# Progress in THz Rectifier Technology: Research and Perspectives
## 3 THz Diode Technology: General Information on Geometric Diode (GD)
#### THz Didee Technology: State of the Art on Geometric Didee (GD)
For a fixed \(d_{neck}\) = 50 nm and \(V_{DS}\) (V) = 0, the resistance (\(\Omega\)) is \(5\times 10^{3}\); instead, for \(V_{DS}\) (V) = 0.5 and d\({}_{neck}\) = 50 nm, the resistance is 4 \(\times\) 10\({}^{3}\). The responsivity \(S\) (V\({}^{-1}\)) assumes 0.1 for \(V_{DS}\) (V) = 0 and 0.3 for \(V_{DS}\) (V) = 0.5. In [87], the authors present a new geometric diode design, referred to as Z-diode, exhibiting improved rectification over 0.1 V compared to the inverse-arrowhead design discussed above. For this type of diode that is able to rectify up to 28 THz, a finite mean-free-path length (MFPL) does exist that maximizes the current asymmetry at a particular voltage. This suggests that the diode can be tuned to maximize the asymmetry. In both structures, inverse-arrowhead (Figure 21a) and Z-diode (Figure 21b), under forward bias condition, electrons drift from left to right, and the geometry allows electrons to pass through the constriction, or neck. However, in the reverse bias condition, these two structures present a substantial difference. In fact, for inverse-arrowhead geometry, electrons drift right to left, more easily through the neck, as the opening is perpendicular to the general drift direction. In the Z-diode, the reverse leakage is reduced as the neck opening is oriented perpendicular to the general drift direction. The strength of the geometric rectification effect depends on the device dimensions relative to \(\lambda_{\text{MFPL}}\). To obtain the I(V) characteristics, both structures used \(\lambda_{\text{MFPL}}\) = 500 nm, neck width \(d_{n}\) = 100 nm, and shoulder width \(d_{s}\) = 1 \(\upmu\)m, indicated in Figure 22a,b. The shoulders are electrodes from which charges are injected. Voltage \(V_{0}\) from \(-\)0.5 to 0.5 V is applied to the electrodes to drive the current through the device. Figure 21: (a) Geometric effect in the inverse-arrowhead diode; and (b) geometric effect in the Z-diode. Reprinted with permission from ref. [87]. Copyright 2021 Nanomaterials. The material used for simulations is graphene, which can be tuned by applying a gate bias set at \(V_{S}=10\) V for the simulations. The graphene subsequently is placed on silicon wafers. In Figure 23a,b, the Z-diode exhibits a greater nonlinear I(V) curve and higher current asymmetry above 0.1 V compared to inverse-arrowhead diode. This is due to the stronger suppression of the reverse current owing to the geometry. Despite these results, Z-diode shows higher resistance at low biases, compared to the inverse-arrowhead diode. This factor must be considered when the diode is integrated to the antenna. In Figure 24, the asymmetry as a function of \(\lambda_{\text{MFPL}}\) is shown. As \(\lambda_{\text{MFPL}}\) approaches zero, the asymmetry approaches 1. Figure 23: Comparison of inverse-arrowhead diode and Z-diode. (**a**) The current–voltage characteristics of both geometries; and (**b**) the resulting current asymmetries. Reprinted with permission from ref. [87]. Copyright 2021 Nanomaterials. Figure 22: (**a**) Relevant dimensions of an inverse-arrowhead diode; and (**b**) a Z-diode. Reprinted with permission from ref. [87]. Copyright 2021 Nanomaterials. With \(d_{neck}\) = 100 nm, the asymmetry in Figure 24 shows a peak around \(\lambda_{\text{peak}}\approx\) 600 nm, then asymmetry drops for \(\lambda_{\text{MFPL}}>\lambda_{\text{peak}}\). The latest studies on graphene GD reviewed in this paragraph are summarized in Table 7.