## 2 Device and Experimental Setup
### Si/SiGe MODFET  
To fabricate THz detectors based on plasma oscillations high-mobility short channels FETs must be used [12; 13]. The double heterojunction SiGe/Si/SiGe allows the fabrication of extremely thin layersof strained silicon (specifically under biaxial tensile strain) sandwiched between unstrained (relaxed) SiGe layers. Figure 1 shows the vertical lay-out of the n-channel strained-Si MODFET [19].  
Both the double heterojunction and the strain of the intermediate pure-silicon layer contribute synergistically to improve the performance of FET devices that are based on the Si/SiGe material system as compared to conventional MOSFETs. On the one hand, the conduction band offsets at the Si/SiGe interface provide confinement (the conduction band offset of the heterojunction Si/Si\({}_{0.70}\)Ge\({}_{0.30}\) is about 180 meV) for electrons in the silicon layer enabling the use of this layer as the 2D channel of n-channel FET transistors by effectively blocking vertical carrier transport and, therefore, limiting the gate current of the transistor, on the other hand, biaxial tensile strain leads to high values of the electron mobility in the 2D channel. The latter is achieved by simultaneously lowering the electron conductivity mass and the electron scattering rate in the transistor channel as compared to bulk Si MOSFETs. Strain of the silicon channel modifies the six-fold degeneracy of the minimum of the conduction band of bulk silicon, under biaxial tensile strain the two valleys with their long axis perpendicular to the hetero-interface become the minimum of the conduction band and channel electrons will essentially occupy these two valleys which reduces the electron conductivity mass [20; 21]. The electron scattering rate in the strained Si channel is reduced as compared to the one in conventional unstrained channels, this is achieved both through the referred lift-off of the valley degeneracy that lowers the probability of intervalley scattering for the electrons in strained-Si channel and by the doping modulation in the structure that allows to replace the intense carrier scattering by ionized impurities in the channel of MOSFETs by the less active remote impurity scattering by the dopants in the supply layer. All the above factors contribute to build up high-mobility electron plasmas in the channel of strained-Si FETs that is a key parameter to detect THz radiation.  
The fabrication of the transistor was detailed in [19]. Its horizontal layout is schematically given in Figure 1. The separation between the ohmic contacts of source and drain is \(L_{sd}=2\)  
Figure 1: Left: Schematic cross section of the transistor under study. Front and back illumination configurations are highlighted by showing the respective incident THz beams in each configuration. Right: Vertical distribution of the energy band diagram under the gate at equilibrium showing the Fermi level. The double-deck supply (two unstrained n\({}^{++}\) Si\({}_{0.7}\)Ge\({}_{0.3}\) highly doped layers) sandwiching the 12 nm-thick strained silicon layer (region of thickness \(w\) highlighted in dark grey and surrounded by two nominally undoped spacer layers) generates a double quantum well inside de channel [15; 19].  
gate electrode had a width of 60 \(\upmu\)m and its length (\(L_{S}\)) was 500 nm. Unlike in conventional FETs the gate electrode of the transistor is not equidistant from source and drain as an asymmetrical position of the Schottky-gate improves THz detection by plasma waves [19].