Design and Simulation of Tunneling Diodes With 2D Insulators for Rectenna Switches

1. Introduction

In general, a typical rectenna, i.e., rectifying antenna, consists of an antenna and rectifying circuit. The rectenna was first developed by Brown in 1963 [1]. The rectifying circuit is used to convert electromagnetic (EM) waves into direct current (DC) electricity. The conventional rectifying circuits work properly with radio-frequency (RF) signals of a range from 3 kHz to 500 kHz. [2] Certain carefully-designed rectifying circuits could be operating at up to 300 MHz with bipolar junction transistors and 2 GHz with integration of multiple MOS devices [3,4]. As the telecommunication is entering into the 5G and soon 6G era, both fast response and large bandwidth are needed, pushing the limit of frequency toward the high end of RF range (>100 GHz) [5]. For example, millimeter waves (30-300 GHz) and terahertz signal will be used in 6G technology [6,7]. The 100 GHz signal demands 10 ps in response time, approaching the limit in transit time for an electron to diffuse across a silicon PN junction diode. Such a long diffusion time places a strict limit on the high-frequency application in converting alternative current (AC) into DC.

On the other hand, optical detection, as an important method for non-ionizing medical detections [8,9], has been increasingly used in wearable electronics, e.g., smart watches, to measure heartbeat, blood sugar, blood oxygen and so on. This technology requires the lights, a kind of high-frequency electromagnetic waves, to penetrate through the skin [10]. The current wearable electronics are often equipped with visible lights, e.g., green and red lights, to perform the biomedical measurement [11]. However, the medical information obtained by such wearable electronics is quite limited and not precise. THz propagation through the biological tissues would be accompanied by much less scattering loss because of its much longer wavelength compared to those of visible or infrared radiation [12]. It is well known that EM waves at 10¹² Hz (THz) are able to image human tissues without harm and provide much more information at a higher resolution in comparison with other methods. For example, ultrasound, another method for non-ionizing detection, with frequencies ranging from 2 MHz to 12 MHz, has a resolution at 1 mm, much lower than that of optical and THz detection. Thus, THz electronics offer excellent safe evaluation, high resolution and precision, all of which are very attractive for future medical detections [13,14]. Since the optical and THz signal frequencies are too high for conventional semiconductor diodes, new diodes with a switching time faster than 1 ps are needed to rectify THz signal for medical detection.

In addition, rectenna has been studied for energy harvesting of 2.4 GHz EM waves for internet-of-things technology [15]. To receive and rectify EM waves at optical frequencies, e.g., solar energy, optical rectennas [16,17] become attractive high-efficiency and low-cost solar cells if fast-switching diodes can be available. The conventional solar cells are based on a semiconductor PN junction whereas electron-hole pairs are generated by photons with energy larger or close to the energy bandgap (E_g) of the semiconductors. Silicon-based solar cells in the most commercially dominated products have a limited efficiency, about 16% for polycrystalline Si, 30% for monocrystalline Si and 55% for multi-junction cells [18,19,20]. In comparison, the rectenna solar cells has a much higher efficiency (> 85%) and can be fabricated at low cost [16].

Therefore, the common technical challenge for the above-mentioned emerging technologies (high-speed telecommunication, THz electronics and rectenna solar cells) hinges on new rectifier diodes. As shown in Figure 1(a), in the conventional semiconductor PN junction diode, the excess carriers are injected to each side of the junction as minority carriers and diffuse through the diode. The diffusion time (τ_s) is close to the smallest value of electron lifetime (τ_e) or hole lifetime (τ_h). The lifetime of minority carrier depends on Auger lifetime due to Auger recombination [21]. In typical, for Si with a doping of 10¹⁸ cm^-3, the diffusion time is within a range from 10 ns to 1 μs, which is corresponding to switching frequencies from 1 MHz to 100 MHz. Optimization of device structures and diode materials, such as Schottky junction diodes and GaN diodes, has been studied to improve the switching frequency to GHz [22]. However, THz and optical frequencies are still too high for the conventional PN junction diodes.

On the other hand, carrier transport based on tunneling can easily exceed the limit of diffusion in PN junctions, reaching the scale of femtoseconds (10^-15 s). The metal-insulator-metal (MIM) junction with an atomically thin insulator between two different metals is a simple yet very effective tunneling diode. A schematic of MIM tunneling diode and its energy barrier for tunneling are shown in Fig. 1(b). The electron tunneling time is determined by the energy barrier profile and applied bias across the barrier. Studies showed that the tunneling time across a tunneling diode could reach femtoseconds [23] and even attoseconds (10^-18 s) in an atomic hydrogen. [24]

The MIM heterostructures have recently been studied as a current rectifying diode [25,26,27,28]. Research interest of MIM diodes was focused on application in rectifying high-frequency electromagnetic waves, THz electronics, infrared light and even conversion of visible light into electricity [16,29,30]. The MIM diodes based on bulk insulators, such as TiO₂, ZnO and NiO, could be applied in 28.3 THz rectenna switches [31]. Amorphous InGaZn oxide was shown to improve turn-on voltage control in the diodes [32]. Amorphous metal electrodes could also improve the current rectifying performance [33]. Recently, MIM diodes based on 2D insulator materials have been reported [34]. MIM diodes with single and multiple insulators have been studied and analyzed for the conversion of infrared light into electricity [35,36]. Despite the rapid progress, there still lacks a comprehensive study that combine first-principle calculation for designing 2D insulator materials, modeling of tunneling diodes, and simulation of rectifier circuits.

In this work, we applied density function theory (DFT) method to design and model MIM tunneling diodes with two-dimensional (2D) materials as the insulators. In the modeling, 1, 2, 3-layer TiO₂, TaO₂ and SnO₂ were designed by oxidizing the corresponding 2D metal-sulfur materials. The monolayer or few-layer 2D materials were placed between two different metals to form a tunneling junction diode. In the device simulation, it is found that the Au/monolayer TiO₂/Al tunneling junction diode exhibits the best rectifying performance. The simulated tunneling current-voltage (I-V) characteristics were fed through a rectifier in PSpice modeling, showing excellent signal rectifying from THz to optical frequencies.

2. Modeling and Simulation Method for Materials, Devices and Circuits

In this study, the atomistic simulations of 2D materials and MIM tunneling diodes were performed in QuantumWise Atomistix Toolkit (ATK) simulation platform [37,38,39] from Synopsys based on density functional theory (DFT). The DFT calculations employed the norm-conserving Pseudo-Dojo pseudopotentials [40] with Perdew-Burke-Ernzerhof (PBE) parametrization of exchange-correlation function [41] for all materials and diode structures. To bring all atoms to the ground state, a 12×12×1 Monkhorst-Pack k-point grid mesh was used for the sampling of the Brillouin zone. The forces were kept to the least at 0.01 eV/Å. For the calculations of carrier transport in the tunneling diodes based on metal/2D insulators/metal heterostructures, we used first-principle calculations integrated with density functional non-equilibrium Green's function (NEGF) method. In addition, the current-voltage (I-V) characteristics was calculated by following the Landauer-Büttiker approach [42]. The design of 2D materials and computation of carrier transport were implemented by using the above-mentioned QuantumWise ATK code. [37]

In the simulation of 2D materials, 1, 2, 3-layer metal-sulfur materials are designed and modeled with structural relaxation. These ultra-thin 2D metal-sulfur materials are usually semiconductors with an energy bandgap. [34] In the structural relaxation in simulation, the position of all atoms and the three-dimensional lattice parameters were optimized with the least Hellmann-Feynman force of 0.01 eV/Å on the metal-sulfur layer materials. In the optimization, Pulay-mixer algorithm was used as a fully self-consistent field (SCF) iteration control with a tolerance value of 10^-5 eV. The maximum number of iteration steps was set at a limit of 100. The self-consistent field computations were strictly tracked to guarantee full convergence within the iteration steps. Periodic boundary conditions were employed along the three directions (in-plane and out-of-plane) with a large vacuum region of 7 Å to minimize the interlayer interaction. [43] Energy band structures and electronic properties of the metal-sulfur layer materials could be calculated once the structure optimization simulation was converged. In the design and simulation of metal-oxide layer materials, we proposed a simulated oxidation process: (1) the sulfur atoms were replaced with oxygen atoms; and (2) the new metal oxide materials were fully optimized by following the similar procedure in obtaining relaxed metal-sulfur layer materials.

The 2D layer oxide insulators were placed between two metal electrodes to construct metal/2D insulators/metal tunneling diodes. There is a 7-Å gap between the 2D insulators and electrodes at each side to protect the layer oxides from chemical reaction with the metal electrodes during simulation. As the layer insulators were surrounded by vacuum, our simulation was able to neglect the effect of substrate and electrodes. The simulation of tunneling current in the metal/2D insulators/metal diodes under a bias voltage was implemented by using DFT method in the Virtual Nanolab ATK package. [37] Generalized Gradient Approximation (GGA) [41] was adopted with PBE exchange correlation to describe and include the electron correlation and exchange energies in the calculation of carrier transport under bias voltage.

The design and modeling of a full-bridge AC/DC power converter built on the proposed MIM diodes was done in OrCAD PSpice simulation tool. [44] In the circuit simulation, a PSpice device model was built for the MIM tunneling diodes by implementing the I-V characteristics and tunneling time obtained in above-mentioned DFT calculations. An AC voltage input of 1.0 V at 100 kHz was applied in the simulation and a DC output was analyzed to evaluate the performance of proposed MIM tunneling diodes. The output voltage as a function of the frequency of received signals from 1 Hz to 1000 THz was simulated based on the calculated tunneling time to analyze the high-frequency performance.

3. Results and Discussion

3.1. Molecular structures and Energy Bands of 2D metal oxide insulators

Figure 2(a) shows the design of MIM tunneling diodes with the 2D insulator material sandwiched between the top and bottom metal electrodes. The two electrodes have a different work function, enabling current rectifying functionality of the MIM diodes. The key element of the diodes is the middle 2D insulator and its interface with metal electrodes. It is desirable to use insulators with a low tunneling barrier height, i.e., high electron affinity, such as TiO₂, SnO₂ and Ta₂O₅, for low-voltage current rectifying [33,34]. Lower barrier height generally leads to higher tunneling rate. However, the efficiency of tunneling current also depends on the quality of the interface between insulator and metal electrodes. The proposed 2D insulators have a smooth and self-passivated surface, very favorable for tunneling. As shown in Figure 2(b), the 2D layer-structured oxide insulators, such as TiO₂, SnO₂ and TaO₂, can be obtained by oxidizing the counter parts 2D metal sulfur layer materials, such as TiS₂, SnS₂ and TaS₂. These 2D layer materials are van de Waals materials with monolayer or multilayer, whereas the S atoms can be replaced with O atoms by oxidation. In the simulation, the oxidation is expressed by replacement of S atoms with O atoms followed by a structural relaxation to achieve stable 2D oxide layer materials.

Figure 3 shows the energy band structures of hexagonal TiS₂ and TiO₂ obtained from the DFT simulation. As mentioned above, the 2D TiO₂ materials are achieved by replacing S atoms in TiS₂ with O atoms followed by a structural relaxation and optimization. The DFT calculation of 2D oxides converged at a minimal force of 0.01 eV/Å, achieving a stable layer structure which can be obtained in experiment and production. After such a proper structural relaxation, energy band structures and electronic properties of each monolayer, bilayer and trilayer structures can be reasonable evaluated.

The result indicates that the 1, 2, 3-layer TiO₂ materials have a significant bandgap and can be considered as insulators. The energy bandgap value increases from 1.8 eV for monolayer TiO₂ to 3.1 eV for trilayer TiO₂. The 2D TiO₂ have a significantly larger bandgap than the counterparts of 2D TiS₂. TiS₂ is considered as a semiconductor with a relatively small energy bandgap. [45,46] The simulated band gap for monolayer materials is lower than that of bulk materials because the spin-orbit coupling (SOC) was not considered in calculation [47,48]. Nonetheless, the materials structure and electrical properties of 2D TiO₂ are successfully modeled and can be used for the simulation of carrier transport, tunneling diodes and voltage conversion circuits.

Similar DFT simulation processes are also performed on the TaS₂ and SnS₂ layer materials, and the TaO₂ and SnO₂ layer materials obtained via oxidation of the metal-sulfur counterparts. Figure 4 shows the molecular structures of the above-mentioned trilayer Materials. The 2D layer materials were designed with thin vacuum region (7 Å) surrounding them to minimize chemical interaction with substrate or electrodes. These 2D TaS₂, SnS₂, TaO₂ and SnO₂ were then optimized with structural relaxation using QuantumWise ATK code. [37,41] The energy band structures of TaS₂ and TaO₂ mono-, bi-, and trilayer are shown in Figure 5. The result indicates that a significant band gap exists in TaO₂ layered materials while the band gap is negligible in TaS₂ layered materials, which has been previously reported [49]. Also, the band gap of 2D TaO₂ (about 0.7 eV) does not change appreciably with increasing number of layers, which is different with that of TiO₂. In addition, the band structures of 2D TaO₂ materials look like the ones of n-type semiconductors with Fermi level merged into the conduction band.

Figure 6 shows the energy band structures of mono-, bi- and trilayer SnS₂ and SnO₂ materials. The 2D SnS₂ layer materials have a significant indirect bandgap about 1.6 eV.

However, the energy band gap of SnO₂ layered materials disappears after the SnS₂ is oxidized with the S atoms being replaced by O atoms. From the observation from the band structures, the SnO₂ layer materials look more like a semimetal with zero bandgap than a semiconductor or insulator. The result indicates that the SnO₂ layer materials are not a good choice as 2D insulators for application in the proposed MIM diodes.

3.2. Design and electrical properties of MIM diodes with 2D insulators

As seen from the DFT calculations, although some 2D metal oxide materials are not a good choice for insulators, excellent 2D materials can be screened and found by using such a simulating oxidation experiment based on DFT calculation. The next step is to design a MIM diode using the modeled 2D insulators and study its electrical properties. As shown in Figure 7, MIM diodes are constructed with monolayer, bilayer or trilayer TiO₂ being sandwiched between Au and Al electrodes. The 2D TiO₂ films act as the smooth, ultra-thin tunneling barrier for electron to transport between two metal electrodes. In the design of Au/TiO₂/Al heterojunction, 9 atomic layers of Au and Al have been employed to maintain the structure of metal during the structural relaxation in the simulation. This significantly increases the computation time in the simulation since a large number of atoms are included. However, this design is sufficiently close to the real devices in which metal films are much thicker than 2D insulators and will not experience structural change due to lattice difference with the 2D materials. It should be noted that the metal structures have an unreal change in structural relaxation if only < 5 atomic layers of metals are used in simulation whereas the thickness of metal is comparable to the inserted 2D insulators. In addition, the design of MIM tunneling diodes is not limited to 2D TiO₂ and can be applied to other 2D insulators.

Figure 8 shows the I-V characteristics of Au/TiO₂/Al tunneling diodes with monolayer, bilayer and trilayer of TiO₂ at room temperature. In the simulation, an electric bias voltage from -1.0 V to 1.0 V is applied on MIM diodes at a step of 0.2V. The I-V curves exhibit a junction-like current rectifying function with low resistance for current flowing from Au electrode to Al electrode and high resistance along the opposite direction. Although all three MIM diodes have current rectifying capability, the current density decreases exponentially with increasing layer numbers of TiO₂ films. In addition, the I-V curves become less exponential, i.e., current on/off ratio within a certain voltage window decreases, as the number of TiO₂ layer increases. This indicates that the rectifying capability decreases with increasing thickness of TiO₂ layer materials. Our study shows that the Au/monolayer TiO₂/Al diode exhibits the best current rectifying characteristics. In the circuit modeling (to be discussed later), we selected the Au/monolayer TiO₂/Al tunneling diode as the switching diode model for voltage conversion and adjusted the current level or diode resistance for application by choosing the right cross-section area. It should be noted that the tunneling time is not be affected by the device area.

The tunneling time is an important parameter for rectifier diodes. It directly determines the upper limit of switching frequency that the rectifier can handle. In this work, the tunneling time of the Au/monolayer TiO₂/Al diode have been studied and calculated for different bias voltages. Figure 9 shows the electron affinity extracted from the simulation for the monolayer TiO₂ between Au and Al electrodes. A trapezoid shape of tunneling barrier is drawn along the extract value of electron affinity for each bias voltage (see Figure 9(a)-(c)). The trapezoid barrier profile will be used for the calculation of tunneling time. The tunneling time can be calculated using the integration equation shown in Figure 1(b) following the method by Buttiker and Sinton [50,51]. As shown in Figure 9(d), the tunneling time decreases slightly from 1.85 fs to 1.65 fs with increasing bias from 0 V to 1.0 V. Such a short switching time enables the proposed diode to effectively rectify high-frequency signal up to 600 THz. It should be noted that the simulation does not consider the impact of impurity and defect at the interface and inside the 2D materials. The interface impurity and defect usually increase tunneling time and decrease tunneling current, which should be an important issue to examine in experiment. Nonetheless, the proposed metal/2D insulator/metal tunneling diodes exhibit excellent current rectifying capability with an ultra-fast switching time reaching femtosecond (10^-15 s).

3.3. Circuit simulation of rectifiers based on 2D MIM tunneling diodes

The performance of 2D MIM tunneling diodes can be full evaluated in a rectifying circuit. Figure 10(a) shows a schematic of rectenna circuit with both an antenna and a full-wave bridge rectifying circuit. In the rectifier circuit, D1, D2, D3 and D4 are identical diodes based on the above-simulated Au/monolayer TiO₂/Al MIM tunneling diode with the I-V characteristics shown in Figure 8 and tunneling time (1.6 fs) derived in Figure 9(d). The diodes have a cross-section area of 10^-4 cm² (i.e., 100 μm × 100 μm), exhibiting an on-state current at the range of 10 mA to 40 mA. The circuit simulation was carried out and analyzed in OrCAD PSpice Integrated Simulation platform [44]. In the circuit design, the antenna is replaced with an AC voltage source which is tunable in voltage and frequency. Both the AC-to-DC conversion and high-frequency performance were studied and analyzed. Figure 10(b) shows that the rectifying circuit effectively converts a 1.0-V, 100kHz AC input, simulated signal received by antenna, into a 0.7-V DC voltage output. The DC output voltage is stabilized within 20 ms, exhibiting a robust AC/DC conversion with the proposed 2D MIM tunneling diodes. Figure 10(c) shows the DC output voltage as a function of frequency of input AC signals in circuit simulation. The rectifying circuit based on the proposed monolayer TiO₂ MIM tunneling diode successfully maintained a DC output voltage of about 0.7 V for up to 800 THz, agreeing with the switching time of the tunneling diodes. Such a frequency range is very attractive for medical detection, rectenna solar cell and high-speed telecommunication.

4. Conclusions

In summary, we have designed, simulated and investigated a family of 2D insulators by oxidizing metal sulfides by using DFT method. The I-V characteristics of metal/insulator/metal junctions with the chosen 2D insulators exhibit excellent rectifying capability with a significant dependence on the number of layers. The diode tunneling time has also been studied, showing promising potential for THz electronics. In addition, we have successfully designed and simulated an AC-to-DC rectifying circuit based on the proposed monolayer TiO₂ MIM tunneling diode. The rectifier is able to robustly convert AC voltage input into DC voltage output. The rectifier circuit is well functional at high frequency up to 800 THz. Such rectifying switches based on the proposed 2D insulator MIM tunneling diodes are very attractive in many applications including medical detection, 5G/6G telecommunication and rectenna solar cells.