# Detection of On-Chip Generated Weak Microwave Radiation Using Superconducting Normal-Metal SET
## 2 Experimental Section
### NISIN SET as a Microwave Photon Detector  
The NISIN detector consists of a small superconducting island connected to two normal-metal leads via small tunnel junctions as shown schematically in Figure 1. The island is capacitively coupled through a floating gate electrode F, to a lead used for DC tuning voltage \(V_{\rm g}\) on one side, and to the source of the microwave signal on the other side. The DC voltage \(V_{\rm g}\) induces the polarization charge on the island, \(q_{\rm g}\equiv n_{\rm g}e=C_{\rm g}V_{\rm g}\), where \(n_{\rm g}\) is the dimensionless gate-induced charge and \(C_{\rm g}\) is the effective coupling capacitance between the voltage lead and the island. The tunneling current through the device, \(I_{\rm NISIN}\), is measured in a symmetric voltage-bias mode (\(\pm V_{\rm b}/2\)) and is considered to be the detector output signal. The charge tunneling mechanism in an NISIN transistor was investigated earlier in various regimes comprising either Andreev reflection [25; 26] or single quasiparticle tunneling [20] as the dominant transport process. In the following, we briefly present the photon-activated charge transfer and signal amplification mechanism in this device. For the purpose of clarity, we address a simplified case of low temperatures, \(k_{\rm B}T\ll\Delta\), where \(k_{\rm B}\) is the Boltzmann constant, and omit the contribution to the tunneling rates of thermally populated electron states above the Fermi level in the normal leads and thermally excited quasiparticles in the superconducting island. A more rigorous model of the tunneling current in the NISIN transistor based on a master equation approach can be found in [20]. The barrier height for electron tunneling from the lead to the superconducting island depends on the island charging energy \(E_{\rm C}=e^{2}/2C_{\Sigma}\) (\(C_{\Sigma}\) is the total capacitance of the island including the capacitance of the junctions and the gate capacitance), superconducting gap energy \(\Delta\), and the gate and bias voltages \(V_{\rm g}\) and \(V_{\rm b}\), respectively, and can be written as: \(E_{\rm t}=E_{\rm C}+\Delta-eV_{\rm b}/2-2E_{\rm C}\cdot n_{\rm g}\). At \(T=0\), if the gate voltage is tuned to an even value of \(n_{\rm g}\) (e.g., \(n_{\rm g}=0\), see the energy diagram shown in Figure 2a), an addition of one extra electron to the island requires an energy equal to at least a threshold energy \(E_{\rm t}^{even}=\Delta+E_{\rm C}-eV_{\rm b}/2\). Therefore, at low bias voltages, \(V_{\rm b}<2(E_{\rm C}+\Delta)/e\), no current passes through the device and the transistor is in Coulomb blockade regime. Changing \(n_{\rm g}\) to an odd integer number (e.g., \(n_{\rm g}=1\), Figure 2b) reduces the barrier height down to the value \(E_{\rm t}^{odd}=\Delta-E_{\rm C}-eV_{\rm b}/2\) and applying a small subgap bias voltage opens a possibility of a single-quasiparticle current through the island. The quasiparticle current includes a train of two-step tunneling cycles in the NISIN double junction (we assume, for simplicity, a symmetric case). In the first step, an electron tunnels from a lead into the superconducting island and occupies a free quasiparticle state. The rate of this process, \(\Gamma_{+}\approx\sqrt{\left(E_{\rm C}+eV_{\rm b}/2\right)^{2}-\Delta^{2}}/e^ {2}R_{T}\sim 10^{10}\) s\({}^{-1}\) (similar  
Figure 1: Equivalent circuit of the NISIN detector. The microwave (RF) signal and the DC tuning voltage, \(V_{\rm g}\), are capacitively coupled to the superconducting island through the floating gate F. NIS tunnel junctions, each with resistance \(R_{\rm T}\) and capacitance \(C_{\rm T}\), are formed between superconducting (Al, crossed boxes) and normal conducting (AuPd, open boxes) electrodes. Figure 2: Energy diagram of the NISIN SET at zero temperature.