# Monolithically Integrated THz Detectors Based on High-Electron-Mobility Transistors
## 6 Results
### Single Detectors  
To verify the theory from Section 2, two measurements were carried out for each detector: a high-resolution DC measurement and a gate voltage sweep under THz radiation. The differential output conductance differentiated according to the gate voltage was computed using the DC measurement. The resulting plane was cut at the drain voltage equal to zero volts and superimposed on the result from the irradiation measurement. The result of these two measurements of the structure A2 is shown as an example in Figure 8. There is an excellent agreement between the maxima, so one can conclude that the theoretical derivation is valid. One can, therefore, predict the optimal gate voltage for resistive mixing with a theoretical analysis based only on a DC measurement. The optical sensitivity was determined using the measured detection current \(I_{\text{Det}}\) and the measured THz power \(P_{\text{THz}}\) at the detector location. The THz power and detection current were measured versus frequency with a step size of 1 GHz. All raw data measurements and the smoothed curves are shown in Figure 9a. The measured frequency range depends on the design frequency. As can be seen from Equation (6) for the sensitivity employed here, we have ignored any losses of the lens and substrate or mismatches from the antenna, and we assumed that the antenna captures the complete power of the source, which provides a pessimistic (lower bound) value for the sensitivity. \[Sen_{opt}=\frac{I_{\text{Det}}}{P_{\text{THz}}}\left[\frac{\text{mA}}{\text{W}}\right] \tag{6}\]  
We determined the noise equivalent power for the individual detector structures based on this optical sensitivity \(Sen_{opt}\) as  
\[NEP_{opt}=\sqrt{\frac{4\,k_{B}\,T}{R_{V_{Gate,opt}}}}\frac{1}{Sen_{opt}}\left[ \frac{\text{W}}{\sqrt{\text{Hz}}}\right] \tag{7}\]  
where \(k_{B}\) is the Boltzmann constant, \(T\) is the temperature in Kelvin, and \(R_{V_{Gate,opt}}\) is the channel's resistance at the gate voltage with the highest detection current. This calculation is based on the fact that the channel's resistance is the noise source of the detector, which was confirmed in [24]. The average of the channel resistances of the five detector structures is 1.1 k\(\Omega\). Figure 9 depicts the measured optical sensitivity and Figure 9 the optical NEP, determined using Equations (6) and (7) for all detector structures highlighted in Figure 6, respectively. The results in Figure 9 highlight in colors the mean values for the respective measurement. The THz power drops from 0.3 THz to 1.5 THz by two orders of magnitude, which is in accordance with the specifications for the THz source. The detected currents at the output from each individual detector are above 1 nA at all frequencies. All THz detector structures show outstanding detector properties in terms of sensitivity and NEP. What should be highlighted here is structure A1, which occupies a significantly smaller area than the other THz detectors, but has a high sensitivity around 200 GHz. Both broadband detector structures A2 and B2 show a flat response up to frequencies around 0.8 THz and a drop in sensitivity beyond 0.8 THz. This drop is probably due to the gate width used (5 \(\upmu\)m) and the associated capacitance in the antenna base. The capacitance connected in parallel to the antenna terminals causes the impedance to transform to lower impedance values, resulting in a smaller voltage swing. There are two clear extreme values for structure C1, a sensitivity maximum at 175 GHz and a sensitivity minimum at 400 GHz, which are probably related to a low feed point impedance and the far field of the antenna structure at 400 GHz. Structure D2 was designed for a frequency of 350 GHz and contains a clear minimum for the NEP and maximum for the sensitivity at 400 GHz with a 3 dB  
Figure 8: Determination of the optimal gate voltage using a high-resolution DC measurement. The theoretical estimation of the normalized drain current (blue solid curve) is an impressive agreement with measured results (red dashed line).