Phonon-blocked junction calorimeter

Abstract

This study introduces the theory of a microcalorimeter based on phonon-blocked superconducting tunnel junctions, integrating on-chip electron cooling and boundary resistance phonon isolation to achieve exceptional energy resolution and rapid thermal response. A general theoretical framework is presented, along with derived approximate analytical expressions for key performance metrics, including cooling factor, thermal time constant, noise equivalent power and energy resolution. The work examines the influence of device parameters, including non-ideal effects such as subgap tunneling and heat backflow, and offers insights into optimizing the detector performance. The findings highlight the potential of the phonon-blocked junction microcalorimeters to rival or even outperform state-of-the-art technologies such as transition-edge sensors, paving the way for applications requiring precise and fast energy spectroscopy.

Figures (6)

• Figure 1: (a) Schematic of the the electric circuit of the system, consisting a pair of NIS junctions and readout circuit. (b) Thermal model of the system, illustrating the heat flows in the electron and phonon channels.
• Figure 2: (a) The relative cooling factor $\eta$ as a function of the normalized bath temperature $T_B/T_c$, and thermal resistivity ratio $\rho$. (b) Comparison of $\eta$ between the numerical result (colored solid lines) and the analytical approximation, Eq. \ref{['eq:TN_approx']} (black dotted lines) as a function of $\rho$.
• Figure 3: (a) Optimal zero-frequency responsivity $S_I(0)$ as a function of the normalized bath temperature $T_B/T_c$ and resistivity ratio $\rho$. The inset compares the numerically optimized bias voltage with the approximate $V_\mathrm{opt}$ at three different $\rho = 0.1,1,10$ from top to bottom. (b) The thermal time constant $\tau_\mathrm{th}$ at optimal bias, scaled by $\gamma V R_T$, as a function of $T_B/T_c$ and $\rho$.
• Figure 4: (a) Numerically optimized total low-frequency NEP at optimal bias and its decomposition into various contributions in Eq.\ref{['eq:NEPcomponent']} (solid colored lines), scaled as $\mathrm{NEP}\cdot\sqrt{R_T}$, as a function of $T_B/T_c$ for an ideal detector with $\rho=1$. Numerical results are also compared with the analytical approximations (dotted colored lines). (b) Numerically calculated normalized energy resolution $\xi$ as a function of $T_B/T_c$ and $\rho$.
• Figure 5: (a) Cooling factor $\eta$ and (b) normalized resolution $\xi$ as a function of bath temperature and bias voltage of a practical detector with $\Gamma = 10^{-3}$. Dashed red line shows the numerical optimal bias voltage, dashed black line the approximation $V_{opt}$. (c) Comparison of the energy resolution results for $\Gamma = 10^{-3}$ (red solid line) and $\Gamma = 10^{-4}$ (blue solid line) as a function of bath temperature. Green solid line = $\Delta E_{\textrm{intrinsic}}$. Inset: thermal time constant as a function of $T_B$.