# Progress in THz Rectifier Technology: Research and Perspectives
### THz Diode Technology: State of the Art on Metal Multi-Insulator Metal (MI\({}^{n}\)M) Diode
Figure 11 shows the cross-sectional views of the MI\({}^{3}\)M tunnel device. These diodes are made of Cr of 100 nm thick, Al\({}_{2}\)O\({}_{3}\) insulator layer of 2 nm thick, HfO\({}_{2}\) insulator layer of 2 nm thick, and Cr\({}_{2}\)O\({}_{3}\) insulator layer of 2 nm thick. The layers are placed on a 550 nm thick SiO\({}_{2}\) film on top of a 500 \(\upmu\)m thick Si substrate not visible in Figure 11. The oxides are placed sequentially in accordance with their ascending potential barrier values (i.e., 0.64 eV, 0.75 eV, and 2.62 eV, for Cr\({}_{2}\)O\({}_{3}\), HfO\({}_{2}\), and Al\({}_{2}\)O\({}_{3}\), respectively). The results are verified at specific voltage values (\(-\)3.0 V, +1.2 V, and +2.7 V, respectively). MI\({}^{3}\)M constrains each well to possess only one allowed state. The _Asym_ for Cr/Cr\({}_{2}\)O\({}_{5}\)-HfO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\)/Cr and Cr/Cr\({}_{2}\)O\({}_{3}\)-Al\({}_{2}\)O\({}_{3}\)-HfO\({}_{2}\)/Cr devices is 5 and 3 around 2.8 V, respectively. Figure 11: Cross-sectional views of the MI\({}^{3}\)M tunnel device. For Cr/Cr\({}_{2}\)O\({}_{3}\)-Al\({}_{2}\)O\({}_{3}\)-HfO\({}_{2}\)/Cr there is a peak 6 around 4.2 V. _N_L for Cr/Cr\({}_{2}\)O\({}_{3}\)-HfO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\)/Cr is 5 at 1 V and 4 at 1.5 V; at 4.2 V, Cr/Cr\({}_{2}\)O\({}_{3}\)-HfO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\)/Cr shows a peak equal to 6. In [65], the authors present MI\({}^{2}\)M composed of Pt/TiO\({}_{2}\)/TiO\({}_{1.4}\)/Ti with high current density and high asymmetry simultaneously. Figure 12 shows the energy band diagram of the Pt/TiO\({}_{2}\)/TiO\({}_{1.4}\)/Ti. An oxygen-non-stoichiometric layer, TiO\({}_{2-\times}\), is used as a second layer. In the schematic, \(\varphi_{1}\) is obtained by subtracting the electron affinity of the dielectric from the work function of metal-1, \(\Delta\varphi\) is the work function difference between metal-1 and metal-2, \(S_{1}\) and \(S_{2}\) are the thicknesses of the insulator 1 and insulator 2. \(\Delta\)EA is the electron-affinity difference between insulator-1 and insulator-2, \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are the respective dielectric constants of the insulators. \(\Delta E_{1}\) and \(\Delta E_{2}\) can be expressed by Equation (10) [65]. \[\Delta E_{1}=\frac{S_{1}\varepsilon_{2}}{S_{1}\varepsilon_{2}+S_{2}\varepsilon _{1}}\Delta\varphi;\ \Delta E_{2}=\frac{S_{2}\varepsilon_{1}}{S_{1}\varepsilon_{2}+S_{2} \varepsilon_{1}}\Delta\varphi \tag{10}\]  
In forward bias condition, insulator 1 acts as a single tunnel barrier; in reverse bias condition, both insulators function as tunnel barriers, leading to high asymmetry. Pt/TiO\({}_{2}\)/TiO\({}_{2-\times}\)/Ti is fabricated on a substrate Si, as shown in Figure 13a. The technique to form the insulator layer is atomic layer deposition (ALD), obtaining high uniformity. The metal pads, Pt (50 nm) and Ti (70 nm) are overlapped for an area of 900 \(\upmu\)m\({}^{2}\). The design parameters are \(\varphi_{1}\) = 1.7 eV, \(\Delta\varphi\) = 1.3 eV, dielectric constant \(\varepsilon_{\rm  
Figure 12: Energy band diagram of the Pt/TiO\({}_{2}\)/TiO\({}_{1.4}\)/Ti. Reprinted with permission from ref. [65]. Copyright 2019 Scientific Reports. Figure 13: (a) MI\({}^{2}\)M fabricated on a silica substrate Si, where the metal pads, Pt and Ti, are overlapped for an area of 900 \(\upmu\)m\({}^{2}\), and (b) cross-sectional view of the diode part, obtained by TEM. Reprinted with permission from ref. [65]. Copyright 2019 Scientific Reports. thicknesses of the oxide layers are \(S_{\text{TiO2}}\) = 3 nm and \(S_{\text{TiO2-x}}\) = 2 nm, respectively. The cross-section in Figure 13b shows the contrast of the upper oxygen-stoichiometric and lower non-stoichiometric oxide layers. The results obtained experimentally for this diode are an average current density at a forward bias of 1 V of 4.2 \(\times\) 10\({}^{6}\) A/m\({}^{2}\) and a maximum asymmetry at 0.45 V of 7.26.