## 3 Results and Discussion
### Terahertz Measurements  
To investigate the coupling of the incoming terahertz radiation with the channel, two types of measurements were performed: (i) front illumination where the radiation excited the device from the top side and (ii) back illumination where the transistor was excited from the bottom side (the substrate side) (see Figures 1a and 2b). It was experimentally observed that the bonding wires could play an important role to couple the incoming terahertz radiations to the channel [24; 25]. This effect should be lowered if the device is excited at its back side. Figure 5 shows the measured photoresponse under CW excitation at 0.15 THz (Figure 5a) and at 0.3 THz (Figure 5b) for both configurations: front and back illumination. The maximum of the device response in the photovoltaic mode was obtained when the gate electrode of MODFET was biased at \(V_{gs}\sim-0.85\) V (i.e., the device was operating at the onset of the subthreshold region) for both frequencies and configurations setups (front and back illumination). The detector response follows the well-known behaviour of a non-resonant (broadband) in agreement with a low value of quality factor (Q = \(\omega\tau<1\)) [26] where \(\omega\) is the angular frequency and \(\tau\) the relaxation time. For the front illumination configuration, the photoresponse decreases by a factor of 2 (from \(\sim\)400 \(\mu\)V to 200 \(\mu\)V) when the frequency rises from 0.15 THz to 0.3 THz. In contrast,  
Figure 4: (**a**) Transfer characteristics of the transistors under study for two values of \(V_{ds}\) (the drain-to-source voltage). (**b**) Measured output characteristics for three values of \(V_{gs}\) (the gate-to-source voltage). an increase by a factor of 2 is obtained under back illumination when the frequency of the source is doubled from 0.15 to 0.3 THz. A numerical model of the transistor was built in the electromagnetic solver software package CSTTM Microwave Studio. 3D simulations solving the Maxwell equations using the Time Domain Solver were performed assuming that a plane wave with a frequency of 0.3 THz propagates along the \(Z\) axis with normal incidence on the top side or on the bottom side of the transistor, i.e., front and back illumination respectively. The electric field magnitude of the incoming wave was assumed to be 1 V/m; the electric field was defined as parallel to the transistor's channel. In Figure 6 the distribution of the normalized internal electric field (\(E_{r}\)) induced by the impinging 0.3 THz beam along the transistor channel is given in dB as:  
\[E_{r}(dB)=20 log_{10}\left(\frac{E}{\frac{1V}{m}}\right), \tag{1}\]  
where the magnitude of the electric field in the right-hand side of equation is expressed in V/m. The magnitude of the induced electric field under back illumination (Figure 6b) is significantly higher than the one obtained under front illumination (Figure 6b) in good agreement with measurements (Figure 5b). This better coupling of the incoming power radiation to the channel is attributed to the low reflexion of the beam and transparency of the silicon substrate to THz radiation. Therefore, in silicon substrate devices, back illumination can significantly enhance the THz photoresponse of the detector. This is an interesting aspect from the technological standpoint because, as pointed out in Section 1, the silicon substrate in Si/SiGe MODFETs also provides the added advantage of CMOS compatibility. To further investigate the above behaviour and the coupling of the terahertz radiation with the electron channel, the device was rotated in the plane perpendicular to the terahertz beam and the photoresponse signal was systematically determined for each angular position of the device. As above discussed, the maximum of the intensity of the response was obtained when the bias of MODFET gate was kept close to the value of the threshold voltage of the device for each angle.