# Microwave SINIS Detectors
## 3 Quantum and Bolometric Response  
The key issue when estimating the efficiency and performance margins of such a detector is the response origin or mechanism of detection. Earlier publications [7] adopted the bolometric approach, which predicts high responsivity at dc or a low frequency signal below 70 GHz for aluminum SINIS. The development of quantum response theory [12] has made it possible to adequately describe processes at higher frequencies. A detailed experimental study of the transition from thermal absorption to quantum efficiency was carried out in [31] (schematic image of SINIS detector--see Figure 4). It was experimentally demonstrated that the thermal contact of the absorber and substrate could significantly reduce the responsivity. The important conclusion drawn in [12,31] is that electron cooling does not lead to an increase in sensitivity. We analyzed the characteristic time constants of energy relaxation in different SINIS structures. The most advantageous was the device with a suspended absorber, without losses of heat to the substrate [14]. The full description of the process of THz photon absorption in SINIS structures is rather complicated; it is not limited to a simple single electron-phonon interaction. For photons with energy significantly above the thermal energy, the energy of the electron that absorbs such a photon should correspond to the high electron temperature of about \(\mathit{l}\!f=kT_{\mathrm{e}}\), that is, 15 K for 350 GHz. The electron-electron interaction time at this temperature is much longer compared to the electron-phonon interaction time. As a result, a high-energy phonon is created. This phonon has three ways to escape: in the substrate, in the superconducting electrodes, or in the electron system with a quantum efficiency of 0.023 electrons per quantum at 1 THz. This is accompanied by the creation of an electron and hole pair, each of which have an energy of \(\mathit{l}\!f/2\). An excited electron with energy \(\mathit{l}\!f/2\) will create a phonon with the same energy of \(\mathit{l}\!f/2\), corresponding to an electron temperature of 7 K, which again will create an electron-hole pair with energies \(\mathit{l}\!f/4\); for this couple, the electron-electron interaction will be more efficient, and this leads to the creation of two excited electrons and one hole, with energy values of \(\mathit{l}\!f/12\) each. At this step, the electron-electron interaction dominates, and leads to the effective multiplication of remaining excitations. Figure 3: Voltage dependences of the electron temperature of the normal absorber of the detector (left scale) and of the voltage and current responses (right scale) at temperatures of (0.095 \(\pm\) 0.01) K and (0.316 \(\pm\) 0.02) K when irradiated with a black body radiation source. Red lines show the results for the temperature of the sample holder \(T\) = 0.32 K, with black lines for the temperature \(T\) = 0.1 K. Solid lines belonging to the right scale show voltage responses, while dotted lines show current responses. Graph from [30]. Estimations of responsivity, in this case, are based on nonequilibrium electron and phonon distribution functions and mechanisms of quantum absorption [12]. The important figure is the quantum efficiency, which is equal to the number of excited and detected electrons for one absorbed photon. It can approach the value of \(n=\textit{hf}/\textit{kT}\). However, if the dc bias is close to the energy gap, electron cooling effectively removes excited electrons from the absorber. Excited electrons cannot be multiplied, and the quantum efficiency drops to n = 1. According to this model, we can distinguish two operation modes: photon counter and quantum detector-multiplier modes. The current responsivity in the first case is \(dq/dE=e/\textit{hf}\), and it is \(e/\textit{kT}\) in the second case.