A Dual-Material Phononic-Chimney Architecture for Zero-TCE Frequency Stabilization in Piezoresistive NEMS Resonators: A Design and Simulation Study

Next-generation Nanoelectromechanical Systems (NEMS) utilizing Thermal-Piezoresistive Resonators (TPRs) are fundamentally limited by parasitic frequency drift induced by internal Joule heating. Current stabilization methods relying on external phase-locked loops negate the footprint advantage of nanoscale sensors. Furthermore, internal structural compensation such as SiO2 composite cladding or Phononic Crystal (PnC) thermal drains suffers from severe thermal insulation and nanoscale surface boundary scattering, respectively. In this paper, we propose and computationally verify a “Phononic-Chimney” architecture. By isolating an active monocrystalline silicon resonant core with a PnC mechanical bandgap, and bypassing horizontal phonon scattering via Z-axis high-K metallic (gold) thermal vents, we demonstrate substantially reduced Temperature Coefficient of Elasticity (TCE) drift without external circuitry. Fully coupled, temperature-dependent finite element multiphysics simulations with thermal expansion, geometric stiffness prestressing, and TCE-driven modulus softening solved self-consistently confirm that peak core self-heating is clamped to ΔT ≈ 1.40 K under full Joule load, and that the resulting resonant frequency drift is reduced to the kHz scale (≈ 1.8 kHz at the nominal design point), a reduction of roughly one to two orders of magnitude relative to an uncompensated PnC anchor under comparable heating. A gold-conductivity sensitivity sweep across a physically plausible physical vapor deposition (PVD) range (35–60 W/mK) shows both ΔT and Δf varying by less than 10% across the range, indicating the architecture is not fragile to realistic manufacturing variance. A controlled, mesh-matched comparison further shows that a 10 nm Ti adhesion layer at the Si/Au interface increases the frequency drift by approximately 0.8% a minor, quantified correction rather than an open unknown. An attempt to estimate material-loss-limited Q via Rayleigh damping under harmonic analysis was found methodologically invalid: the damping term does not engage under ElmerFEM’s harmonic StressSolve formulation, confirmed both empirically and via corroboration on Elmer’s user forum. No Q-factor figure is reported; the methodological limitation and path forward are described in Section 4.7 and Section 7. A corrected methodology for material-loss Q, together with anchor-loss Q (which requires a separate absorbing-boundary formulation), remains open and is discussed in Section 7.