling current mechanism having an electron transit time of femtoseconds, the MIM diode can operate at hundreds of terahertz frequencies. Therefore, MIM diodes attract increasing attention for use in optical rectennas, which contribute to energy harvesting techniques including solar energy conversion, waste-heat utilization, and environmental thermal radiation.^10–14 

Low resistivity is essential to obtain a low resistor–capacitor time constant and, hence, a high current density at high cutoff frequencies. Moreover, a high rectification performance is obtained in terms of the large current density asymmetry at forward and reverse biases. However, the tunnel current is exponentially and inversely dependent upon the barrier height and insulator thickness.^15,16 The current asymmetry originates from the asymmetric barrier shape caused by the work function difference between metals. Several studies have been reported to overcome the trade-off relationship between the current density and asymmetry. For example, controlled resonant tunneling in an MIM diode exhibits enhanced nonlinearity at low bias voltage.^17–19 In addition, controlling the barrier shape with multiple insulator layers considerably improves the diode performance.^20–22 Moreover, geometrically asymmetric MIM diodes provide an appealing strategy for high rectification owing to the enhancement of the electric field.^23–26 However, the electric field enhancement is strongly dependent on the geometrical structure of the electrodes and the precision of fabrication, which makes it challenging to scale up MIM diodes for low-cost energy harvesting applications.

In this study, we developed an MIM tunnel diode wherein metal nanoparticles (NPs) are formed at the interface of the tunneling layer and electrode to implement an electric field concentration effect. Simulations of the electric field distribution are performed to verify the strong electric field concentration at the NPs, and an analysis of the diode properties considering the variation of the tunneling barrier shape due to the electric field concentration is conducted to investigate the increase in current density and expression of asymmetry. This effect is examined by evaluating a tunneling diode in which NPs are formed by controlling the initial process of atomic layer deposition (ALD). The self-assembly of NPs provides a more robust electric field enhancement in the tunneling diode compared with the methods that require high precision control in fabrication.²⁷ Furthermore, metallic NPs can easily be assembled with typical electrodes to form MIM diodes and integrated with various types of antennas to develop high-performance rectenna systems.

A schematic of an NPs-containing MIM diode with a vertically stacked structure is shown in Fig. 1(a). The Pt NPs were distributed on the interface of the TiO₂ insulator and sandwiched Pt/Pt metal electrodes to form a PtNPs/TiO₂/Pt MIM diode. The Pt NPs contribute to the electric field concentration by forming geometrical electrodes within the entire contact interface of the top electrode. The electric field distribution of the unit cell from the MIM diode containing NPs was analyzed using the Ansys Maxwell electromechanical simulation tool. To describe the structural features of the asymmetric electrodes, the asymmetric ratio of electrodes (AREs) is defined as the ratio of the pitch size p to the diameter r of the NPs. The maximum intensity of the electric field was investigated with various AREs [Fig. 1(b)]. Notably, the electric field enhancement is almost proportional to the value of ARE for ARE < 2.5. A further enhancement is limited because the pitch size is large enough for each NP to play the role of an independent electrode. The potential distribution in the heatmap confirms the strong electric field concentrated at the NPs. Therefore, size-controlled NP arrays are required to obtain a strong electric field concentration.

The potential barrier shape was determined using the effective work function $φ$ = 5.3 eV for both the PtNPs and Pt electrodes, which are based on the crystallographic orientation of electrodes according to the results obtained via XRD and reported in the literature.²⁸ The electron affinity χ = 3.9 eV and relative dielectric constant κ = 10 for TiO₂ were obtained from the literature and empirical inference.^29,30 A schematic of the band diagrams of the PtNPs/TiO₂/Pt MIM diode at different biases are shown in Fig. 1(c). The same barrier height at the zero-bias indicates that the effect of the work function difference has been eliminated, and a uniform electron density distribution is present in the tunnel layer. Upon the application of a voltage to the electrodes, the electron density becomes condensed at the PtNPs electrode side. The effective width of the tunnel barrier decreases in the forward bias and increases in the reverse bias directions, and the tunneling probability of electrons is subsequently improved or suppressed in the corresponding bias direction, respectively. The shaping of the potential barrier induced by the electric field concentration effect was utilized to analyze the IV characteristics of this system via the WKB approximation method³¹ (see the supplementary material). To observe the remarkable enhancement of rectification performance by the electric field concentration effect, the IV characteristics were investigated using a 5.5-nm-thick TiO₂ insulator. The effective mass of electrons $m*$ = 0.16 $× m$ was determined using the relationship between the film thickness of the insulator, reported in the literature.²⁹ The calculated current density and asymmetry of the PtNPs/TiO₂/Pt MIM diodes are shown in Figs. 1(d) and 1(e), respectively. The improvement in the rectification performance is consistent with the analysis of the tunneling barrier shaping process considering the electric field concentration effect.

The PtNPs/TiO₂/Pt MIM diode was fabricated on a quartz substrate. A 70-nm-thick Pt layer was deposited by radio frequency magnetron sputtering (Shibaura, CEF-4ES), preceded by an 8-nm-thick titanium adhesion layer. A photoresist was applied and patterned via lithography (SUSS, MicroTec MA6), and the bottom of the Pt electrodes on the MIM diode was formed by ion beam milling (Hakuto, IBE-KDC 75). A 5.5-nm-thick TiO₂ layer was deposited via ALD. Ti[N(CH₃)₂]₄ was used as the precursor, and the stage temperature was 200 °C. The Pt NPs were grown on the surface of TiO₂ at 300 °C over 20 cycles. Trimethyl-methylcyclopentadienyl platinum and oxygen were used as the precursor and reaction gases, respectively. A 0.5-nm-thick TiO₂ layer was deposited on Pt NPs via ALD to ensure the formation of the array of separate NP islands. Finally, a 70-nm-thick Pt film was deposited as the top electrode under the same conditions used for the formation of the bottom electrode. The schematic of the fabrication process is shown in Fig. S1 of the supplementary material.

The growth behavior of nanometals deposited via ALD has been well researched.^32,33 Uniform NPs are synthesized via island growth at the initial stage, as described by the Volmer–Weber growth mode.³⁴ The excellent self-assembly nucleation of Pt in ALD has been reported in several studies.^35–37 We fabricated arrays of island Pt NPs using ALD and confirmed the deposition using transmission electrode microscopy (TEM) [Fig. 2(a)]. The Pt was grown by ALD over 20 cycles on the substrate and, Al₂O₃ was coated as the protection layer. The self-assembled array of Pt NPs was observed in the magnified images. The MIM diodes without and with NPs have been fabricated [Figs. 2(b) and 2(c)]. The estimated boundaries between the top electrode and insulator are depicted by the red dotted lines. A slightly wavy interfacial boundary was observed in the sample of the MIM diode without NPs, which was attributed to the grain growth of Pt during the deposition of the top electrode via sputtering. A clear concave–convex interfacial boundary was observed in the sample of MIM diode with NPs, which demonstrated that the geometrical electrodes were formed by embedding the uniform Pt NPs arrays in the tunneling layer via ALD. The upper interfacial boundaries were fitted using a circular arc to analyze the geometrical electrodes, which are shown by white dashed lines. The structural features were extracted from the TEM images for modeling the fabricated MIM diodes (see the supplementary material). ARE = 0.5 and ARE = 2 were obtained on the fabricated MIM diodes without NPs and with NPs, respectively.

The plots of current density and asymmetry vs voltage for the diodes without and with PtNPs are shown in Fig. 3. The IV characteristics were measured at room temperature in the darkroom with a source measurement unit (Keithley, 2461-900-02A). The IV curves were swept from −1 to +1 V to demonstrate the rectification performance for energy harvesting of thermal radiation at near-infrared wavelengths. The measured and calculated results are shown by the dots and solid lines, respectively. An asymmetry of 5.9 at 1 V was obtained for the Pt/TiO₂/Pt MIM diode. This asymmetry could be caused by slightly asymmetrical electrodes due to fabrication with ARE = 0.5. A 5.5-nm-thick insulator was used to calculate the IV characteristics of the MIM diode without NPs by direct tunneling. Good agreement with the experimental results provides evidence for the electric field concentration effect of the dominant tunneling mechanism in a fabricated MIM diode. A maximum current density of $2.9×105$ A/m² and an asymmetry of 63 at 1 V were observed for the PtNPs/TiO₂/Pt MIM diode. Improvements of 21 and 11 times were observed for the current density and asymmetry of this diode, respectively, compared to the fabricated MIM diode without NPs. The theoretical analysis of the barrier shape can be found in the supplementary material, indicating that the electron tunneling probability is improved by the large asymmetric electrodes. Therefore, this significant improvement in rectification is attributed to the electric field concentration effect generated by embedding the NPs in the tunneling layer. The IV characteristics were calculated based on the extracted parameters of d = 5.2 nm and ARE = 2. The calculated results are shown to be almost consistent with the measured results in terms of improvements in current density and asymmetry. These results verify the strong electric field concentration effect in the PtNPs/TiO₂/Pt MIM diode. The complicated electric field distribution in the fabricated MIM diodes caused by the self-assembled NPs' inability to form perfectly periodic arrays may help to explain the minor deviation of the asymmetry expression from the measured results.³⁸ 

The diode efficiency η_diode was calculated from the impedance matching efficiency η_c and quantum efficiency $ηβ$ (see the supplementary material). The diode performance in optical rectenna systems can be evaluated by considering the current density and maximum asymmetry. The performances of the proposed MIM diodes are shown in Fig. 4, where the measured result of the MIM diode with NPs was improved by 231 times compared to the MIM diode without NPs. We demonstrated two conventional approaches to control the diode's performance with dashed lines, which control the insulator thickness d and the work function difference $Δφ$⁠. Notably, the diode performance shows a clear trade-off by controlling the thickness. In addition, increasing the work function difference improves the current density, while the asymmetry is only marginally improved. However, the MIM diode with NPs achieved considerable asymmetry with the enhancement of the electric field concentration effect by controlling ARE, which broke the trade-off relationship. Notably, $Δφ$ = 0 was used in the performance calculation to exclude other effects. It indicates that the proposed MIM diode with NPs has significant potential to realize high rectification performance by integrating with the low barrier height and favorable work function difference.

In this study, we developed a MIM diode with metal NPs that was grown via self-assembly at the interface of the insulator and electrodes over the entire diode plane. The embedded Pt NPs serve as geometrical electrodes to modify the electric field distribution in the tunneling layer. The tunneling probability of electrons is controlled by the barrier height, which is attributed to the electric field concentration effect. Consequently, the current density and asymmetry increase simultaneously. A theoretical improvement in the rectification efficiency compared to a symmetric MIM diode is expected by implementing a MIM diode with NPs due to strong electric field enhancement. PtNPs/TiO₂/Pt MIM diode was fabricated by coating a substrate with island-grown Pt NPs via ALD, and the geometrical features of the structure were confirmed using TEM images. The performance of the MIM diode with NPs was experimentally confirmed demonstrating an improvement of 231 times compared to the fabricated MIM diode without NPs. In this study, the improvement of tunneling performance was primarily attributed to the electric field enhancement. The comprehensive current transport mechanisms of MIM diode with NPs will be investigated, including the deviation of NPs' work function owing to electrostatic interactions and other potential minor conduction mechanisms.^39,40 Further analysis, including varying the diameter of NPs and operating temperature, is required to address these issues. Improving the rectification efficiency is expected by integrating this approach with well-designed high-frequency-response tunnel diodes.

See the supplementary material for the fabrication details, the IV characteristics evaluation of the electric field concentration effect, the discussion on MIM diode with electric field concentration effect, and the evaluation method of optical rectenna efficiency.

We would like to gratefully acknowledge that this paper is based on results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO). Part of this work was supported by the Japan Society for the Promotion of Science (JSPS) (Grant No. 22J11167).