# Microwave SINIS Detectors
## 3 Quantum and Bolometric Response
With an increase in frequency, the current responsivity of the photon counter drops, and when using a bolometer detector, the multiplier remains high--see Figure 5. The blue curve corresponds to the bolometric mode at a bias close to the gap voltage, with \(dI/dP=e/2 kT=2.2\times 10^{4}\) A/W; the dashed blue line is the half-gap bias, and \(dI/dP=e/0.5\Delta=5\times 10^{4}\) A/W; the red curve represents the photon counter mode, with \(dI/dP=e/\textit{hf}=762\) A/W at 350 GHz. In Table 1, we also present the estimated voltage and current responsivity for a signal frequency of 350 GHz and a bath temperature of 280 mK. The maximum voltage responsivity is calculated at the half-gap voltage bias and a dynamic resistance of 35 k\(\Omega\) for an SINIS detector with a normal resistance of 1 k\(\Omega\). The moderate multiplication of hot electrons occurs at about half gap. Detection with high quantum efficiency can be obtained using the SINIS structure with a suspended normal metal absorber made of heavy metal. In SINIS, the Kapitza resistance between Al and Pd is high, and the electron-phonon interaction is low. For comparison, it is also important to mention that optimal resistance for quantum multiplication is 5 k\(\Omega\), contrary to the case of electron cooling, wherein the optimal resistance is about 0.5 k\(\Omega\). Our measurements of SINIS detectors with suspended absorbers made of Cu, Hf, and Pd confirm the model of quantum absorption at 350 GHz with a quantum efficiency reaching 15 electrons for one photon [14] (Figure 6). Figure 4: SINIS detector: (**a**) top view, schematic image (**left**) and SEM photo (**right**); (**b**) schematic image of SINIS detector with suspended absorber; (**c**) schematic image of SINIS detector with absorber on substrate. S—superconductor, I—insulator, A—absorber (normal metal), P—pads (supply electrodes). Figure 5: Calculated frequency dependence of current responsivity for the SINIS detector at a bath temperature of 0.28 K. The top blue curve is Respl = \(e/kT\) for a bolometer multiplier at a bias voltage close to the energy gap without strong electron cooling; the dashed blue line is the bias at the half gap with Respl = \(e/2 kT\), and the red curve is the photon counter, Respl = \(e/hf\) in the case of strong electron cooling. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operation Mode** & \begin{tabular}{c} **Current** \\ **Responsivity** \\ \end{tabular} & \
\begin{tabular}{c} _\(\mathit{dI}/\mathit{d}P\)_ \\ **(A/W)** \\ \end{tabular} &
\begin{tabular}{c} _\(\mathit{dV}/\mathit{d}P\)_ \\ **(V/W)** \\ \end{tabular} \\ \hline Photon counter with electron cooling & \(e/\mathit{l}t\) & 762 & \(2.6\times 10^{7}\) \\ \hline Practical detector at half gap where R\({}_{\mathrm{d}}\) = 35 k\(\Omega\) & \(2/V_{\mathrm{\Delta}}\) & \(5\times 10^{3}\) & \(1.75\times 10^{8}\) \\ \hline Quantum detector close to gap where R\({}_{\mathrm{d}}\) = 2 k\(\Omega\) & \(e/2 kT\) & \(2.2\times 10^{4}\) & \(4.4\times 10^{7}\) \\ \hline Electric detector at dc & \(2k/(\mathrm{R_{d}}e\Sigma\
u T^{4})\) & \(3.7\times 10^{5}\) & \(1.3\times 10^{10}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Current and voltage responsivities for the main SINIS detector operation modes at 350 GHz. Figure 6: Current response at a bath temperature of 120 mK for a black body radiation power of 60 fW.