Characterization of Silicon-Membrane TES Microcalorimeters for Large-Format X-ray Spectrometers with Integrated Microwave SQUID Readout

TL;DR

This work addresses the need for high-resolution soft X-ray spectroscopy in catalysis and Resonant Inelastic X-ray Scattering by developing a large-format TES array on all-silicon SOI membranes with integrated microwave SQUID readout. An electro-thermal model, validated through I–V, complex admittance, and pulsed-laser experiments, captures the device physics, including a significant hanging heat-capacity component, and predicts energy resolution performance. Laser-calibrated spectra demonstrate energy-resolved photon counting and enable correction for thermal crosstalk, with measured resolution approaching 0.9 eV at carbon-edge energies and model-driven projections to ~0.3 eV at 300 eV through design optimizations and Tc reduction. The results establish a robust design and modeling framework to realize a 10k-pixel, high-throughput soft X-ray spectrometer for NSLS-II, enabling fast, damage-free RIXS measurements on radiation-sensitive carbon-based catalysts.

Abstract

We present the electro-thermal characterization of transition-edge sensor (TES) detectors suspended on Si membranes fabricated using a silicon-on-insulator (SOI) wafer. The use of an all-silicon fabrication platform, in contrast to the more commonly used silicon nitride membranes, is compatible with monolithic fabrication of integrated TES and SQUID circuits. The all-silicon architecture additionally allows efficient use of focal plane area; the readout circuitry may be positioned out of the focal plane by bending a thinned portion of the chip. Compatibility with integrated fabrication and efficient use of focal plane area provide a path to an efficient soft X-ray spectrometer. This work is motivated by our goal to develop a 10,000-pixel TES spectrometer to overcome critical measurement limitations in catalysis research. The characterization of fragile, carbon-based intermediates via techniques like Resonant Inelastic X-ray Scattering (RIXS) is often precluded by the slow, high-flux nature of existing technologies. The new instrument will allow for fast RIXS measurements to be made without causing sample damage. We verify the detector models and measure the energy resolution using a pulsed optical laser, demonstrating the viability of this approach for the final instrument to be deployed at the National Synchrotron Light Source II (NSLS-II).

Figures (11)

• Figure 1: (Top) A focused combined photograph of detector box containing a 24-pixel TES array bent 90 degrees around the corner using a a section of $\sim$ 4µ m thick flexible silicon. The TES detector array is wire-bonded to an inductor chip, a shunt chip and finally a microwave multiplexer chip that is instrumented using a single coaxial feedline. Copper "ground bosses" are machined from the detector cold plate for RF cavity mode suppression (dotted white square, and inset). (Bottom) A 24-pixel integrated chip, showing the TES, inductors, shunts and SQUIDs fabricated on the same die in a 19+ layer process singh2025lithographic.
• Figure 2: Schematic representation of a single TES detector. The Mo film (blue) is wet-etched to create two 7µ m wide filaments that are used to define $T_\mathrm{c}$. The sensor and its "sidecar" absorber are suspended on a $\sim$ 4µ m thick silicon membrane (grey). Membrane perforations (red) are used to define the thermal conductance of the device to the bath. The jagged outermost boundary represents the outline of back etch which defines the Si membrane.
• Figure 3: Power-law fits to the bias power vs. bath temperature for a single representative pixel at bias points high in the transition where the current dependence of the resistance is vanishingly small. Fit results at 80% $R_n$: $G_\mathrm{30mK} = 21pW/K$, $n = 3.8$, and $T_\mathrm{c} = 53mK$.
• Figure 4: Summary plot of thermal conductance vs. leg aspect ratio ($\Sigma w/l$) for 10 TES detectors. The data are fit with a single free parameter $a$, representing the thermal conductance of bulk of the Si membrane, which is connected in series with the calculable link conductances to the bath.
• Figure 5: Complex admittance plots for a single pixel taken at bias points between 10% and 90% $R_n$ (blue to red). The magnitude, real, imaginary parts of $Y_\mathrm{TES}$ vs. excitation frequency are shown along with the Nyquist plot (clockwise from bottom left). Systematic deviations from model are observed below 40Hz.