Niobium Nitride CPW Resonators

• Niobium nitride CPW resonators are superconducting distributed microwave devices characterized by high critical temperatures, kinetic inductance, and resilience in magnetic fields.
• They are fabricated using techniques such as reactive sputtering and ALD on low-loss substrates, with design optimizations including precise impedance engineering and e-beam lithography.
• Their performance hinges on managing trade-offs between dielectric two-level system loss, quasiparticle dynamics, and kinetic inductance, enabling versatile applications in cQED and hybrid systems.

Niobium nitride coplanar waveguide resonators are superconducting distributed microwave resonators patterned from NbN thin films in CPW geometry, typically on silicon, silicon dioxide, sapphire, or related low-loss substrates, and operated from the single-photon regime in circuit QED to high-power, high-field, and millimetre-wave regimes. Across the literature, NbN resonators are valued for their relatively high critical temperature, high critical magnetic field, and comparatively large kinetic inductance, but their measured behavior is equally shaped by dielectric two-level systems, quasiparticle dynamics, vortex physics, and geometry-dependent impedance engineering (Foshat et al., 2023, Foshat et al., 21 Jun 2025, Yu et al., 2020, Zhao et al., 24 Aug 2025).

1. Material systems and fabrication routes

NbN CPW resonators have been realized in several thin-film and substrate combinations, with reactive sputtering as the dominant deposition route. A 100 nm NbN-on-Si platform for quarter-wave resonator arrays used BOE removal of native SiO$_x$, reactive sputtering in an MP 600 S Plassys system with Ar flow $25\ \mathrm{sccm}$, N$_2$ flow $3.0\ \mathrm{sccm}$, base current $0.85\ \mathrm{A}$, and sputter time $15\ \mathrm{min}$, followed by ZEP-based e-beam lithography and CF$_4$/Ar anisotropic dry etch (Foshat et al., 2023). A single-photon quasiparticle study used 100 nm NbN on a 525 $\mu\mathrm{m}$ high-resistivity silicon wafer, grown by reactive DC sputtering of Nb in Ar/N$_2$ plasma after BOE removal of native SiO$_x$, with Ar flow $25\ \mathrm{sccm}$0, N$25\ \mathrm{sccm}$1 flow $25\ \mathrm{sccm}$2, base current $25\ \mathrm{sccm}$3, and sputtering time $25\ \mathrm{sccm}$4 (Foshat et al., 21 Jun 2025).

Thin, strongly disordered NbN has also been used deliberately to maximize kinetic inductance. A 10 nm sputtered NbN film on Si/$25\ \mathrm{sccm}$5 exhibited $25\ \mathrm{sccm}$6, $25\ \mathrm{sccm}$7, and $25\ \mathrm{sccm}$8, with the deposition performed in a Plassys MP600S confocal sputter system after a $25\ \mathrm{sccm}$9 h wafer heat at $_2$0, 30 s Ar milling at 350 V, and DC magnetron sputtering at $_2$1 with Ar:N $_2$2 for 11 s (Yu et al., 2020). A magnetic-field-compatible reflection resonator platform used lift-off-patterned NbN on intrinsic silicon, with film thicknesses 72, 80, 94, and 217 nm; the 80 nm film on intrinsic Si had $_2$3, $_2$4, $_2$5, and $_2$6 (Mandal et al., 2020).

An alternative film route is plasma-enhanced ALD NbN. That work fabricated planar lumped-element rather than CPW resonators, but it remains relevant because it directly linked thin-film parameters to microwave loss. Reported ALD growth rates were $_2$7 at $_2$8 and $_2$9 at $3.0\ \mathrm{sccm}$0; 300-cycle films yielded sheet resistances $3.0\ \mathrm{sccm}$1 at $3.0\ \mathrm{sccm}$2 and $3.0\ \mathrm{sccm}$3 at $3.0\ \mathrm{sccm}$4, with extracted $3.0\ \mathrm{sccm}$5 and $3.0\ \mathrm{sccm}$6, respectively (Sheagren et al., 2019). This suggests that ALD is a viable materials route for NbN CPW resonators when ultrathin-film uniformity is the primary constraint.

Platform	Explicit film/substrate details	Representative reported figures
Quarter-wave NbN array	100 nm NbN on 525 $3.0\ \mathrm{sccm}$7 Si	$3.0\ \mathrm{sccm}$8 at single photon, 100 mK (Foshat et al., 2023)
Single-photon quasiparticle study	100 nm NbN on high-resistivity Si	$3.0\ \mathrm{sccm}$9, $0.85\ \mathrm{A}$0 (Foshat et al., 21 Jun 2025)
High-impedance field-resilient CPW	10 nm NbN on Si/$0.85\ \mathrm{A}$1	$0.85\ \mathrm{A}$2, $0.85\ \mathrm{A}$3 up to $0.85\ \mathrm{A}$4 (Yu et al., 2020)
Reflection resonator for hybrid magnonics	72–217 nm NbN on intrinsic Si	$0.85\ \mathrm{A}$5 at 20 mK, zero field (Mandal et al., 2020)

2. Resonator architectures and circuit descriptions

The dominant NbN implementations are distributed transmission-line resonators coupled to a feedline in hanger or notch geometry. In the 100 nm array study, three quarter-wave resonators were capacitively coupled to a common CPW feedline on Si, with resonator width $0.85\ \mathrm{A}$6, gap $0.85\ \mathrm{A}$7, and lengths $0.85\ \mathrm{A}$8, $0.85\ \mathrm{A}$9, and $15\ \mathrm{min}$0 for one sample and $15\ \mathrm{min}$1, $15\ \mathrm{min}$2, and $15\ \mathrm{min}$3 for another, targeting the 4–8 GHz band (Foshat et al., 2023). The single-photon quasiparticle study used distributed-element CPW notch resonators on Si with center trace width $15\ \mathrm{min}$4 and gap $15\ \mathrm{min}$5, and explicitly discussed resonances at 4.45 and 5.95 GHz (Foshat et al., 21 Jun 2025).

Half-wave implementations span both moderate-impedance and ultra-high-impedance regimes. Thin-film NbN $15\ \mathrm{min}$6 hanger resonators on Si/$15\ \mathrm{min}$7 were realized with three characteristic impedances by varying the center conductor width $15\ \mathrm{min}$8 while keeping the gap $15\ \mathrm{min}$9 fixed: $_4$0 for $_4$1, $_4$2 for $_4$3, and $_4$4 for $_4$5 (Yu et al., 2020). A different half-wave platform, designed as a single-port reflection resonator on intrinsic Si, used a $_4$6 center trace and $_4$7 CPW section, with operation near 4.6–5 GHz (Mandal et al., 2020). At much higher frequency, a two-port half-wave NbN CPW resonator parametric amplifier used a 100 nm film on Si with center strip width $_4$8, gap $_4$9, and resonator length $\mu\mathrm{m}$0, and was operated on its 11th harmonic near $\mu\mathrm{m}$1 (Zhao et al., 24 Aug 2025).

The standard circuit relations recur throughout this literature. The quarter-wave comparative study on superconducting nitrides and metals writes

$\mu\mathrm{m}$2

with $\mu\mathrm{m}$3 the kinetic inductance per unit length, $\mu\mathrm{m}$4 the geometric inductance per unit length, and $\mu\mathrm{m}$5 the capacitance per unit length (Kim et al., 25 Sep 2025). For the 100 nm NbN quarter-wave arrays, the reported line parameters were

$\mu\mathrm{m}$6

giving

$\mu\mathrm{m}$7

for the kinetic inductance fraction (Foshat et al., 2023). In the 10 nm high-impedance platform, the film-scale kinetic inductance was inferred from

$\mu\mathrm{m}$8

which yielded $\mu\mathrm{m}$9 (Yu et al., 2020).

Parameter extraction is equally standardized. Notch-type transmission fitting in the quarter-wave arrays used a full complex $_2$0 model,

$_2$1

with $_2$2 (Foshat et al., 2023). The single-photon quasiparticle study explicitly relied on the notch-type resonator circuit model of Probst et al. (Foshat et al., 21 Jun 2025), while the high-impedance $_2$3 work fit the inverse normalized transmission,

$_2$4

(Yu et al., 2020).

3. Dissipation channels: TLS, quasiparticles, and kinetic inductance

The low-power microwave loss of NbN CPW resonators is repeatedly attributed to two-level systems. In the 100 nm quarter-wave array study, the internal quality factor decreased from $_2$5 in a high-power regime with $_2$6 to $_2$7 in the single-photon regime at $_2$8, and the reported power dependence was fitted by a TLS saturation model (Foshat et al., 2023). The same work decomposed the total loss as

$_2$9

with

$_x$0

and extracted $_x$1, $_x$2, and $_x$3 from the low-temperature power sweep (Foshat et al., 2023). The reflection-geometry NbN resonators on intrinsic Si similarly showed a small increase of $_x$4 with increasing intracavity photon number, which the authors interpreted as TLS saturation (Mandal et al., 2020).

At elevated temperature, quasiparticles and kinetic inductance dominate. In the single-photon study at 5.95 GHz, $_x$5 at $_x$6, rose to $_x$7 at $_x$8, and then fell to $_x$9 at $25\ \mathrm{sccm}$00; the resonance frequency showed a red shift beginning around $25\ \mathrm{sccm}$01–$25\ \mathrm{sccm}$02 (Foshat et al., 21 Jun 2025). That work modeled NbN in the dirty limit using

$25\ \mathrm{sccm}$03

with $25\ \mathrm{sccm}$04 controlling dissipation and $25\ \mathrm{sccm}$05 the inductive superfluid response, and concluded that purely thermal Mattis-Bardeen quasiparticles are insufficient to explain the low-temperature loss. Its clearest quantitative signature of nonequilibrium poisoning was a residual quasiparticle density saturating at

$25\ \mathrm{sccm}$06

at $25\ \mathrm{sccm}$07 (Foshat et al., 21 Jun 2025).

The same theme appears in the quarter-wave array work, but with different emphasis. There, the temperature-dependent frequency shift was modeled as

$25\ \mathrm{sccm}$08

and the reported interpretation was that the increase in kinetic inductance at higher temperatures is the main reason for the frequency shift (Foshat et al., 2023). A common misconception is therefore that single-photon NbN resonators at $25\ \mathrm{sccm}$09 are limited only by thermal quasiparticles. The combined data do not support that simplification: at low power and low temperature, TLS loss is prominent, while residual nonequilibrium quasiparticles remain experimentally visible (Foshat et al., 2023, Foshat et al., 21 Jun 2025).

4. Temperature, weak heating, and the sign of resonance-frequency shifts

Temperature sweeps in NbN resonators reveal a crossover rather than a single monotonic law. In the 100 nm quarter-wave arrays, $25\ \mathrm{sccm}$10 improved from the millikelvin regime toward $25\ \mathrm{sccm}$11 and then degraded rapidly above that scale, while the resonance redshift at elevated temperature was attributed primarily to increasing kinetic inductance (Foshat et al., 2023). In the 5.95 GHz single-photon study, the same crossover appeared as a low-temperature regime where TLS loss weakens with temperature, followed by a higher-temperature regime where quasiparticle dissipation and kinetic inductance dominate (Foshat et al., 21 Jun 2025).

A transferable lesson on frequency-shift sign comes from niobium, not NbN, but it is directly relevant to NbN interpretation. Under optical irradiation, a superconducting Nb quarter-wave CPW resonator showed three regimes: below $25\ \mathrm{sccm}$12, increasing radiation power produced a positive monotonic frequency shift; around $25\ \mathrm{sccm}$13, the response was nonmonotonic; above $25\ \mathrm{sccm}$14, increasing radiation power produced a negative monotonic shift (Wang et al., 2013). The paper interpreted the low-temperature positive shift as TLS thermalization in dielectric regions and the higher-temperature negative shift as kinetic-inductance increase due to quasiparticles (Wang et al., 2013). Because the same competition between dielectric TLS dispersion and superconducting inductive response exists in NbN CPW resonators, this suggests that a frequency shift under weak heating, stray light, or optical loading in NbN is not generically “MKID-like” and does not have a fixed sign.

An earlier niobium quarter-wave study also documented a low-temperature blue shift of resonant frequency and a modest decrease in $25\ \mathrm{sccm}$15 between 20 mK and 1180 mK, attributing the shift mainly to TLS-induced dielectric-constant changes at low temperature (Li et al., 2013). For NbN, the practical implication is not material equivalence but interpretive caution: larger $25\ \mathrm{sccm}$16 changes the balance, yet dielectric TLS effects can still dominate the low-temperature response if participation is high enough (Wang et al., 2013, Li et al., 2013).

5. Magnetic-field resilience and operation in extreme conditions

Magnetic-field resilience is one of the defining motivations for NbN CPW resonators. A half-wave single-port reflection platform on intrinsic Si reported $25\ \mathrm{sccm}$17 at 20 mK and zero field, and found that for films thinner than 100 nm, internal quality factor greater than 1000 can be maintained up to parallel magnetic field of $25\ \mathrm{sccm}$18 and perpendicular magnetic field of $25\ \mathrm{sccm}$19 (Mandal et al., 2020). The same paper identified nearly quadratic frequency dispersion in parallel field, nearly linear dispersion in perpendicular field, and extracted $25\ \mathrm{sccm}$20 from the perpendicular-field frequency shift (Mandal et al., 2020).

The most extreme directly demonstrated NbN field tolerance was achieved in the 10 nm high-kinetic-inductance $25\ \mathrm{sccm}$21 platform. There, internal quality factors $25\ \mathrm{sccm}$22 were maintained in the many-photons regime up to $25\ \mathrm{sccm}$23 in-plane and $25\ \mathrm{sccm}$24 out-of-plane, and for the highest-impedance $25\ \mathrm{sccm}$25 resonator the authors explicitly stated $25\ \mathrm{sccm}$26 at $25\ \mathrm{sccm}$27 even in the single-photon regime (Yu et al., 2020). The field resilience was attributed mainly to suppression of vortex nucleation in the $25\ \mathrm{sccm}$28-wide center conductor, which the paper stated was smaller than the London penetration depth of NbN, so vortices were expected only in the ground plane (Yu et al., 2020).

More moderate-thickness quarter-wave arrays confirm that useful low-power performance persists in the few-hundred-mT range. In 100 nm NbN arrays on Si, the resonance-frequency shift under in-plane field was fit by

$25\ \mathrm{sccm}$29

and the authors verified that $25\ \mathrm{sccm}$30 stays well above $25\ \mathrm{sccm}$31 up to $25\ \mathrm{sccm}$32 at $25\ \mathrm{sccm}$33 and $25\ \mathrm{sccm}$34 (Foshat et al., 2023). That same study also observed hysteretic low-field structure, including a jump around 16–32 mT and a frequency maximum shifted to $25\ \mathrm{sccm}$35, which was attributed to vortex mobility, remanent field, or trapped flux (Foshat et al., 2023).

These results converge on a consistent field picture. Parallel field mainly introduces pair breaking and kinetic-inductance change, while perpendicular components accelerate vortex-mediated loss. Thin films help by suppressing vortex-related dissipation in parallel field, but the same thinning generally increases kinetic inductance and geometry sensitivity (Mandal et al., 2020, Yu et al., 2020, Foshat et al., 2023).

6. Functional regimes, applications, and design tradeoffs

NbN CPW resonators have been used in several distinct regimes. In cQED and hybrid quantum circuits, their attraction lies in combining usable single-photon $25\ \mathrm{sccm}$36 with tolerance to finite magnetic field. The 100 nm quarter-wave arrays reached single-photon $25\ \mathrm{sccm}$37 at 100 mK and remained above $25\ \mathrm{sccm}$38 at $25\ \mathrm{sccm}$39, explicitly motivating operation in high-field cQED and quantum sensing (Foshat et al., 2023). In hybrid magnonics, a single-port half-wave NbN resonator at $25\ \mathrm{sccm}$40 was strongly coupled to acoustic and optical magnon modes in CrCl$25\ \mathrm{sccm}$41, with $25\ \mathrm{sccm}$42 and $25\ \mathrm{sccm}$43, demonstrating that the cavity mode remains coherent enough in field to support strong hybridization (Mandal et al., 2020).

A second application axis is high impedance. The 10 nm $25\ \mathrm{sccm}$44 platform realized $25\ \mathrm{sccm}$45 up to $25\ \mathrm{sccm}$46, and the authors emphasized that higher impedance increases zero-point voltage fluctuations according to the qualitative scaling $25\ \mathrm{sccm}$47, which is useful for coupling to systems with small electric dipole moments (Yu et al., 2020). The corresponding tradeoff is stronger self-Kerr nonlinearity: for $25\ \mathrm{sccm}$48, the high-impedance resonances became strongly asymmetric and unstable (Yu et al., 2020).

A third application regime is kinetic-inductance parametric amplification at millimetre wavelength. A two-port half-wave NbN CPW resonator operated on its 11th harmonic at $25\ \mathrm{sccm}$49 showed a passive 3 dB bandwidth of $25\ \mathrm{sccm}$50, and with a pump at $25\ \mathrm{sccm}$51 and $25\ \mathrm{sccm}$52 at the amplifier input produced $25\ \mathrm{sccm}$53 gain with $25\ \mathrm{sccm}$54 3 dB gain bandwidth (Zhao et al., 24 Aug 2025). The current-dependent nonlinear inductance was written as

$25\ \mathrm{sccm}$55

and the material rationale was that high normal-state resistivity reduces the nonlinear current scale while increasing the kinetic-inductance contribution (Zhao et al., 24 Aug 2025).

An additional boundary case is the ultra-narrow NbN nanowire embedded in CPW, which ceases to behave as a lumped inductor at GHz frequencies. A 100 nm wide, $25\ \mathrm{sccm}$56 long NbN nanowire in series with a 50 $25\ \mathrm{sccm}$57 CPW displayed a first self-resonance near $25\ \mathrm{sccm}$58 at 1.5 K and zero bias, while simulations showed approximately ideal inductive behavior only up to about 4 GHz (Santavicca et al., 2016). The resonance corresponded to a half-wave standing wave along a slow-wave, high-impedance transmission line, not a parasitic lumped $25\ \mathrm{sccm}$59 resonance (Santavicca et al., 2016). For NbN CPW resonators more generally, this establishes a design limit: increasing kinetic inductance and geometric compactness also lowers the onset of distributed self-resonance.

The central tradeoff is therefore structural. Thin and disordered NbN raises $25\ \mathrm{sccm}$60, impedance, nonlinear response, and magnetic-field resilience, but can depress $25\ \mathrm{sccm}$61 through mismatch, higher participation of lossy interfaces, stronger nonlinearity, and greater sensitivity to vortices or nonequilibrium quasiparticles (Yu et al., 2020, Foshat et al., 21 Jun 2025). Thicker and wider NbN lowers $25\ \mathrm{sccm}$62 and may simplify impedance engineering, but generally sacrifices compactness and some field tolerance (Mandal et al., 2020, Foshat et al., 2023). The literature does not point to a single optimal NbN CPW resonator; it instead defines a family of operating points whose dominant constraints are set by TLS participation, kinetic inductance fraction, quasiparticle management, and field geometry.