Electrothermal behavior of superconducting nanowires buried in a commercial CMOS process

Superconducting films native to a commercial CMOS process enable co-integration of superconducting devices (high-kinetic-inductance elements and nanowire detectors) with cryogenic CMOS on one monolithic die. Such films are buried in the front-end-of-line, beneath the back-end-of-line metal stack, an environment that might quench a self-heated hot spot. Current-voltage characteristics are reported for titanium nitride (TiN) nanowires in the polycrystalline-silicon resistor layer of a 22 nm FD-SOI process, and measured retrapping currents are compared with thermal models for longitudinal conduction to the contacts and interfacial phonon cooling into the stack. The wires are strongly hysteretic, with switching-to-retrapping current ratios I sw/I r of 7.4-9.8, sustaining a normal hot spot. For two wires of length ell = 50 micrometers and widths W = 0.50 and 1.00 micrometers, over bath temperatures T b = 0.15-1.19 K, I r follows the interfacial form (T hs n - T b n)(1/2) with n = 4 (T hs, the effective hot-spot temperature), and is strongly inconsistent with the (T hs - T b)(1/2) constant-kappa longitudinal-conduction limit; free-exponent fits give n = approximately 4.8-5.0. An effective cooling coefficient Sigma K = 7.9(3) W/(m squared K 4) describes the data: 31(21) times below the acoustic- (diffuse-) mismatch value for a single clean interface, and approximately 12 times below the lowest previously reported comparable nanowire coefficient. The model-based film thermal conductivity is kappa = approximately 20 mW/(m K). Across lengths ell = 1-50 micrometers, I r matches neither ell(-1) of pure longitudinal conduction nor ell 0 of pure interfacial cooling; a two-channel model reproduces I r(ell) with crossover length ell* = approximately 3.5 micrometers predicted, to an O(1) prefactor, from Sigma K and kappa.