Design optimization of silicon nitride nanomechanical resonators for thermal infrared detectors: a guide through key figures of merit

TL;DR

This work addresses the lack of a unified framework for designing silicon nitride thermomechanical IR detectors by presenting a validated analytical model that maps geometry, tensile stress, and absorber properties to key performance metrics, including the thermal time constant $\tau_{th}$, noise-equivalent power $NEP$, and specific detectivity $D^*$. It systematically explores drumhead and trampoline geometries under bare SiN and broadband absorber configurations, deriving how heat transfer (conduction vs radiation), heat capacity, and temperature responsivity shape performance. The study reveals that drumheads generally outperform trampolines in $D^*$ and response speed for bare SiN, while absorbers enable broadband operation at the expense of peak sensitivity, guiding application-specific design decisions. By connecting analytical predictions with experimental benchmarks, the framework provides a practical path toward approaching the fundamental photon-noise limit for room-temperature IR detectors and informs the optimization of next-generation spectroscopic and imaging sensors.

Abstract

Thermomechanical infrared (IR) detectors have emerged as promising alternatives to traditional photon and thermoelectric sensors, offering broadband sensitivity and low noise without the need for cryogenic cooling. Despite recent advances, the field still lacks a unified framework to guide the design of these nanomechanical systems. This work addresses that gap by providing a comprehensive design guide for IR thermal detectors based on silicon nitride drumhead and trampolines. Leveraging a validated analytical model, we systematically explore how geometry, tensile stress, and optical properties influence key performance metrics such as thermal time constant, noise-equivalent power, and specific detectivity. The analysis encompasses both bare silicon nitride and structures with broadband absorber layers, revealing how different parameter regimes affect the trade-off between sensitivity and response speed. Rather than focusing on a single device architecture, this study maps out a broad design space, enabling performance prediction and optimisation for a variety of application requirements. As such, it serves not only as a reference for benchmarking existing devices but also as a practical tool for engineering next-generation IR sensors that can operate close to the fundamental detection limit. This work is intended as a foundational resource for researchers and designers aiming to tailor IR detectors to specific use cases.

Figures (12)

• Figure 1: Schematic representation (not in scale) of the two designs under investigation in this work. a) square drumhead with the geometric variables studied highlighted: $h$ is the thickness of the SiN layer, hence of the structure, and the lateral size $L$. In addition to these two, for a b) trampoline we study also the influence of the tethers' width, $w$, and length, $L_t$.
• Figure 2: Influence of the tether length $L_t$ on the figures of merit: a) thermal time constant $\tau_{th}$, b) noise equivalent power NEP, and c) specific detectivity $D^*$ at $\lambda_{SiN} = 11.86µ\m$ for plain SiN resonators without a dedicated IR absorber. The dashed black line in c) marks the room-temperature sensitivity limit. For all panels, the stress is fixed at $\sigma = 200MPa$, the thickness $h = 50n\m$, and the tether width at $w = 5µ\m$.
• Figure 3: Influence of the tether length $L_t$ on the figures of merit: a) thermal time constant $\tau_{th}$, b) noise equivalent power NEP, and c) specific detectivity $D^*$ for a SiN resonator with an IR absorber. The dashed black line in c) marks the room-temperature sensitivity limit for $\alpha_{abs}=50\%$. For all panels, the stress is fixed at $\sigma = 200MPa$, the thickness $h = 50n\m$, and the tether width at $w = 5µ\m$.
• Figure 4: Effect of the thickness $h$ over SiN absorptance at its absorption peak $\lambda_{SiN}=11.86µ\m$ (blue line) and the hemispherical emissivity (orange line). Both grow as the SiN gets thicker. $\alpha_{SiN}(\lambda_{SiN})$ has a maximum for $h\eqsim250n\m$ and later shows a local minimum for $h\eqsim700n\m$. The green line is the ratio $\alpha(\lambda_{SiN})/\sqrt{\epsilon_{SiN}}$, and it has a maximum for $h=151n\m$.
• Figure 5: Influence of the thickness $h$ on the figures of merit: a) thermal time constant $\tau_{th}$, b) noise equivalent power (NEP), and c) specific detectivity $D^*$ at $\lambda_{SiN} = 11.86µ\m$ for plain SiN resonators without a dedicated IR absorber. The dashed black line in c) marks the room-temperature sensitivity limit. For all panels, the stress is fixed at $\sigma = 200MPa$, the tether length at $L_t = 50µ\m$, and the tether width at $w = 5µ\m$.