## 2 Quasi-Static Analysis Using the Proposed Equivalent Circuit Model
### Analysis Using a Small-Signal Method at The Subthreshold Region
The total output current is comprised of the current of the AC component and the DC component and is expressed as follows:  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]1  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]2  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]3  
where the DC current in (20) is ignored because only a capacitor is present in the \(z_{GD}\) and hence AC current flows at the total current. Substituting with the input voltage of (1) and the output voltage of (18) in (17), the total output current is modified as  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]4  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]5  
where the first term in (21) cannot exist because it is a dc voltage and is summarized as (22) using (19). The analysis for the detector operating in the subthreshold region assumes that the current of the detector device is a drain current of the weak inversion as shown in (23) [26]. The drain current in weak inversion can be transformed as (24) by Taylor's series as follows:  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]6  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]7  
where \(I_{s}\) is a constant proportional to \(W/L\), \(n\) is a nonideality factor, \(V_{T}\) is \(kT/q\). The plasmonic conversion transconductance for the weak inversion is expressed as a function of input voltage and obtained using (24) as follows:  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]8  
Substituting (22) with (12) and (25) and assuming that the AC voltage disappears by the filter, the output node is extracted only for the DC voltage as  
\[i_{d}(t)=g_{c}(t)\cdot v_{IN}(t). \tag{9}\]9  
\[g_{c}(t)=k_{n}\bigg{(}v_{gs}(t)+V_{GS}-V_{th}-\frac{v_{ds}(t)}{2}\bigg{)}, \tag{10}\]0 Schematic diagram of the proposed small-signal analysis for the plasmon detector core. The signal detected on the output node by the detector device in (26) is obtained as  
\[g_{c}(t)=k_{n}\bigg{(}v_{gs}(t)+V_{GS}-V_{th}-\frac{v_{ds}(t)}{2}\bigg{)}, \tag{10}\]1  
The voltage responsivity and NEP of the detector operating in the subthreshold region are expressed from (27) as follows:  
\[g_{c}(t)=k_{n}\bigg{(}v_{gs}(t)+V_{GS}-V_{th}-\frac{v_{ds}(t)}{2}\bigg{)}, \tag{10}\]2  
\[g_{c}(t)=k_{n}\bigg{(}v_{gs}(t)+V_{GS}-V_{th}-\frac{v_{ds}(t)}{2}\bigg{)}, \tag{10}\]3  
where \(z_{DS}\) corresponds to the output resistance \(R_{out}\) and a constant \(\sqrt{4 KT/I_{s}^{3}\cdot\left(1/nV_{T}\right)^{3}}\) is replaced by A for simplification purposes. As shown in (28) and (29), the voltage responsivity and NEP are represented as a function of \(V_{GS}\), similar to the analysis results in strong inversion. The NEP is associated with voltage responsivity and decreases when the voltage responsivity increases. The voltage responsivity exhibits the quadratic function form for \(V_{GS}\) where the maximum voltage responsivity exists. Equation (28) does not mean that the voltage responsivity and the incident voltage of the THz signals are in inverse proportion because the output resistance in the plasmon detector depends on the incident power of the THz signals. The input and output resistance should be increased to improve the voltage responsivity. It is important to increase the output resistance to increase the voltage responsivity because the input impedance has limits to be improved at high frequency due to the parasitic capacitances at the gate input node.